Radio Channel Measurements and Modeling for Smart Antenna Array Systems Using a Software Radio Receiver

William G. Newhall

Dissertation submitted to the Faculty of Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Electrical and Computer Engineering

Committee Jeffrey H. Reed (Chairman) Warren L. Stutzman William H. Tranter Brian D. Woerner C. Patrick Koelling

April 2003 Blacksburg, Virginia

© 2003 William G. Newhall

Keywords: Propagation Measurement, Channel Modeling, Vector Channels, Smart Antenna, Software Radio, Multipath, Wireless Communications.

Radio Channel Measurements and Modeling for Smart Antenna Array Systems Using a Software Radio Receiver

William G. Newhall

Abstract

This dissertation presents research performed in the areas of radio wave propagation measurement and modeling, smart antenna arrays, and software-defined radio development. A four-channel, wideband, software-defined receiver was developed to serve as a test bed for wideband measurements and antenna array experiments. This receiver was used to perform vector channel measurements in terrestrial and air-to-ground environments using an antenna array. Measurement results served as input to radio channel simulations based on three geometric channel models. The simulation results were compared to measurement results to evaluate the performance of the radio channel models under test. Criteria for evaluation include RMS delay spread, excess delay spread, signal envelope fading, antenna diversity gain, and gain achieved through the use of a two-dimensional rake receiver.

This research makes contributions to the wireless communications field through analysis, development, measurement, and simulation that builds upon past theoretical and experimental results. Contributions include a software-defined radio architecture, based on object oriented techniques, that has been developed and successfully demonstrated using the wideband receiver. This research has produced new wideband vector channel measurements to provide extensive characterization results facilitating simulation of emerging wireless technology for commercial and military communications systems. Original ways of interpreting multipath component strength and correlation for antenna arrays have been developed and investigated. A novel geometric air-to-ground ellipsoidal channel model has been developed, simulated, and evaluated. Other contributions include an evaluation of two popular radio channel models, a geometric channel simulator for producing channel impulse responses, and analytical derivation results related to channel modeling geometries and multipath channel measurement processing.

In addition to new results, existing theory and earlier research results are discussed. Fundamental theory for antenna arrays, vector channels, multipath characterization, and channel modeling is presented. Contemporary issues in software radio and object orientation are described, and measurement results from other propagation research are summarized.

To those who steadfastly encourage life accomplishments. Family, and friends close enough to call family.

iii

iv

Acknowledgements

I have received an enormous amount of support from colleagues, friends, and family throughout my graduate work. I would like to thank Jeff Reed, Bill Tranter, Brian Woerner, Warren Stutzman, and Pat Koelling for their direction and participation on my committee. I also greatly appreciate many other professors and staff at Virginia Tech for their input and support, especially Tim Pratt, Bill Davis, Charles Bostian, Bob Boyle, Dennis Sweeney, and Krishnan Ramu.

I am thankful for the friendship and assistance of my fellow graduate students and Virginia Tech graduates, including Max Robert, James Hicks, Fakhrul Alam, Sesh Krishnamoorthy, Raqib Mostafa, Ramesh Palat, Mostafa Howlader, Roger Skidmore, Ran Gozali, Tom Biedka, Chris Anderson, Jody Neel, Philip Balister, Carl Dietrich, Gaurav Joshi, Kai Dietze, Neiyer Correal, Matt Valenti, and Kathyayani Srikanteswara. I greatly appreciate the help of the MPRG staff, including Jenny Frank, Hilda Reynolds, Shelby Smith, Beth Huffman, and Cindy Graham.

I could not have accomplished so much without my colleagues and friends at Grayson Wireless. I thank Ken Talbott, Greg Bump, Jon Dubovsky, Casey Elder, Ron Bryan, Mark Priest, Steve Trice, Tom Conley, Tim Garrett, and Terry Garner.

To my terrific friends, Mike Metzgar, Jennifer Lesser, Michele Kolet, and Neal Kegley, I owe thanks for your friendship and a space in your lives.

v

Bob Newhall and Barbara Ruebush, my brother and sister, have provided an immeasurable amount of encouragement, and I thank them for being there for me.

I would mostly like to thank my parents, Robert and Roberta Newhall, whose constant and limitless support, encouragement, and advice had a great part in bringing my work and dreams to completion.

vi

Table of Contents

List of Figures ...... xi List of Tables...... xxiii Chapter 1 Introduction ...... 1 1.1 Motivation and Challenges in Wireless...... 1 1.2 Foundations of Progress in Wireless ...... 4 1.3 Research Issues Covered ...... 5 1.4 Organization of This Dissertation ...... 7 Chapter 2 Signal Fundamentals for Antenna Arrays ...... 9 2.1 Complex Signal Fundamentals ...... 9 2.1.1 The Complex Envelope...... 10 2.1.2 Converting Bandpass Signals to Complex Envelopes...... 11 2.1.3 The Narrowband Approximation...... 13 2.2 Signals for Smart Antennas ...... 16 2.2.1 The Purpose of Smart Antennas...... 16 2.2.2 A Signal Model for Antenna Arrays...... 18 2.2.3 Vector Channels ...... 23 2.2.4 Array Steering Vectors ...... 25 2.2.5 Spatial Signatures ...... 26 2.3 Channel and Signal Characteristics in Multipath Environments ...... 27 2.3.1 Multipath Amplitude and Time Delay...... 28 2.3.2 Number of Multipath Components...... 30 2.3.3 Fading Envelope ...... 31 2.3.4 Direction of Arrival ...... 33 2.3.5 Signal Envelope Correlation Coefficient ...... 34 2.4 Summary...... 35 Chapter 3 A Multi-Channel, Software-Defined Measurement Receiver ...... 37 3.1 Architecture Motivation...... 37 3.2 The Software Radio Methodology ...... 39 3.2.1 Physical Architecture...... 40 3.2.2 Division of Hardware and Software ...... 41 3.2.3 Benefits of the Methodology...... 42 3.3 The Measurement Receiver Concept...... 43 3.3.1 Processing Tradeoffs...... 43 3.3.2 Examples and Applications...... 44 3.4 System Specifications and Analysis...... 45 3.4.1 Target Applications...... 45 3.4.2 Design Goals ...... 46 3.4.3 RF Specifications...... 47 3.4.4 System Specifications ...... 48 3.4.5 Link Analysis ...... 49 3.4.6 RF Section Analysis...... 49 3.4.7 Noise Analysis...... 50

vii

3.5 Measurement Receiver Hardware ...... 51 3.5.1 RF Front End ...... 52 3.5.2 Sampling Section...... 53 3.5.3 Complete System...... 54 3.6 Theory and Application of Object Orientation ...... 54 3.6.1 Objects ...... 55 3.6.2 Object Orientation Concepts...... 55 3.6.3 Application of Object-Oriented Methods to Software Radios...... 57 3.7 Measurement Receiver Software ...... 59 3.7.1 Signal Acquisition with the Hardware-Specific Receiver Object ...... 60 3.7.2 Radio Receiver and Processing Functions ...... 62 3.7.3 Display/File Interface Functions ...... 62 3.7.4 Multithreading and Inter-Object Communications...... 63 3.7.5 Automatic Gain Control...... 65 3.7.6 Example of Measurement Receiver Software Application...... 66 3.8 FPGA-Based Transmitter ...... 69 3.8.1 Transmitter Hardware...... 69 3.8.2 Transmitter Verification...... 70 3.9 Summary...... 72 Chapter 4 Multipath Channel Models for Antenna Arrays ...... 75 4.1 The Purpose of Radio Channel Models...... 76 4.2 Channel Model Classification...... 78 4.3 Existing Geometric Channel Models...... 79 4.3.1 Multipath Channel Impulse Response ...... 79 4.3.2 Geometrically Based Single-Bounce Elliptical Model...... 81 4.3.3 Geometrically Based Single-Bounce Circular Model ...... 86 4.3.4 Elliptical Sub-Regions Model ...... 88 4.3.5 Other Channel Models ...... 92 4.4 Three-Dimensional Ellipsoidal Channel Model...... 95 4.4.1 The Ellipsoidal Scattering Region...... 95 4.4.2 Applications of the Bounded Ellipsoid ...... 96 4.4.3 Axis Lengths and Normalized Excess Delay ...... 99 4.5 Geometric Air-to-Ground Ellipsoidal Channel Model...... 101 4.5.1 Analytical Specification of Scattering Region...... 103 4.5.2 Generating the Ellipsoid and Scatterers on the Rotated Axes...... 107 4.5.3 Direction-of-Arrival Statistics...... 111 4.5.4 Joint Direction-of-Arrival and Time-Delay Statistics ...... 114 4.6 Summary...... 119 Chapter 5 Channel Measurements ...... 121 5.1 Survey of Radio Channel Measurements ...... 121 5.1.1 Terrestrial Measurements...... 122 5.1.2 Air-to-Ground Measurements ...... 127 5.2 Rooftop-Level Measurement Campaign...... 131 5.2.1 Measurement Overview ...... 131 5.2.2 Multipath RMS Delay Spread ...... 132 5.2.3 Distribution of Multipath Components...... 135

viii

5.2.4 Multipath Strength Correlation Coefficients Versus Delay...... 137 5.3 Dense Scatterer Measurement Campaign...... 148 5.3.1 Measurement Overview ...... 148 5.3.2 Multipath RMS Delay Spread ...... 151 5.3.3 Multipath Excess Delay Spread...... 160 5.3.4 Distribution of Multipath Components...... 161 5.3.5 Strength of Multipath Components Versus Delay...... 169 5.3.6 Multipath Strength Correlation Coefficients Versus Delay...... 186 5.4 Air-to-Ground Measurement Campaign...... 188 5.4.1 Measurement Overview ...... 190 5.4.2 Multipath RMS Delay Spread ...... 191 5.4.3 Multipath Excess Delay Spread...... 194 5.4.4 Distribution of Multipath Components...... 195 5.5 Summary...... 200 Chapter 6 Wideband Vector Channel Simulation ...... 203 6.1 Simulation Overview...... 204 6.2 Simulation Geometries ...... 207 6.2.1 Simulating the ESR Model Geometry ...... 207 6.2.2 Simulating the GBSBE Model Geometry...... 209 6.2.3 Simulating the GAGE Model Geometry...... 209 6.3 Multipath Component Distribution, Strength, and Delay...... 213 6.3.1 Distribution of Multipath Components in Delay...... 213 6.3.2 Multipath Delay...... 214 6.3.3 Strength Modeling for ESR and GBSBE...... 216 6.3.4 Strength Modeling for GAGE ...... 218 6.3.5 Line of Sight Components ...... 220 6.3.6 Log-Normal Multipath Strength Variation ...... 221 6.3.7 Rayleigh Fading...... 223 6.4 Direction of Arrival...... 226 6.4.1 Direction of Arrival for ESR and GBSBE ...... 226 6.4.2 Direction of Arrival for GAGE ...... 228 6.5 Summary...... 228 Chapter 7 Channel Model Evaluation...... 229 7.1 Elliptical Sub-Regions Channel Model...... 231 7.1.1 Simulation Parameters ...... 231 7.1.2 Multipath Signal Strength ...... 233 7.1.3 RMS Delay Spread ...... 242 7.1.4 Excess Delay Spread...... 246 7.1.5 Multipath Fading ...... 248 7.1.6 Antenna Diversity...... 250 7.1.7 Two-Dimensional Rake Receiver...... 256 7.1.8 ESR Comparison Summary ...... 264 7.2 Geometrically Based Single-Bounce Elliptical Channel Model...... 266 7.2.1 Simulation Parameters ...... 266 7.2.2 Multipath Signal Strength ...... 268 7.2.3 RMS Delay Spread ...... 275

ix

7.2.4 Excess Delay Spread...... 278 7.2.5 Multipath Fading ...... 280 7.2.6 Antenna Diversity...... 281 7.2.7 Two-Dimensional Rake Receiver...... 288 7.2.8 GBSBE Comparison Summary...... 295 7.3 Geometric Air-to-Ground Ellipsoidal Channel Model...... 296 7.3.1 Simulation Parameters ...... 297 7.3.2 RMS Delay Spread ...... 299 7.3.3 Multipath Signal Strength ...... 301 7.3.4 Excess Delay Spread...... 304 7.3.5 Multipath Fading ...... 305 7.3.6 Antenna Diversity...... 305 7.3.7 Two-Dimensional Rake Receiver...... 308 7.3.8 GAGE Comparison Summary...... 311 7.4 Summary...... 312 Chapter 8 Conclusion...... 315 8.1 Summary of Research...... 315 8.2 Original Contributions ...... 317 8.3 Future Work...... 319 8.4 Closing...... 320 Epilogue...... 321 Appendix A Measurement Receiver MATLAB Signal Interface ...... 323 A.1 MATLAB Interface Overview...... 323 A.2 Workspace Variables...... 324 A.3 Real-Time Plotting ...... 325 A.4 Example M-File...... 326 A.5 Steps for Developing m-files for the Measurement Receiver...... 329 Appendix B VT-STAR Development...... 331 B.1 Overview...... 331 B.2 VT-STAR Transmitter...... 331 B.3 VT-STAR Receiver ...... 333 Appendix C Channel Model Simulator Parameters...... 337 C.1 Top Level Structures ...... 337 C.2 Channel Parameters Structure...... 338 C.3 Intermediate Plots...... 339 C.4 Vector Channel Structure...... 340 C.5 Multiple Simulation Runs ...... 341 References ...... 343 Author Biographical Notes ...... 351

x

List of Figures

Figure 2-1. Block diagram of the down-conversion process for extracting in-phase and quadrature signal components from a bandpass signal...... 13 Figure 2-2. Location of elements of an antenna array...... 18 Figure 2-3. Signal sources surrounding antenna array...... 20 Figure 2-4. Geometry for a uniformly spaced, linear antenna array...... 20 Figure 2-5. Transmitted signal and impulse response of a multipath vector channel...... 28 Figure 2-6. Relative strengths of multipath components used to determine excess delay spread...... 29 Figure 2-7. Isoprobability contours for the composite complex signal envelope due to Rayleigh and Rician fading in a multipath environment...... 33 Figure 3-1. Block diagram of the major components of a practical software radio receiver...... 41 Figure 3-2. Functionality distribution of software radios versus legacy radio methodology...... 42 Figure 3-3. Block diagram of the measurement receiver hardware, including the RF hardware that performs a frequency translation to a band that can be sampled by the 1 gigasample/sec sampling section...... 52 Figure 3-4. (a) The RF front end of the four-channel receiver, showing the tubular filters and connectorized RF components. (b) The complete system, showing the oscilloscope used for sampling, a signal generator used for the local oscillator, and another signal generator used to generate a test signal...... 54 Figure 3-5. Flow of signal data through the processing of the measurement receiver software..60 Figure 3-6. Class hierarchy of hardware-specific receiver objects...... 62 Figure 3-7. Relationships among the measurement system software modules and external interfaces...... 63 Figure 3-8. Block diagram of hardware and software components of automatic gain control. ...66 Figure 3-9. Block diagram of the software module that measures the strength, delay, and phase of multipath components arriving at the receiver...... 68 Figure 3-10. Power-delay profile (amplitude and phase) computed by measurement receiver...68 Figure 3-11. Block diagram of the measurement system transmitter, including a PLD that is programmable to produce the data required for the particular experiment...... 69 Figure 3-12. Wideband transmitter used for generating BPSK-modulated signal...... 70

xi

Figure 3-13. Output of transmitter acquired with measurement receiver (in-phase component, quadrature component, and relative phase shown)...... 71 Figure 3-14. Signal constellation as demodulated by measurement receiver (phase rotation of constellation has not been applied for illustration purposes; the diagonal dashed line indicates the decision boundary)...... 71 Figure 3-15. Transmitter signal acquired with measurement receiver after symbol decisions have been made...... 72 Figure 4-1. Uses for channel models shown from the standpoints of functionality and system implementation...... 76 Figure 4-2. Physical layout of the geometrically based single-bounce model...... 82 Figure 4-3. Ellipses E1 and E2 that define scattering region between delays t and t+Dt for the GBSBE model...... 83 Figure 4-4. Geometry for the geometrically based single-bounce circular model...... 86 Figure 4-5. Probability density function for direction of arrival for the GBSB macrocell model with d=5 km and r=100, 300, 1000 m...... 87 Figure 4-6. Geometry for the elliptical sub-regions channel model...... 90 Figure 4-7. Base station and mobile station orientation for Lee's geometric model...... 92 Figure 4-8. Geometry of base station, mobile station, and scatterers for the typical urban model...... 93 Figure 4-9. Geometry of base station, mobile station, and two scattering regions for the bad urban model...... 93 Figure 4-10. Orientation of mobile station and base station among city streets for the urban street geometric model, indicating types of propagation...... 94 Figure 4-11. Geometry of the ellipsoid (a=2, b=1) bounding surface for maximum multipath delay: (a) three-dimensional view, (b) top view, (c) side view...... 97 Figure 4-12. Locations of uniformly distributed scatterers throughout the ellipsoide bounding surface; transmitter and receiver are located at foci...... 98 Figure 4-13. An urban model based on the ellipsoidal geometry useful for three-dimensional direction of arrival simulation and analysis...... 99 Figure 4-14. Scatterer distribution boundaries around transmitter and receiver for normalized excess delay of 0.05, 0.3, and 0.9...... 100 Figure 4-15. Ratio of minor to major axis of elliptical scatterer boundary versus normalized excess delay...... 101 Figure 4-16. Geometry, distance, and angle definitions for the geometric air-to-ground ellipsoidal model...... 102 Figure 4-17. Unit vectors that define the axes for the ellipsoid model geometry...... 108 Figure 4-18. Views of the ellipsoid, ground plane, and scattering region: (a) The oblique view shows the overall geometry of the model and the ellipse outlining the scattering region, (b) The end view shows the y-axis width of the scattering region, (c) The side view shows the x-length of the scattering region which is clearly dependent upon the major axis elevation angle, (d) The top view shows the perfectly elliptical shape of the scattering region, (e) The ground-bounded view limits the ellipsoid to z<0 to show that the analytical scattering region exactly matches the ground-ellipsoid intersection...... 110 Figure 4-19. Marginal probability density function of direction of arrival for y=30 and y=80...... 113

xii

Figure 4-20. Joint probability density functions for direction of arrival and normalized multipath delay for several elevation angles El...... 117 Figure 4-21. Marginal DOA and delay PDFs for the air-to-ground model...... 118 Figure 5-1. The measurement system was positioned on the roof of Whittemore near the corner of the building, and the receiver array was mounted on a stand approximately six feet above roof level...... 131 Figure 5-2. Sample power-delay profiles recorded at elements 2 and 3 of the antenna array. The solid line is the channel 2 PDP, and the dotted line is the channel 3 PDP...... 133 Figure 5-3. Complementary CDF for RMS delay spread based on measurements...... 135 Figure 5-4. Number of signal components versus excess propagation delay...... 136 Figure 5-5. One set of power-delay profiles acquired simultaneously at each antenna element for multipath magnitude correlation processing...... 139 Figure 5-6. Delay bins evenly divide the delay between the first arriving signal component and the last arriving signal component...... 141 Figure 5-7. Map of the plaza where measurements were performed...... 149 Figure 5-8. Photo of measurement site with transmitter in the foreground at the LOS1 location...... 149 Figure 5-9. Sample power-delay profile from dense scatterer measurement site (NLOS1)...... 150 Figure 5-10. RMS delay spread CCDF for NLOS1...... 153 Figure 5-11. RMS delay spread CCDF for NLOS2...... 153 Figure 5-12. RMS delay spread CCDF for NLOS3...... 154 Figure 5-13. RMS delay spread CCDF for NLOS4...... 154 Figure 5-14. RMS delay spread CCDF for NLOS5...... 155 Figure 5-15. RMS delay spread CCDF for NLOS6...... 155 Figure 5-16. RMS delay spread CCDF for LOS1...... 158 Figure 5-17. RMS delay spread CCDF for LOS2...... 158 Figure 5-18. RMS delay spread CCDF for LOS3...... 159 Figure 5-19. RMS delay spread CCDF for LOS4...... 159 Figure 5-20. Average number of signal components using 16 delay bins for NLOS1...... 161 Figure 5-21. Average number of signal components using 16 delay bins for NLOS2...... 162 Figure 5-22. Average number of signal components using 16 delay bins for NLOS3...... 162 Figure 5-23. Average number of signal components using 16 delay bins for NLOS4...... 163 Figure 5-24. Average number of signal components using 16 delay bins for NLOS5...... 163 Figure 5-25. Average number of signal components using 16 delay bins for NLOS6...... 164 Figure 5-26. Average number of signal components using 16 delay bins for LOS1...... 164 Figure 5-27. Average number of signal components using 16 delay bins for LOS2...... 165 Figure 5-28. Average number of signal components using 16 delay bins for LOS3...... 165 Figure 5-29. Average number of signal components using 16 delay bins for LOS4...... 166 Figure 5-30. Average number of signal components using 16 delay bins for all NLOS measurements...... 166 Figure 5-31. Average number of signal components using 16 delay bins for all LOS measurements...... 167 Figure 5-32. Relationship between two multipath components arriving with different delays with all other factors held constant...... 171

xiii

Figure 5-33. NLOS1 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 173 Figure 5-34. NLOS1: PDF created using data points and corresponding theoretical Gaussian distribution...... 173 Figure 5-35. NLOS2 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 174 Figure 5-36. NLOS2: PDF created using data points and corresponding theoretical Gaussian distribution...... 174 Figure 5-37. NLOS3 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 175 Figure 5-38. NLOS3: PDF created using data points and corresponding theoretical Gaussian distribution...... 175 Figure 5-39. NLOS4 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 176 Figure 5-40. NLOS4: PDF created using data points and corresponding theoretical Gaussian distribution...... 176 Figure 5-41. NLOS5 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 177 Figure 5-42. NLOS5: PDF created using data points and corresponding theoretical Gaussian distribution...... 177 Figure 5-43. NLOS6 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 178 Figure 5-44. NLOS6: PDF created using data points and corresponding theoretical Gaussian distribution...... 178 Figure 5-45. LOS1 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 181 Figure 5-46. LOS1: PDF created using data points and corresponding theoretical Gaussian distribution...... 181 Figure 5-47. LOS2 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 182 Figure 5-48. LOS2: PDF created using data points and corresponding theoretical Gaussian distribution...... 182 Figure 5-49. LOS3 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 183 Figure 5-50. LOS3: PDF created using data points and corresponding theoretical Gaussian distribution...... 183

xiv

Figure 5-51. LOS4 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values...... 184 Figure 5-52. LOS4: PDF created using data points and corresponding theoretical Gaussian distribution...... 184 Figure 5-53. Location of the transmitter antenna under aircraft fuselage and wing...... 190 Figure 5-54. Ground location of the receiver array for the air-to-ground measurements...... 190 Figure 5-55. Sample power-delay profile for 7.5 degree elevation angle...... 192 Figure 5-56. Sample power-delay profile for 15 degree elevation angle...... 192 Figure 5-57. Sample power-delay profile for 22.5 degree elevation angle...... 193 Figure 5-58. Sample power-delay profile for 30 degree elevation angle...... 193 Figure 5-59. RMS delay spread CCDF for all measured elevation angles...... 194 Figure 5-60. Average number of signal components using 16 delay bins for 7.5 degree elevation angle...... 196 Figure 5-61. Average number of signal components using 16 delay bins for 15 degree elevation angle...... 196 Figure 5-62. Average number of signal components using 16 delay bins for 22.5 degree elevation angle...... 197 Figure 5-63. Average number of signal components using 16 delay bins for 30 degree elevation angle...... 197 Figure 5-64. Average number of signal components using 16 delay bins for each elevation angle...... 198 Figure 5-65. Average number of signal components using 16 delay bins for all air-to-ground measurements...... 199 Figure 6-1. Block diagram of wideband vector channel simulator...... 204 Figure 6-2. Geometry plot produced by the simulator for the ESR model showing a top view of transmitter (+) and receiver (o) locations, elliptical boundaries, scatterer locations, and propagation paths...... 208 Figure 6-3. Geometry plot produced by the simulator for the GBSBE model showing a top view of transmitter (+) and receiver (o) locations, elliptical boundary, scatterer locations, and propagation paths...... 208 Figure 6-4. Geometry plot produced by the simulator for the GAGE model showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 45 degrees...... 210 Figure 6-5. Geometry plot produced by the simulator for the GAGE model, showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 90 degrees...... 211 Figure 6-6. Geometry plot produced by the simulator for the GAGE model, showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 0 degrees...... 212 Figure 6-7. Dense uniform distribution of scatterers in the seventh scattering region for the GAGE model...... 214 Figure 6-8. Absolute propagation delay for the GBSBE and ESR models is calculated using (a) the distance from the transmitter to the center of the receiver array by way of the scatterer and (b) the distance between parallel lines through the receiver array center and the array element drawn orthogonally to the propagation path...... 215

xv

Figure 6-9. Absolute propagation delay for the GAGE model is calculated using (a) the distance from the transmitter to the center of the receiver array by way of the scatterer and (b) the distance between parallel lines through the receiver array center and the array element drawn orthogonally to the propagation path...... 216 Figure 6-10. Typical strength-versus-delay plot (ESR model) for a channel impulse response affected only by log-distance path loss and reflection loss (non-line-of-sight channel).....217 Figure 6-11. Top and side view of propagation environment for air-to-ground radio channels...... 219 Figure 6-12. Example strength-versus-delay plot (GAGE model) for a channel impulse response affected only by log-distance path loss and reflection loss...... 220 Figure 6-13. Simulated channel impulse response for the ESR model after the LOS component is added...... 221 Figure 6-14. Simulated channel impulse response for the ESR model after the log-normal strength variation has been applied...... 222 Figure 6-15. Channel impulse response of four array element superimposed on one plot after correlated Rayleigh fading has been applied...... 226 Figure 6-16. Definition of direction of arrival for the ESR and GBSBE models...... 227 Figure 6-17. Definition of direction of arrival for the GAGE model...... 227 Figure 7-1. A block diagram of the process for evaluating channel models...... 230 Figure 7-2. Example of geometric channel simulation (elliptical sub-regions model) showing transmitter location (plus symbol at focus), receiver location (circle at other focus), scatterers (dots), propagation paths (yellow lines), and elliptical sub-region boundaries. .233 Figure 7-3. NLOS 1 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 235 Figure 7-4. NLOS 2 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 235 Figure 7-5. NLOS 3 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 236 Figure 7-6. NLOS 4 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 236 Figure 7-7. NLOS 5 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 237 Figure 7-8. NLOS 6 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 237

xvi

Figure 7-9. NLOS 6 simulated multipath strength (ESR) for 1000 impulse responses (without Rayleigh fading): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 238 Figure 7-10. NLOS 6 simulated multipath strength (ESR) for 1000 impulse responses (Rayleigh fading, no log-normal deviation): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. Standard deviation about best-fit line of 5.4 dB results...... 239 Figure 7-11. LOS 1 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 240 Figure 7-12. LOS 2 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 240 Figure 7-13. LOS 3 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 241 Figure 7-14. LOS 4 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 241 Figure 7-15. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS1 (b) NLOS2.243 Figure 7-16. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS3 (b) NLOS4.243 Figure 7-17. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS5 (b) NLOS6.244 Figure 7-18. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS6 simulated using log-normal variation about best-fit power (dB) versus log-delay line, and (b) NLOS6 simulated using log-normal variation and Rayleigh fading for multipath components...... 244 Figure 7-19. RMS delay spread CCDF for simulated (ESR) channels (a) LOS1 (b) LOS2...... 246 Figure 7-20. RMS delay spread CCDF for simulated (ESR) channels (a) LOS3 (b) LOS4...... 246 Figure 7-21. Signal strength CDF for each NLOS location derived from (a) channel impulse response simulations (ESR) and (b) measured channels...... 249 Figure 7-22. Signal strength CDF for each LOS location derived from (a) channel impulse response simulations (ESR) and (b) measured channels...... 249 Figure 7-23. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 251 Figure 7-24. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 251 Figure 7-25. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 252

xvii

Figure 7-26. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 252 Figure 7-27. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS5 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 253 Figure 7-28. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS6 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 253 Figure 7-29. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 254 Figure 7-30. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 255 Figure 7-31. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 255 Figure 7-32. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 256 Figure 7-33. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 257 Figure 7-34. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 258 Figure 7-35. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 258 Figure 7-36. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 259 Figure 7-37. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS5 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 259 Figure 7-38. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS6 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 260 Figure 7-39. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 261 Figure 7-40. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 262

xviii

Figure 7-41. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 262 Figure 7-42. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels...... 263 Figure 7-43. Example of geometric channel simulation (GBSBE model) showing transmitter location (plus symbol at focus), receiver location (circle at other focus), scatterers (dots), propagation paths (yellow lines), and elliptical boundary for uniformly distributed scatterers...... 268 Figure 7-44. NLOS1 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 269 Figure 7-45. NLOS2 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 270 Figure 7-46. NLOS3 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 270 Figure 7-47. NLOS4 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 271 Figure 7-48. NLOS5 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 271 Figure 7-49. NLOS6 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 272 Figure 7-50. LOS1 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 273 Figure 7-51. LOS2 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 273 Figure 7-52. LOS3 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 274

xix

Figure 7-53. LOS4 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown...... 274 Figure 7-54. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS1 (b) NLOS2...... 276 Figure 7-55. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS3 (b) NLOS4...... 276 Figure 7-56. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS5 (b) NLOS6...... 277 Figure 7-57. RMS delay spread CCDF for simulated (GBSBE) channels (a) LOS1 (b) LOS2.278 Figure 7-58. RMS delay spread CCDF for simulated (GBSBE) channels (a) LOS3 (b) LOS4.278 Figure 7-59. Signal strength CDF for each NLOS location derived from (a) channel impulse response simulations (GBSBE) and (b) measured channels...... 280 Figure 7-60. Signal strength CDF for each LOS location derived from (a) channel impulse response simulations (GBSBE) and (b) measured channels...... 281 Figure 7-61. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 282 Figure 7-62. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 282 Figure 7-63. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 283 Figure 7-64. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 283 Figure 7-65. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS5 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 284 Figure 7-66. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS6 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 284 Figure 7-67. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 285 Figure 7-68. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 286 Figure 7-69. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 286 Figure 7-70. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 287

xx

Figure 7-71. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 288 Figure 7-72. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 289 Figure 7-73. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 289 Figure 7-74. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 290 Figure 7-75. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS5 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 290 Figure 7-76. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS6 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 291 Figure 7-77. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 292 Figure 7-78. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 293 Figure 7-79. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 293 Figure 7-80. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels...... 294 Figure 7-81. Example of geometric air-to-ground channel model simulation showing transmitter location (plus symbol at elevated ellipsoid focus), receiver location (circle at ellipsoid and ground ellipse shared focus), scatterers (dots), propagation paths (green lines), and sub- region boundaries of constant propagation delay...... 298 Figure 7-82. CDF of RMS delay spread for four elevation angles for (a) simulated (GAGE) channel impulse responses and (b) measured channels. A constant reflection loss was used...... 299 Figure 7-83. CCDF of RMS delay spread for four elevation angles for (a) simulated (GAGE) channel impulse responses and (b) measured channels. Reflection loss was defined to be a function of elevation angle...... 300 Figure 7-84. Scatter plot of multipath strength versus log of propagation delay for the 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles...... 302 Figure 7-85. Scatter plot of multipath strength versus log of propagation delay for the 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles...... 302

xxi

Figure 7-86. Scatter plot of multipath strength versus log of propagation delay for the 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles...... 303 Figure 7-87. Scatter plot of multipath strength versus log of propagation delay for the 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles...... 303 Figure 7-88. Signal strength CDF for each air-to-ground elevation angle derived from (a) channel impulse response simulations and (b) measured channels...... 305 Figure 7-89. CDF of received signal strength using maximal ratio combining and using a single antenna for 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...... 306 Figure 7-90. CDF of received signal strength using maximal ratio combining and using a single antenna for 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...... 306 Figure 7-91. CDF of received signal strength using maximal ratio combining and using a single antenna for 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...... 307 Figure 7-92. CDF of received signal strength using maximal ratio combining and using a single antenna for 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...... 307 Figure 7-93. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...... 309 Figure 7-94. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...... 309 Figure 7-95. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...... 310 Figure 7-96. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...... 310 Figure A-1. Data flow through measurement receiver to MATLAB workspace...... 324 Figure A-2. Sample m-file listing showing how to use the signal data and produce real-time plots...... 327 Figure A-3. MATLAB interface application launched from the measurement receiver software...... 328 Figure A-4. Spectrum plot produced by m-file listed in Figure A-2...... 328 Figure B-1. Transmitter section of VT-STAR...... 332 Figure B-2. Photograph of VT-STAR transmitter section...... 333 Figure B-3. Receiver section of the VT-STAR...... 334 Figure B-4. Photograph of VT-STAR receiver RF section...... 334

xxii

List of Tables

Table 2-1. Comparison of relative signal bandwidth for a 1.25 MHz-wide CDMA signal used for voice and data services, where the base information bit rate is 19.2 Kbps and the carrier frequency is 825 MHz, in a multipath environment with a 4 ms excess delay...... 15 Table 2-2. Advantages of using smart antennas at a transmitter or receiver...... 17 Table 2-3. Expressions for computing signals incident on the elements of an antenna array. ....23 Table 3-1. Target applications of measurement receiver...... 46 Table 3-2. High-level design goals for measurement receiver...... 47 Table 3-3. Radio frequency (RF) specifications for measurement receiver...... 48 Table 3-4. System specifications for measurement receiver...... 49 Table 3-5. Measurement system link analysis for outdoor radio channel (1 mile, line-of-sight).49 Table 3-6. Measurement receiver RF section analysis for outdoor radio channel...... 50 Table 3-7. System noise analysis and noise results for outdoor radio channel...... 51 Table 3-8. Description of the generic hardware-specific receiver object interface functions...... 61 Table 4-1. Requirements of channel models versus radio access technology...... 77 Table 4-2. Equations that describe the intersection of a tilted, three-dimensional excess delay bounding volume and a planar surface containing scatterers...... 106 Table 5-1. Results of a wideband measurement campaign in a suburban environment [Wil01]...... 122 Table 5-2. Results of a spatial-temporal measurement campaign [Lar99]...... 124 Table 5-3. Summary of results of campaign to measure correlation of spatial signatures [Kav00]...... 125 Table 5-4. Results of a measurement campaign using a light aircraft to study land mobile satellite communications [Smi91]...... 127 Table 5-5. Summary of results for a campaign that measured land mobile satellite channels [Jah96]...... 129 Table 5-6. Results of an air-to-ground measurement campaign [Dye98]...... 130 Table 5-7. Details of the measurement system setup and transmitter/receiver locations for the Whittemore roof measurements...... 132 Table 5-8. RMS delay spread statistics...... 134 Table 5-9. Distribution of multipath components among delay bins of power-delay profiles. .136

xxiii

Table 5-10. Processing details for signal component correlation processing...... 144 Table 5-11. Correlation coefficients for signal component magnitude across antenna elements (4 delay bins)...... 145 Table 5-12. Correlation coefficients for signal component magnitude across antenna elements (8 delay bins)...... 145 Table 5-13. Correlation coefficients for signal component magnitude across antenna elements (16 delay bins)...... 146 Table 5-14. Transmitter-receiver separation for each transmitter location...... 150 Table 5-15. Link budget for terrestrial measurements on the VT campus...... 151 Table 5-16. RMS delay spread results for NLOS locations for the dense scatterer measurement campaign...... 152 Table 5-17. Summary of RMS delay spread results for dense-scatterer measurement site...... 156 Table 5-18. RMS delay spread results for LOS locations for the dense-scatterer measurement campaign...... 157 Table 5-19. Excess delay spread values for NLOS locations...... 160 Table 5-20. Excess delay values for LOS locations...... 160 Table 5-21. Average number of signal components per delay bin per profile for NLOS measurements...... 167 Table 5-22. Average number of signal components per delay bin per profile for LOS measurements...... 168 Table 5-23. Average number of signal components per power-delay profile for LOS and NLOS measurements...... 169 Table 5-24. Path loss exponent, standard deviation of multipath strength about best-fit line, and intercept of best-fit line for NLOS measurements...... 179 Table 5-25. Path loss exponent, standard deviation of multipath strength about best-fit line, intercept of best-fit line, and LOS strength above best-fit line for LOS measurements.....185 Table 5-26. Summary of multipath strength results for all measurements at the dense-scatterer site...... 186 Table 5-27. NLOS Measurement Results (4 propagation delay bins)...... 187 Table 5-28. NLOS Measurement Results (8 propagation delay bins)...... 187 Table 5-29. NLOS Measurement Results (16 propagation delay bins)...... 188 Table 5-30. Link budget calculations for each of the four elevation angles measured...... 189 Table 5-31. RMS delay spread results for the air-to-ground measurement campaign...... 191 Table 5-32. Excess delay spread values for air-to-ground measurements...... 195 Table 5-33. Average number of signal components per delay bin per profile for air-to-ground measurements...... 199 Table 5-34. Average number of signal components per power-delay profile for each elevation angle measured during air-to-ground measurements...... 200 Table 6-1. Input parameters used by the wideband vector channel model simulator...... 206 Table 6-2. Relationship between correlation coefficients of Gaussian random variables and correlation coefficients of Rayleigh random variables computed from the envelope of the Gaussian random variables...... 224 Table 7-1. Major simulation parameters for elliptical sub-regions model for NLOS channels. 232 Table 7-2. Major simulation parameters for elliptical sub-regions model for LOS channels....232 Table 7-3. RMS delay spread results for simulations (ESR) and measurements of NLOS dense scatterer locations...... 242

xxiv

Table 7-4. RMS delay spread results for simulations (ESR) and measurements of LOS dense scatterer locations...... 245 Table 7-5. Excess delay spread values for simulated (ESR) and measured NLOS channel impulse responses...... 247 Table 7-6. Excess delay spread values for simulated (ESR) and measured LOS channel impulse responses...... 247 Table 7-7. Approximate diversity gain for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels...... 254 Table 7-8. Approximate diversity gain for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels...... 256 Table 7-9. Approximate fading levels differences between 2-D rake output and single channel output for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels...... 260 Table 7-10. Approximate fading levels differences between 2-D rake output and single channel output for LOS locations computed from simulated (ESR) channel impulse responses and measured channels...... 263 Table 7-11. Major simulation parameters for GBSBE model for NLOS channels...... 267 Table 7-12. Major simulation parameters for GBSBE model for LOS channels...... 267 Table 7-13. RMS delay spread results for simulations (GBSBE) and measurements of NLOS dense scatterer locations...... 275 Table 7-14. RMS delay spread results for simulations (GBSBE) and measurements of LOS dense scatterer locations...... 277 Table 7-15. Excess delay spread values for simulated (GBSBE) and measured NLOS channel impulse responses...... 279 Table 7-16. Excess delay spread values for simulated (GBSBE) and measured LOS channel impulse responses...... 279 Table 7-17. Approximate diversity gain for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels...... 285 Table 7-18. Approximate diversity gain for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels...... 287 Table 7-19. Approximate fading levels differences between 2-D rake output and single channel output for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels...... 291 Table 7-20. Approximate fading levels differences between 2-D rake output and single channel output for LOS locations computed from simulated (GBSBE) channel impulse responses and measured channels...... 294 Table 7-21. Major simulation parameters for geometric air-to-ground ellipsoidal channel model...... 298 Table 7-22. Reflection losses as a function of elevation angle used to produce the most accurate RMS delay spread results for the GAGE model...... 300 Table 7-23. RMS delay spread results for air-to-ground simulations using the GAGE model versus measurements...... 301 Table 7-24. Excess delay spread values for simulated and measured air-to-ground channel impulse responses...... 304 Table 7-25. Approximate diversity gain for simulated and measured air-to-ground channel impulse responses...... 308

xxv

Table 7-26. Approximate fading levels differences between 2-D rake output and single channel output for air-to-ground channels computed from simulated channel impulse responses and measured channels...... 311 Table A-1. Description of variables passed into MATLAB workspace by measurement receiver...... 326 Table B-1. Specifications for VT-STAR transmitter and receiver...... 335

xxvi Chapter 1

Introduction

Wireless communications has enabled the creation of a world once only dreamed about in fiction. Wireless devices and capabilities that are commonplace today but were unimaginable in the not-too-distant past are the result of an unrelenting quest for understanding through research and development in radio technology. Wireless has become pervasive throughout advancements in fields ranging from farming to medicine. With the emergence of every new mobile application involving storing, displaying, or communicating information, a new application for wireless is born.

1.1 Motivation and Challenges in Wireless

Commercial wireless communication is a primary driver of the development of radio technology. One of the biggest challenges in commercial wireless is satisfying an enormous and growing demand for mobile communications with a limited and fixed amount of resources. Expectations for mobile communications have risen to the point where wireless quality of service needs to equal or exceed that of wire line. The success of early voice cellular systems had whetted the appetite of consumers who now crave instant messaging, web browsing, electronic mail, and many other types of services normally offered through wired Internet access but until just

1 CHAPTER 1 – INTRODUCTION recently not truly practical over wireless links. As the wireless subscriber base grows and service offerings expand, the simple fact is that wireless networks need to provide more bi- directional bits-per-second in any given area.

Voice communication capabilities over wireless networks has matured to a level of acceptable quality and reliability where wireless phones have become an acceptable replacement for home and office. Widespread coverage and acceptable unit costs drive the more adventurous to exclusive use of wireless, forgoing diminishing advantages of wire line. Up until recently, a major drawback was the loss of reasonable data connectivity speeds for those who chose the wireless route. While the maximum wire line modem speed of 53.3 kbps1 falls short of blazing data speed, circuit-switched wireless phone transfer rates of 19.2 kbps or less dissatisfy even the most modest of Internet enthusiasts. Emerging today are not only paper standards that promise higher data rates but also actual system deployments whose delivered capabilities rival those of wire line in at least a stochastic sense. Early deployments of CDMA-2000-1xRTT [IS2000], known in the field by a variety of nicknames for obvious conversational reasons, have demonstrated payload data rates exceeding 100 kbps.

However, challenges in addressing bits-per-second issues are only aggravated by a growing acceptance of high-speed, home Internet access offered by DSL, cable modem, direct satellite, and even Ethernet directly to residences. As more of the population goes online with fast wired connections, expectations for quick data access will rise and Internet service developers will become less concerned with building low transfer rate requirements into their applications. Developments are needed in wireless to permit continued growth in the application and use of wireless for commercial services. Practical smart antennas that fit the forms of contemporary devices need to be developed to fully exploit spatial properties of signals, since all received energy not transmitted by the desired sender is interference to the desired recipient, and all transmitted energy not received by the desired recipient is interference to all other users. Modulation schemes that tolerate coexistence in the frequency and time domains need to be pursued. New multiple access techniques and spectrum sharing algorithms need to be developed

1 Although modems are capable of 56 kbps, U.S. law restricts transmission speeds over analog telephone lines to 53.3 kbps.

2 CHAPTER 1 – INTRODUCTION

so that frequency spectrum can be fully occupied, since vacancies observed within allocated bands on a spectrum analyzer equate to wasted resources. Developments in these areas are essential to industry, or we risk being decelerated to a state analogous to trying to conduct business today with the voice and data communication capabilities of decades ago.

A less visible but important driver of technical advances in wireless involves development for military and civil applications related to national defense, law enforcement, public safety, and navigation, where performance of wireless systems concerns not productivity and profit but life and limb. Increasingly burdening requirements are being placed on military wireless communication systems, as tactical military operations today rely on video from unmanned drones, intercepted communications, and airborne communications nodes for relaying voice and data from the field. Efficient and safe operations require reliable, uninterrupted radio links that achieve low probability of detection and low probability of intercept while simultaneously achieving the highest performance possible.

Outside of the military, civilians rely on wireless communication systems for safety so that emergency personnel, law enforcement agents, utilities employees, air traffic controllers, and a variety of other service personnel can do their jobs. While deficiencies may be tolerable today, a rise in demand and capability requirements will accelerate the need for wireless engineers to strive for faster and more efficient communication systems. As an example, present day civilian aviation radio communication is a snapshot of history, where large airliners and general aviation aircraft alike use amplitude modulation (resulting in signal quality similar to that of broadcast AM radio) for communications with air traffic control. This relatively low quality and congested system is the primary method that most commercial and private pilots use for collision avoidance to steer clear of other aircraft, for weather avoidance to circumnavigate weather phenomena such as thunderstorms, and for navigational guidance to descend to altitudes as low as 200 feet above ground during instrument approaches. Developments in aviation data communications are needed to more effectively get weather data, clearances, and traffic information into the cockpit. Developments in wireless technologies that serve the public and the nation in other ways are likewise needed.

3 CHAPTER 1 – INTRODUCTION

Indeed, we have become a society dependent upon wireless to sate our appetite for communications and mobility. Advances in wireless communications facilitate advances in all areas of civilization, moving us forward as fast as our growing expectations for quality and ease of life and work.

1.2 Foundations of Progress in Wireless

Frequency spectrum is the raw material with which wireless services are built. Long before a swarm of electromagnetic fields exponentially consumed the frequency spectrum around the planet, pioneering experimenters in radio produced the first intentional manmade disturbances in the spectrum distinguishable from noise with crude but inventive devices. Wireless communications was truly born when the first spark gap transmitters splattered energy into RF bands, but accounts of wireless experiments started to become noteworthy in public memory around the time following the first wireless transmission across the English Channel in 1899 by Guglielmo Marconi. The world seriously took notice on December 12, 1901, the date when global wireless communications was born by Marconi’s first successful reception of radio signals across the Atlantic between the Poldhu station in Cornwall, England, and Signal Hill in Newfoundland.

In these early days of radio, preservation of frequency spectrum was not a concern and government regulation of the airwaves as we know it today was nonexistent. In the Radio Act of 1912, which mandated federal licensing of all radio stations [DoC14] and banished amateur use to the “less useful” radio bands above 1.5 MHz [Wes00], the United States government showed its first bit of concern over this newly discovered natural resource called radio frequency spectrum. Over the next several decades, all of the radio frequency spectrum between 9 KHz and 300 GHz would be allocated for commercial, military, and private use [DoC96]. The price tag placed on spectrum would truly be realized in the 1990s when the average consumer developed a perceived need for anywhere, anytime, instant communications. During this time period, the privilege to use spectrum throughout a particular geographical region by service providers could cost millions of dollars after outbidding a competitor in an auction for slices of bandwidth.

4 CHAPTER 1 – INTRODUCTION

Advances since the early exploration of radio have been made in many sub-fields of wireless communications, all working towards the goal of more efficient use of radio resources. Multiple access techniques have evolved to allow users to share spectrum in a manner that allows soft, sometimes imperceptible degradation of service to occur when capacity is taxed rather than forcing hard failures of mobile links. Adaptive antenna array systems have aged through a period of adolescence in academia and have been accepted in industry as a viable path to increased quality and capacity for commercial networks. Software-defined radios, once a concept merely evangelized but not realized because of digital signal processing constraints, have found their way in early form into commercial products. Developments in coding algorithms, RF hardware, integrated circuits, and many other areas have all improved the quality of personal communications devices in terms of reliability, cost, function, form factor, and overall desirability of integrating such devices into everyday life. As applications for wireless become more plentiful, development of wireless technology through academic and industrial research must continue to ensure capacity never reaches the point of saturation.

1.3 Research Issues Covered

As with all focused research, the work described in this dissertation was performed with the intent of contributing to the mosaic of wireless developments directed toward advancing basic theory and practical knowledge in the field. The research presented here reaches into the coupling among three areas in wireless communications: radio channel measurements and modeling; smart antenna arrays; and design, development, and application of software radio technology.

Behaviors of the actual hardware and software that implement radio communications devices are either deterministic in nature or, at least, well understood stochastic processes. Once designed, a piece of hardware can generally be modeled and implemented in a simulator, and changes to model are likely related to changes in the hardware. Behavior of radio channels, however, is typically a moving target, requiring evolutions of modeling and characterization to support leading-edge developments in technology and the latest applications of wireless. To support this evolution, this research addresses channel measurement and modeling related to smart antenna arrays.

5 CHAPTER 1 – INTRODUCTION

Literature on basic signal and antenna array theory was gathered and reviewed to provide a foundation of well understood and accepted theory. This dissertation reviews complex signal fundamentals, signal representations for smart antenna arrays, and channel characteristics related to smart antenna performance. Vector channels, a term used to describe multidimensional channel impulse responses for antenna arrays, are a common theme throughout all discussions of new and old developments.

A large part of the initial research was dedicated to the development of a software-defined measurement receiver for characterizing wideband vector channels. Measurement results from this system were required in order to pursue subsequent research topics. The design of the measurement system receiver and transmitter included provisions to serve as a test bed for antenna array experiments and as a platform for experiments requiring high-speed sampling and wideband signal acquisition.

Once the operational measurement system had been developed, channel modeling literature was reviewed. Of interest were existing channel models that base results on propagation environment geometry; these geometric channel models provide spatial and temporal signal information for simulating wireless communications systems. Through this research, accepted channel modeling techniques were used to produce a new geometric channel model for air-to-ground communications.

With channel modeling techniques and considerations in mind, measurement campaigns were designed and conducted using the new measurement system to characterize channels and collect received signal data relevant to evaluation of a subset of the channel models studied. Three multipath environments were characterized with information on channel impulse responses and the effect of the channel on received signals. Two terrestrial environments were measured. The first environment was used to characterize vehicular rooftop-to-ground environment, and the second was used to characterize a dense-scatterer ground-to-ground environment. An airborne measurement campaign was conducted to measure air-to-ground channels, where the ground- based receiver was surrounded by structures that obstructed and reflected radio signals.

6 CHAPTER 1 – INTRODUCTION

Traditional and newly developed methods of processing signal data were employed to produce measurement results.

A channel model simulator was developed to produce channel impulse responses using the three channel models under evaluation. The simulator accepts as input sets of results from the terrestrial and airborne measurement campaigns. Methods used to simulate strength, delay, and direction of arrival of multipath components are described.

Finally, three geometric channel models were evaluated by comparing their output with measurements of the channels they were intended to represent. Comparisons were made between simulations and measurements with regard to processed parameters including RMS delay spread, excess delay spread, multipath component strength distributions, multipath fading characteristics, antenna diversity gain, and gain achieved through the use of a two-dimensional rake receiver. Accuracies and discrepancies are discussed for each result.

1.4 Organization of This Dissertation

Chapter 2 provides a review of signal representation and radio channels from the perspective of analysis and design of antenna arrays. Notation is defined and key concepts related to antenna arrays are discussed, and parameters for characterizing signals and channels are presented. Chapter 3 describes the development of the vector channel receiver antenna array test bed and wideband measurement system, explaining system specifications and capabilities of the software and hardware. Topics related to software-defined radio, object orientation, RF hardware, and software architecture are covered. The FPGA-based transmitter used to produce wideband signals for power-delay profile measurement is also described. Chapter 4 begins with a review of existing radio channel models and an introduction to new models. The newly developed geometric air-to-ground model is documented, including analytical and simulated results for temporal-spatial multipath characteristics. Chapter 5 gives a review of past channel measurements and presents results of the new measurements completed for this research. In Chapter 6, details of the channel simulator used to implement three geometric channel models are presented. Finally, Chapter 7 presents evaluations of channel models based on their ability to accurately produce results in comparison to measured channels. Output from the channel model

7 CHAPTER 1 – INTRODUCTION simulator and results of the measurement campaigns described in the earlier chapters serve as the basis for this comparison.

Together, these chapters unite theory, simulation, and measurement. Detailed data presented in each chapter provides opportunities for additional analysis. Documentation of the measurement system hardware and software supports evolution of the current system or development of new systems. As much as it is the author’s intent to provide answers and information to solve problems, it is also the intent to raise new questions and launch further research.

8 Chapter 2

Signal Fundamentals for Antenna Arrays

Analysis and simulation of antenna arrays requires consideration of multiple time-domain signals simultaneously. With a single signal source present, the minimum number of signals that needs to be represented is equal to the number of array elements. When multiple signals are present in a multipath environment, the number of signals that must be considered grows rapidly. This chapter reviews fundamental signal concepts and introduces signal representations for antenna arrays. Also, characterization of signals and radio channels through which they propagate is discussed.

2.1 Complex Signal Fundamentals

In this section, basic signal principles that form the foundation for antenna array signal processing are presented. For a given bandpass signal2, all of the information is contained in its complex envelope representation. Phase, amplitude, and relative frequency (time-varying phase) characteristics can be preserved when the carrier is removed from a bandpass signal. The

2 A bandpass signal is a waveform that has a spectral magnitude that is nonzero for frequencies concentrated in a

band about a frequency w = ±wc and that has negligible spectral magnitude elsewhere [Cou90]. The frequency wc is the carrier frequency. The bandpass signal generally has negligible spectral magnitude at wc = 0 (DC).

9 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

complex representation of signals simplifies analysis and simulations of systems without compromising accuracy of results.

2.1.1 The Complex Envelope

Sinusoids provide a set of basis functions with which all wireless communication signals can be represented. In formation is conveyed using sinusoidal signals by time-varying their amplitude, phase, and/or frequency. Let us first define the signal ~r (t) , which is a real-valued, bandpass signal given by ~ r (t) = R(t)cos(w c t +q (t)). ( 2.1 )

This signal has a carrier frequency w c , and the time-varying amplitude and phase are given by R(t) and q (t), respectively. This signal can also be expressed as

~ r (t) = Re{r(t)exp( jw ct)}. ( 2.2 )

The complex-valued signal r(t) is called the complex envelope of signal r~(t) , and r(t) contains ~ all of the information of r (t) except for the carrier frequency w c . The time varying amplitude R(t) in equation ( 2.1 ) is related to the complex envelope r(t) by

R(t) = r(t) = (Re{r(t)})2 + (Im{r(t)})2 . ( 2.3 )

The time varying phase q (t) in equation ( 2.1 ) is related to the complex envelope r(t) by

æ Im{r(t)}ö q (t) = Ðr(t) = arctanç ÷ . ( 2.4 ) è Re{r(t)}ø

The complex envelope r(t) can be represented using two real-valued functions, rI (t) and rQ (t) , given by

rI (t) = Re{r(t)}= R(t)cos(q (t)) ( 2.5 )

and

rQ (t) = Im{r(t)}= R(t)sin (q (t)). ( 2.6 )

10 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

The function rI (t) is called the in-phase component or simply the I-component. The function rQ (t) is called the quadrature component or simply the Q-component. The in-phase and quadrature components are combined to form r(t) using

r(t) = rI (t)+ jrQ (t). ( 2.7 )

If we combine equation ( 2.7 ) with equation ( 2.2 ), a direct relationship between the bandpass signal and the I- and Q-components is produced, ~ r (t) = Re{r(t)exp( jw ct)}

= Re{(rI (t)+ rQ (t))(exp( jw ct))} ( 2.8 ) = Re{(rI (t)+ rQ (t))(cos(w ct)+ j sin (w ct))}

= Re{rI (t)cos(w ct) + jrI (t)sin (w ct)+ jrQ (t)cos(w ct)- rQ (t)sin(w c t)}.

Therefore, ~ r (t) = rI (t)cos(wct)- jrQ (t)sin (wct). ( 2.9 )

The use of real-valued in-phase and quadrature signal components allows processing in analog circuits, where only real-valued voltages and currents exist; also, native instructions of digital signal processors generally only operate on real-valued arguments.

The complex envelope r(t) is typically a baseband signal, since the carrier has been removed from the signal. As such, the complex envelope r(t) may be called a complex baseband signal.

2.1.2 Converting Bandpass Signals to Complex Envelopes

Bandpass signals can be converted to their equivalent baseband complex envelops using a process known as quadrature down-conversion (or complex down-conversion). Consider the bandpass signal of the form ~ r (t) = R(t)cos(w c t +q (t)). ( 2.10 )

~ The in-phase component can be extracted by multiplying the bandpass signal r (t) by 2cos(w c t) and low-pass filtering the result. This is demonstrated by first performing the multiplication:

11 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

~ r (t)(2cos(w ct)) = R(t)cos(w ct +q (t ))(2cos(w c t))

= 2R(t)cos(w ct +q (t))cos(w ct)

æ 1 1 ö = 2R(t)ç cos(w ct +q (t) +w c t) + cos(w ct +q (t)-w ct)÷ ( 2.11 ) è 2 2 ø

= R(t)(cos(2w ct +q (t))+ cos(q (t)))

= R(t)cos(2w ct +q (t))+ R(t)cos(q (t)) .

Then, the low-pass filtering attenuates components with frequencies near 2w ct :

~ LPF{r (t)(2cos(w ct))}= R(t)cos(q (t)) ( 2.12 )

= rI (t) .

The quadrature component can be extracted by multiplying the bandpass signal r~(t) by

- 2sin (w ct) and low-pass filtering the result.

~ r (t)(- 2sin(w c t)) = R(t)cos(w ct +q (t ))(- 2sin (w ct))

= -2R(t)cos(w ct +q (t))sin (w ct)

æ 1 1 ö = -2R(t)ç sin (w ct +q (t) +w ct) - sin (w ct +q (t)-w ct)÷ ( 2.13 ) è 2 2 ø

= R(t)(sin (2w ct +q (t)) + sin (q (t)))

= R(t)sin (2w ct +q (t)) + R(t)sin (q (t)).

As in the previous case, the low-pass filtering attenuates components with frequencies near

2w ct :

~ LPF{r (t)(- 2sin (w ct))}= R(t)sin (q (t)) ( 2.14 )

= rQ (t).

12 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

LPF rI (t)

wcutoff << 2wc ~ r (t) = R(t)cos(wct +q (t)) 2cos(wct)

LPF rQ (t)

wcutoff << 2wc

- 2sin(wct)

Figure 2-1. Block diagram of the down-conversion process for extracting in-phase and quadrature signal components from a bandpass signal.

Figure 2-1 illustrates the process of extracting in-phase and quadrature signal components from a bandpass signal using conventional signal processing blocks. This process can be performed using analog components or in the digital domain after a signal has been sampled and quantized.

2.1.3 The Narrowband Approximation

Signals can be classified as wideband or narrowband, but the wideness or narrowness of a signal’s bandwidth is a relative measure and must be defined in a particular context. The bandwidth of signals can be measured relative to several quantities, including carrier frequency, information rate, multipath delay, and antenna bandwidth.

First consider a signal symbol (or chip) period relative to the period of its carrier. Define a time shift t that is large compared to the period of the sinusoidal carrier. That is, the time shift t may be up to a few carrier periods in duration. The resulting real, bandpass signal with a time shift t can be written as ~ r (t +t ) = Re{r(t +t )exp( jw c (t +t ))}. ( 2.15 )

Now assume that the symbol period of the modulating signal is very large compared to the period of the sinusoid. For example, the symbol period may be 20 or more times the carrier

13 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

period3. This large ratio in periods implies that the symbol period is also very large compared to the time shift t. If the modulating signal is filtered such that the filter bandwidth is on the order of the symbol (or chip) rate, as is usually the case4, then because of the slowly varying nature of the modulating signal compared to the short duration of t, the following approximation can be made for the complex envelope

r(t +t ) » r(t) . ( 2.16 )

This approximation is called the narrowband array approximation [Ree02]. Therefore, equation ( 2.16 ) may be rewritten as ~ r (t +t ) » Re{r(t)exp( jw c (t +t ))}. ( 2.17 )

Since the carrier is purely sinusoidal, the time shift in the exponential argument can be rewritten as a phase shift, where the phase shift is given by

y = w ct . ( 2.18 )

Therefore, the expression for the real, bandpass signal given in equation ( 2.15 ) can be written as ~ r (t +t ) » Re{r(t)exp( j(w ct +y ))}. ( 2.19 )

The salient point of this discussion is to show that a time shift t, which is small compared to the symbol period, can be represented solely by a phase shift of the carrier frequency.

Antenna array elements are typically spaced at distances equal to fractional wavelengths of the carrier frequency, implying that a time shift t due to excess propagation delay between elements is on the order of the carrier period. If the symbol period is large compared to this time shift, then the narrowband array approximation applies. However, the signal may still be considered wideband in certain contexts. For example, consider an IS-2000 bandpass signal. A 1.2288 Mcps (megachip per second) PN sequence modulates an 825 MHz carrier to produce a bandpass signal filtered to a bandwidth of approximately 1.25 MHz. The signal carries data at a rate up to

3 A good example is the proposed IS-2000/CDMA-2000 3X standard, which specifies a 3.75 Mcps chip rate at a carrier frequency in the 800 MHz band. Even at this high chip rate (considered “wideband” by today’s standards), the ratio of the chip period to carrier period is still very large, (1/3.75)/(1/800) = 213. 4 For example, the IS-95 and IS-2000 1X standards specify a chip rate of 1.2288 Mcps and a filter bandwidth of approximately 1.25 MHz.

14 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

19.2 kbps and is received by a monopole antenna (with 2% bandwidth relative to center frequency) in a multipath environment with excess propagation delays up to 4 ms in duration. Table 2-1 shows the contexts in which the signal may be considered wideband. The ratio of the signal bandwidth (approximately the chip rate) to the carrier frequency is small, so that the signal can be considered narrowband relative to the carrier, and therefore, the narrowband approximation actually is valid regardless of context. The ratio of the signal bandwidth to the information bit rate is large, and in this context the signal can be considered wideband. The ratio of the bandwidth to the inverse of the multipath excess delay is large, so that this signal may be considered wideband and may experience frequency-selective fading. With regard to the antenna bandwidth, the ratio of signal bandwidth to antenna bandwidth is very small, and the signal would be considered narrow band in this context.

Table 2-1. Comparison of relative signal bandwidth for a 1.25 MHz-wide CDMA signal used for voice and data services, where the base information bit rate is 19.2 Kbps and the carrier frequency is 825 MHz, in a multipath environment with a 4 ms excess delay. Signal bandwidth relative to… Ratio Wideband? Carrier frequency 1.25 MHz / 825 MHz = 0.0015 No Information rate 1.25 MHz / 19.2 KHz = 65 Yes Multipath delay 1.25 MHz / ( 1 / (4ms) ) = 5 Yes Antenna bandwidth 1.25 MHz / ( (2%)(825 MHz) )= 0.076 No

Measurements discussed in following chapters used a signal produced by phase modulating a 2050 MHz carrier with chip rate of 80 Mcps, which is unquestionably wideband compared to today’s common communication systems. However, in the context of antenna arrays, the narrowband approximation still applies because the chip period is large compared to the carrier frequency, (1/80)/(1/2050) = 25.6, and equations ( 2.16 ) through ( 2.19 ) still hold true. Therefore, even when using a signal modulated by a 80 Mcps data source for measurements, the narrowband approximation can be applied to represent time shifts due to array element spacing as phase shifts of the carrier.

15 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

2.2 Signals for Smart Antennas

A smart antenna at a receiver is an antenna array system that uses signal processing algorithms to adapt to radio environments by selecting or combining in some way the signals received by each element of the antenna array [Ree02]. A smart antenna at a transmitter transmits different signals at each element to produce a desired effect at a receiver on the other end of the radio link. Unless otherwise specified as a transmitter antenna, the term smart antenna will be used in most cases to describe a receiver antenna.

Smart antennas are far advanced compared to their passive ancestors whose processing capabilities included at most statically combining signals from different elements. Rather than existing as a resonant conductor designed to passively capture the surrounding electromagnetic fields, smart antennas have the ability to actively select desired signals out of an environment of interferers and noise. The smart antenna encompasses not only the elements of the array, but also the signal processing that lies behind the array.

2.2.1 The Purpose of Smart Antennas

Smart antennas provide a means of strengthening desired signals and suppressing unwanted signals at a radio receiver using an array of two or more antennas as elements of the array through spatial filtering, often called beamforming [Ng02]. The overall purpose of using a smart antenna array in a wireless system is to improve the ability of a wireless system to efficiently convey error-free information over a radio channel and to increase the capacity of the system.

A smart antenna system requires a receiver or transmitter to have additional processing capabilities. The burden of additional processing may be offset by the advantages listed in Table 2-2.

16 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

Table 2-2. Advantages of using smart antennas at a transmitter or receiver. Factor Effect of using smart antennas Capacity The intentional direction of energy from transmitter antennas reduces the amount of interference throughout the wireless network. The ability to perform spatial filtering at receiver antennas reduces the effect of remaining interfering signals. In interference-limited system, this means that more users can be active on the network for a given level of performance. Reliability Smart antennas increase reliability (or equivalently lower error rates) by providing an increase in antenna gain for the signals of a desired user and a decrease in gain for undesired signals and environmental noise. The result is a higher quality radio link for stations in the fringe region of reception. Data rates For a given error rate, the amount of data that can be transmitted through a wireless link is limited by the energy-per-bit and the noise-plus-interference level. The reduction of interference and the increase in antenna gain (an increase of received power at the receiver) means that shorter bit periods (higher data rates) can be used compared to that of a system without smart antennas. Energy An increase in antenna gain through the use of smart antennas means that lower transmitter power can be used for a given situation, resulting in longer battery life for mobile stations. The reduction of interference at the receiver has the same effect of requiring a lower transmitter power. Bandwidth While smart antennas may not directly affect the bandwidth of signal, smart antennas enables a communications system to use its allocated bandwidth more efficiently. By reducing the amount of transmitted and received interference throughout the band, a larger number of users can operate within the allocated bandwidth of an interference-limited wireless network. Location Smart antennas can provide direction of arrival information, which can be used by geo-location systems to locate a mobile station in the coverage area of a wireless network.

17 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

2.2.2 A Signal Model for Antenna Arrays

In order to study channel measurement and modeling techniques for smart antennas, it is necessary to understand conventional signal models for smart antennas. Widely used definitions compiled from several sources (including [Chr00] [Ert99] [Ng02] [Ree02] [Vib02]) are used to set many of the conventions for the rest of this work. However, the notation used here rigorously keeps track of the signals at each antenna element as well as the sources from which they originate. In this section, a general expression is derived for determining the complex envelope of a signal at any element of an antenna array.

First consider the antenna array with elements located as shown in Figure 2-2. This figure shows the general case of L antenna elements, and the location of the lth element is specified by position vector rl , which extends from the axis origin to element l.

z

Element 2 Element 1

Element 3

… …

Element l

rl … … Element L

y x

= Antenna array element

Figure 2-2. Location of elements of an antenna array.

Now consider a set of M point signal sources surrounding the antenna array as shown in Figure 2-3. The assumption is made that the distances between all pairs of elements is much less than the distance between signal sources and the antenna array (i.e., the array is small compared to the

18 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

distances between the array and the signal sources). Given this assumption, signals radiated from the point sources appear as plane waves when reaching the array. The location of signal

source m is defined by position vector m m , which extends from the axis origin to source m.

Next consider the relative time of arrival of signals received by the antenna elements from each signal source. Because relative time of arrival, not absolute time of arrival, is of importance, the choice of a reference point is arbitrary. For simplicity, the axis origin is chosen. The relative time of arrival observed at the lth element of a signal from the mth source is given by the scaled dot product of the source position vector with the element position unit vector,

r × mˆ (f ,q ) t = t (f ,q ) = l m m ( 2.20 ) l,m l m m c

where

mˆ (fm ,q m ) = m m / m m . ( 2.21 )

th The vector mˆ (fm ,q m ) is a unit vector in the direction of the m source given by the angles

(fm ,q m ), and c is the speed of propagation of the plane wave (the speed of light in free space,

8 3x10 m/s). A negative t l,m means that the signal arrives at the origin before arriving at the

antenna element; a positive t l,m means that the signal arrives at the antenna element before arriving at the origin.

The expression for delay given by equation ( 2.20 ) is very useful for antenna arrays with elements located in two or three dimensions, such as a square or circular array, and for situations where signal sources surround an array in three dimensions. A more specific and common antenna geometry is the case of a uniformly spaced, linear antenna array surrounded by sources that lie on a plane5. Figure 2-4 shows the case where the antenna elements are located along the x-axis, and the sources line on the x-y plane.

5 Such is the case when an antenna array is used at a base station and the signal sources are mobile stations surrounding the base station at a distance much greater than the height of the base station antenna array.

19 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

z Source 3

Source 2 … Source m

Source 1

mm …

Antenna Source M Array qm

f m y x = Signal source

Figure 2-3. Signal sources surrounding antenna array.

y

Source m

) f m cos( d fm l-1) 1 ( 2 … l … L x d

Figure 2-4. Geometry for a uniformly spaced, linear antenna array.

The time of arrival relative to the axis origin for the plane waves from source m at antenna element l is given by

(l -1)d cos(f ) t = t (f ) = m . ( 2.22 ) l,m l m c

~ Now consider expressions for the signals incident on the antenna array elements. Let xl (t) be th ~ the bandpass output signal of the l of L isotropic antenna elements. The signal xl (t) consists of

20 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

~ ~ a bandpass signal contribution sl (t) and a bandpass additive noise contribution nl (t), expressed by ~ ~ ~ xl (t) = sl (t)+ nl (t). ( 2.23 )

~ The signal sl (t) may be the sum of multiple signals incident on the array, so that

M ~ ~ sl (t) = å sl ,m (t), ( 2.24 ) m=1

~ th th where sl,m (t) is the contribution of the m signal source at the l antenna element. Using the

time shift t l,m computed using ( 2.20 ) or ( 2.22 ), the signal contribution from each source can be expressed as ~ ~ sl,m (t) = sm (t +t l,m ), ( 2.25 )

~ th where sm (t) is the signal from the m source at the axis origin; for the case of the linear array in ~ ~ Figure 2-4, the first element is located at the origin, so sm (t) = s1,m (t) . Now, equation ( 2.24 ) can be rewritten so that the signal at the lth element is sum of time shifted signals from each of the M sources, given by

M ~ ~ sl (t) = å sm (t +t l ,m ), ( 2.26 ) m=1

th where t l,m is the time shift governed by ( 2.20 ) or ( 2.22 ). The m signal from each source can

be expressed as a complex envelope sm (t) in the equation

~ sm (t) = Re{sm (t)exp( jw ct)}. ( 2.27 )

The time-shifted version of the signal from the mth source is expressed as ~ sm (t +t l,m ) = Re{sm (t +t l,m )exp( jw c (t +t l,m ))}. ( 2.28 )

By applying the narrowband approximation from equation ( 2.17 ), the time-shifted signal from the mth source can be approximated with ~ sm (t +t l,m ) » Re{sm (t)exp( jw c (t +t l,m ))}. ( 2.29 )

21 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

The time shift t l,m is equivalently expressed using a phase shift y l ,m where

y l,m = w ct l,m ( 2.30 )

so that the time-shifted signal from the mth source can be written as ~ sm (t +t l,m ) » Re{sm (t)exp( jw ct +y l ,m )} ( 2.31 )

= Re{sm (t)exp( jw ct)exp( jy l,m )}.

From here forward the approximation will be assumed to be an equality. Using ( 2.31 ), the expression in ( 2.26 ) for the signal at the lth element can be rewritten as

M ~ sl (t) = åRe{sm (t)exp( jw ct)exp( jy l,m )}. ( 2.32 ) m=1

~ Because the real part of a sum of complex numbers is equal to the sum of the real parts, sl (t) can be written as

M ~ ì ü sl (t) = Reíå sm (t)exp( jw ct)exp( jy l,m )ý, ( 2.33 ) îm=1 þ

which is equivalent to

M ~ ìæ ö ü sl (t) = Reíçå sm (t)exp( jy l,m )÷exp( jw ct)ý = Re{sl (t)exp( jw ct)}. ( 2.34 ) îè m=1 ø þ

~ th From this equality, it is seen that the complex envelope sl (t) of the signal at the l element of the array is equal to the sum of phase-shifted complex envelopes of the signals at the origin from the M signal sources. This relationship can be written as

M sl (t) = å sm (t)exp( jy l,m ). ( 2.35 ) m=1

Table 2-3 summarizes the expressions for computing the complex envelope of signals at elements of an antenna array given arbitrary locations of elements and sources.

22 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

Table 2-3. Expressions for computing signals incident on the elements of an antenna array. Array and Signal Source Parameters Expression Number of antenna elements L Number of signal sources M Index of antenna element l Index of signal source m th Position vector for l antenna element rl th Position vector for m signal source m m

th Unit vector in the direction of the m source mˆ (fm ,q m )

th th Complex envelope of signal from m source at l sl,m (t) antenna element th Complex envelope of signal from m source at axis sm (t) origin th th Time shift of signal from m source at l element relative rl × mˆ (fm ,q m ) t l,m = t l (fm ,q m ) = to axis origin c th th Phase shift of signal from m source at l element y l,m = w ct l,m relative to axis origin Complex envelope of signal received by lth element M sl (t) = å sm (t)exp( jy l,m ) m=1

2.2.3 Vector Channels

Received signals, noise contributions, and channel impulse responses can be represented in vector notation (as in [Ree02] and [Vib02]) to facilitate analysis and processing for antenna arrays. The signals sl (t) arriving at an antenna array with L elements can be expressed in vector form using

és1 (t)ù ês (t)ú s(t) = ê 2 ú . ( 2.36 ) ê M ú ê ú ës L (t)û

23 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

The output of the array is represented in vector form as the sum of signal sources and independent noise sources, given by

é x1 (t)ù é s1 (t)ù én1 (t)ù êx (t)ú ês (t)ú ên (t)ú x(t) = ê 2 ú = ê 2 ú + ê 2 ú = s(t)+ n(t). ( 2.37 ) ê M ú ê M ú ê M ú ê ú ê ú ê ú ëxL (t)û ës L (t)û ënL (t)û

The elements of the noise vector n(t) are assumed to contribute independent and additive noise signals. Each noise contribution can be a noise source based on the system noise figure of each receiver branch referenced to the output port of each antenna element.

To relate the received signal to the transmitted signal, the concept of the vector channel is introduced. Elements of the vector channel consist of the channel impulse response between the th th m source and the l antenna element. If mm (t) is the transmitted signal and hl ,m (t) is the impulse response between the mth source and lth antenna element, then the received signal at element l contributed by the mth source is given by

sl,m (t) = hl ,m (t)* mm (t). ( 2.38 ) where * represents convolution. In vector form, the received signal is written as

éh1,m (t)* mm (t)ù ê ú h2,m (t)* mm (t) s (t) = ê ú = h (t)* m (t). ( 2.39 ) m ê M ú m m ê ú ëhL,m (t)* mm (t)û

The vector h m (t) is a vector channel impulse response and represents a vector channel. Using

th h m (t), the output of the array due to the m source can be related to the transmitted signal of the mth source with

é h1,m (t)* mm (t)+ n1 (t)ù ê ú h2,m (t)* mm (t)+ n2 (t) x (t) = ê ú = h (t)* m (t) + n(t) . ( 2.40 ) m ê M ú m m ê ú ëhL,m (t)* mm (t)+ nL (t)û

24 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

One vector channel exists between each source and the antenna array. If M sources are present, then the output of the array is given by

M x(t) = n(t) + åh m (t)* mm (t) . ( 2.41 ) m=1

Equation ( 4.41 ) completely describes the output of an isotropic-element antenna array that is surrounded by M signal sources transmitting through M vector channels.

Vector channels modeled by h m (t) simply express a relationship between the signal radiated by a transmitter antenna and the signals (plane waves) incident on a receiver antenna array. Vector channels do not describe the effects of antenna radiation patterns (amplitude and phase characteristics), but if ideally isotropic array elements are assumed, then the output of the array can be computed.

2.2.4 Array Steering Vectors

Array steering vectors express the relationship between the signals (plane waves) incident upon an antenna array and the output of the antenna array. This relationship is a function of the radiation patterns of the antenna elements and the relative positions of the elements. Let th Gl (f,q ) be the radiation pattern of the l antenna element. If this radiation pattern is included in the expression in ( 2.35 ), then signal contribution to the output of the lth antenna element due to all M sources is given by

M sl (t) = å sm (t)Gl (fm ,q m )exp( jy l,m ), ( 2.42 ) m=1

th where fm and q m specify the angles to the m source from the antenna array. The radiation pattern and phase shift terms, which are functions of array geometry and element radiation pattern, can be expressed by a single term al (f,q ) given by

al (f,q ) = Gl (f,q )exp( jy l,m ), ( 2.43 )

so that sl (t) can be expressed as

25 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

M sl (t) = å sm (t)al (f,q ). ( 2.44 ) m=1

By including the noise contribution term in ( 2.44 ), the output of the lth of the antenna array is given by

M xl (t) = nl (t)+ sl (t) = nl (t) + å sm (t)al (f,q ). ( 2.45 ) m=1

In vector form, this relationship can be written as

M x(t) = n(t) + å sm (t)a(f,q ). ( 2.46 ) m=1

If only once source s1 (t) is present, then the a common result is obtained, given by

x(t) = s1 (t)a(f,q ) + n(t) . ( 2.47 )

The vector a(f,q ) is called the array steering vector. The array steering vector includes two influences: the antenna element radiation pattern and phase differences due to relative propagation distances among the antenna elements. In practical antenna arrays, the effect of mutual coupling of antenna elements should be included in the array steering vector. Mutual coupling has the effect of changing the radiation pattern of the individual array elements.

2.2.5 Spatial Signatures

In a multipath channel, multiple plane waves will be incident on an antenna array even if only one source is present. Let K be the number of multipath components arriving from a single source that would cause signal s1 (t) to be incident on the array along the direct path. Then the output of the array can be expressed as

K x(t) = n(t) + åa k (t)s1 (t -t k )a(fk ,q k ) . ( 2.48 ) k=1

The factor a k (t) is a (possibly time-varying) complex value that describes the strength and phase

of the multipath component, and a(fk ,q k ) specifies the steering vector for each of the multipath

26 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

components. If multipath delays are much smaller than the reciprocal of the signal bandwidth, then following approximation can be made

1 s1 (t -t k ) » s1 (t) for t k << . ( 2.49 ) BW(s1 (t))

Using this approximation, the output of the array can be written as

æ K ö x(t) = n(t) + çåa k (t)a(fk ,q k )÷s1 (t), ( 2.50 ) è k =1 ø

since s1 (t) is no longer dependent upon k because t k is removed from its argument. This expression can be written more simply as

x(t) = n(t) + a(t)s1 (t), ( 2.51 ) where

K a(t) = åa k (t)a(fk ,q k ). ( 2.52 ) k =1

The function a(t) is called the spatial signature of s1 (t). Spatial signatures are influenced by three factors: the antenna element radiation pattern; phase differences due to relative propagation distances among the antenna elements; and the summation of multipath components incident on the array. Because of the approximation made in ( 2.49 ), the definition of spatial signature is valid only for signals that are narrowband with respect to excess multipath delays of the channel.

2.3 Channel and Signal Characteristics in Multipath Environments

Several attributes of signals and channel responses must be characterized in a manner that is relevant to the performance of radio systems. Signal strength and propagation delay is an important factor for all communications systems. Antenna arrays add the requirement for joint characterization of signals where relative signal strengths and channel characteristics can have an impact on potential gains in multipath environments. The characteristics discussed in this section lay a foundation for measurement processing and channel modeling discussed later.

27 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

2.3.1 Multipath Amplitude and Time Delay

Multipath strength and time delay must be considered together when characterizing a radio channel. Let the transmitted signal from a single source be an impulse with unity magnitude at t=0 as shown in Figure 2-5. The signal is transmitted through the L-dimensional vector channel to an antenna array with L elements. The impulse response of each channel is the corresponding received signal shown in Figure 2-5. The delay and amplitude of multipath components in each dimension of the vector channel can be quantified using excess delay spread, mean delay, and RMS delay spread.

1 Signal Transmitted t a a1,1 1,3 h1 (t) a1,2 a1,4

t a h2 (t) a 2,1 2,3 a 2,2 a 2,4

t … …

a hL (t) a L,1 L,3 a L,2 a L,4

t

Figure 2-5. Transmitted signal and impulse response of a multipath vector channel.

Excess delay spread is a measure of the spread of multipath components based on some defined threshold. The impulse response is normalized so that the strength of multipath components is expressed as a dB-level relative the strongest component, as shown in Figure 2-6. For the response shown in the figure, the excess delay spread Dt 10 dB for the 10 dB level is the time difference between the first and third signal components. The excess delay spread Dt 20dB for the 20 dB level is the time between the first and fifth components. Excess delay spread values are

28 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

important for defining input parameters for geometric channel modeling. Excess delay spreads determine, for example, the range around the transmitter and receiver within which multipath- causing reflectors must be modeled (discussed in detail in Chapter 4).

0 dB

-10 dB

a k -20 dB

t

Dt10dB Dt 20dB

Figure 2-6. Relative strengths of multipath components used to determine excess delay spread.

Mean delay is a measure of the average propagation delay between a transmitting antenna element and a receiving antenna element. The delay of each component is weighted by its strength. Mean delay is calculated using

K 2 åa k t k k =1 t = K , ( 2.53 ) 2 åa k k =1

where K is the number of multipath components to be included in the calculation. While mean delay may not have a direct impact on inter-symbol interference (ISI) like RMS delay spread, mean delay does have an effect on system planning in wireless networks that require precise synchronization of clocks at transmitting and receiving stations6.

6 Direct-sequence spread-spectrum systems require synchronization of chip clocks at the transmitter and receiver, and the amount of relative lead or lag of the clocks is determined by mean delay. This relative lead or lag becomes important for handoffs in mobile communication systems.

29 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

RMS delay spread is a measure of the spread of multipath components about the mean delay. RMS delay spread [Cav00] is the second central moment of the received multipath components computed using

K 2 2 åa k (t k -t ) k=1 s t = K . ( 2.54 ) 2 åa k k =1

When RMS delay spread becomes larger than approximately 10% of the symbol period, inter- symbol interference causes an increase in symbol error rate for an unequalized receiver [Chu87].

Realizable measurements systems cannot resolve multipath components with infinitely small time delay resolution. As a result, the impulse responses for vector channels shown in Figure 2-5 can never be exactly measured. Measured impulse responses consist of the true impulse response convolved with the time response of the finite-bandwidth system; therefore, multipath components in the impulse response are represented with relatively wide components rather than ideal impulses7. In practice, equations ( 2.53 ) and ( 2.54 ) can be used for the measured responses to achieve good approximations for mean delay and RMS delay spread.

2.3.2 Number of Multipath Components

The number and distribution of multipath components has been statistically characterized by past research efforts based on measured data. A Poisson distribution [Cou97] is used, whose probability density function is given by

¥ f Poisson (x) = å P(k)d (x - k), ( 2.55 ) k =0 where

lk P(k) = exp(- l) . ( 2.56 ) k!

7 Although a finite-bandwidth system would in theory have an infinitely wide time response, noise floors limit the time-domain response of the measurement system to a finite width.

30 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

The mean of the distribution l is the single parameter that needs to be characterized for this distribution.

The number of multipath components in a theoretical impulse response is limited only to the number of reflecting objects that induce multipath in the environment. In practical systems, multipath components may arrive at an antenna with a strength undetectable by the receiver. The count of multipath components is dependent upon the amplitude threshold selected. For measurements, this implies that the measurement system needs to have a sensitivity better than that of the target communication systems for which the measurements are being performed. This ensures that multipath components detectable by the target system will be detectable by the measurement system.

2.3.3 Fading Envelope

When an antenna element receives multipath components from a narrowband source, the envelope of the resultant signal will fluctuate in amplitude due to constructive and destructive combination of the narrowband signals. The time varying nature of the envelope is due to the motion of the receiver, transmitter, or reflectors in the environment. This motion causes minute frequency shifts (time varying phases of multipath components) known as Doppler shifts. The time-varying phase of each multipath component changes at different rates depending upon the directions of motion, and the resulting amplitude fluctuation is called fading.

A model developed by Clarke [Cla68] showed that a mobile receiver experiences Rayleigh fading when a large number of narrowband multipath components arrive with equal strength and from uniformly distributed angles in azimuth. Let the complex received signal envelope at a 8 single antenna element be r(t), and let the received signal envelope magnitude be re (t) , where

r(t) = re (t)exp( jf(t)). ( 2.57 )

The Rayleigh distribution for signal envelope fading [Cav00] is then given by

8 The magnitude of the complex envelope is frequently called simply the signal envelope. As such, re is used to represent this real-valued envelope.

31 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

r æ r 2 ö p (r ) = e expç- e ÷ , r ³ 0 , ( 2.58 ) Rayleigh e 2 ç 2 ÷ e s r è 2s r ø

2 where s r is the variance of r(t), which is the power in the composite signal. This distribution assumes that there is no dominant component incident on the antenna element; a dominant line- of-sight contribution disqualifies the Rayleigh distribution.

If a dominant signal component is present, then a Rician distribution is observed for the fading envelope [Cav00]. The dominant component is defined to have a power larger than the diffuse components by a factor of K. This factor is called the Rician K-factor, and if K=0, then Rayleigh fading results. The Rician probability density function is given by

r æ r 2K ö æ r 2 ö p (r ) = e I ç e ÷expç- e - K ÷ , r ³ 0 and K ³ 0 , ( 2.59 ) Rician e 2 0 ç ÷ ç 2 ÷ e s r è s r ø è 2s r ø

th where I 0 (×) denotes the modified 0 -order Bessel function of the first kind given by

1 p I y = exp y cost dt . 0 ( ) ò ( ) ( 2.60 ) 2p -p

The difference between the Rayleigh and Rician cases can be visualized using isoprobability contours for the complex signal r(t) shown in Figure 2-7. The Rician-fading signal consists of a specular component rs (t) and a zero-mean Gaussian diffuse component rd (t), and the composite signal is given by

r(t) = rs (t) + rd (t). ( 2.61 )

2 If the variance of the diffuse component is s r , then the magnitude of the specular component is given by

rs (t) = s r 2K . ( 2.62 )

The result is a nonzero mean that produces the offset in the isoprobability contours. Note that the phase of the composite signal is dependent on the relative amplitude between the specular

32 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS and diffuse components, and the phase distribution for the Rician case is no longer uniform like the Rayleigh case. Im{r} Rician …

… … … s 2K r … … … Re{r} Rayleigh …

Figure 2-7. Isoprobability contours for the composite complex signal envelope due to Rayleigh and Rician fading in a multipath environment.

2.3.4 Direction of Arrival

The direction of arrival of multipath around a receiver can be characterized in a way similar to that for multipath time delay. The concept of center of gravity and square root of the second central moment can be used for the angles of incident multipath components. Let angle fk be the azimuthal angle of arrival for the kth of K multipath components. The mean angle of arrival is compute using

K 2 åa k fk k =1 f = K , ( 2.63 ) 2 åa k k =1

th where a k is the voltage amplitude of the k multipath component. The angle spread of the multipath components [Ber02] is given by

K 2 2 åa k (fk - f ) k =1 s f = K . ( 2.64 ) 2 åa k k=1

33 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

This definition of angle spread is not the only one used by researchers. While in general, angle spread parameters are used to characterize spatial power distributions for arriving multipath, the metrics may vary. For example, the concept of excess delay spread can be adopted from time delay characterization and applied to direction of arrival characterization, whereby the angle spread is the widest difference in angle between two multipath components arriving with a power above a particular threshold.

Measurements have shown a high correlation between angle spread and delay spread [Mas00]. In both line-of-sight and non-line-of-sight environments, angle spread tends to increase with delay spread. The correlation coefficient between angle spread and delay spread computed from a set of measurements in a metropolitan environment was 0.7. As would be expected, angle

spread s f measured in non-line-of-sight environments is typically wider than angle spread measured in line-of-sight environments.

2.3.5 Signal Envelope Correlation Coefficient

Spatial separation of antenna elements causes fading due to multipath to be different at each element. The correlation coefficient computed for signal envelopes at pairs of antenna elements is a factor in determining the potential gains of using smart antennas. For example, appreciable

diversity gain is achieved when envelope correlation coefficients exceed 0.7 [Kit95]. If r1 (t) and

r2 (t) are the envelopes of received signals from two antenna elements, then the correlation

coefficient r12 can be computed directly using

t2 r t - r r t - r dt ò( 1 ( ) 1 )( 2 ( ) 2 ) t1 r12 = , ( 2.65 ) t2 t2 r t - r 2 dt r t - r 2 dt ò ( 1 ( ) 1 ) ò ( 2 ( ) 2 ) t1 t1 where

1 t2 r = r (t)dt , t > t ( 2.66 ) 1 t - t ò 1 2 1 2 1 t1

and

34 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

1 t2 r = r (t)dt , t > t . ( 2.67 ) 2 t - t ò 2 2 1 2 1 t1

When performing measurements in practice, the means r1 and r2 may be time-varying values

due to large-scale path loss changes and shadowing. As such, the values of t1 and t2 are chosen for a time period during which large scale path loss does not vary significantly but a long duration of signal fading due to multipath is observed.

2.4 Summary

The metrics of antenna array signal characteristics, including multipath delay, multipath strength, signal envelope fading, direction of arrival, and correlation coefficient, are fundamental concepts for measurement and modeling radio channels for antenna arrays. For measurements systems built on a digital signal processing platform, the actual implementations of processing routines to compute the referenced characteristics adhere closely to the definitions in theoretical discussions. Understanding these characteristics is important for analysis of algorithms, development of systems, interpretation of measurement results, and use of channel models based on measurements.

35 CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

This page intentionally left blank.

36 Chapter 3

A Multi-Channel, Software-Defined Measurement Receiver

In this chapter, the development of a new measurement receiver is described. The measurement receiver was built to serve channel measurement and radio test bed needs as they had arisen throughout the research presented in this dissertation. First, the motivation behind the architecture and methodology is discussed. Principles of the concept of software radio are emphasized. This chapter combines modern techniques from the fields of wireless communications and software development to describe a unique approach to receiver design. The hardware and software of the receiver are described, and the bases for major hardware and software design decisions are discussed. An example application of the measurement receiver is also presented.

3.1 Architecture Motivation

The wideband, multi-channel, software-defined measurement receiver (herein simply called the measurement receiver) was designed to meet the needs of performing measurements for modern communications systems. Early radio communications systems, such as narrowband analog and

37 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

digital wireless telephone networks, could rely largely upon single-channel signal envelope measurements or simple multipath delay characterization. As wireless communications technology enters an era of widespread use of complex antenna array algorithms and very wide bandwidth modulation to handle a growing number of high-data-rate users, a more advanced measurement receiver is required. The measurement receiver discussed here was developed to meet the requirements of current channel modeling and smart antenna research and was designed to be scalable for future needs.

The salient features that demonstrate the design to be a novel approach to measurement receiver architecture include:

· Software-defined radio functionality · Object-oriented, multi-threaded software implementation · Standardized internal communications interface · External signal data interface · Forward compatibility for algorithm development · Network support for external simulations

Software-defined functionality means that most of the functions performed by the receiver are executed in software that can be controlled and modified while the receiver is operating. Multi- threading allows several processing algorithms to operate on received signals in parallel. Object- oriented software implementation affords a programmer a template and interface for developing new radio modules. The measurement system’s internal communications interface controls the delivery of signal data to each of the processing modules and relieves the programmer of the responsibility of synchronizing data reading and writing events. The external signal data interface gives an engineer the ability to connect existing MATLAB or C simulations to actual radio signal data, providing a straightforward way to test simulations and processing algorithms in real world environments. The signal data collected by the measurement system is forward compatible in that the data is stored in a raw format that can be used by future processing algorithms; all signal information is preserved using this raw format. The measurement system supports supplying signal data to external simulations (simulations executed on another PC or

38 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

other processing platform) by providing a TCP/IP network interface for exporting data in real time.

3.2 The Software Radio Methodology

Widespread acceptance of the concept of a software-defined radio, frequently called simply a software radio9, began in the 1990s when digital signal processors were developed that could provide sufficient processing capability. Between 1990 and 2000, an abundance of technical articles appeared that began to define the characteristics, requirements, and applications of the nebulous software radio concept (e.g., [Bur00], [Erb98], [Lee00], [Mit93], [Mit95]). Because of the versatility and mutability of the software radio, no exact definition has ever been universally accepted and probably never will be. However, commonalities among definitions suggest that the following characteristics describe the core of the software radio concept:

· Definition and implementation of radio functions in software · Dynamic reconfigurability of processing at every layer of protocol stack at runtime · Placement of the A/D (or D/A) converter close to the antenna (i.e., minimization of hardware functionality between A/D or D/A and the antenna)

In a software radio, a majority of the radio functions are performed by some type of signal processor. The processor may use sequential instruction execution (in the case of a traditional digital signal processor integrated circuit), combinational logic (in the case of a programmable logic device or a field-programmable gate array), or a combination of both. In each case, the radio functionality is defined in a software radio by a program of instructions or logic gates that completely specify how the radio will operate on sampled signal data and how it will behave at all protocol layers. The programming of a software radio is reconfigurable as the radio is operating, allowing the radio to adapt to changing channel conditions or conform to communication standards with agile protocol characteristics. Placement of the A/D converter operationally close to the antenna is an indication that hardware functionality is minimized.

9 Some literature, for example [Wol00], distinguishes between “software radio” and “software-defined radio” by excluding radios that perform RF/IF frequency conversion from the class of “software radio.” However, in this dissertation, frequency conversion is considered to be signal conditioning, and hence “software radio” and “software-defined radio” are used interchangeably.

39 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

While in its purest form, a software radio would sample signals directly from the receiver antenna port without the aid of analog RF components, the use of a frequency down-conversion stage is generally an acceptable practice10 in software radio design [Bad00], [Dix01], [Mit95].

The fact that a that a radio employs digital techniques is not a sufficient condition for the radio to be considered software-defined. For example, while the phase-locked loop (PLL) of a receiver may be digitally controlled, the frequency channel selection would in actuality be implemented using the PLL hardware, which is only incidentally controlled by the digital portion of the receiver (supported by [Mit95]). However, a radio that samples an entire frequency band, crossing multiple frequency channels, and then extracts individual channels through software processing would be using software radio techniques for channelization.

3.2.1 Physical Architecture

The physical architecture of a practical software radio receiver can be represented by the block diagram shown in Figure 3-1. (adapted from [Bur00] and [Mit95]). The antenna is a hardware component required by all radio systems for receiving electromagnetic signals transmitted through the wireless channel. RF signal conditioning is performed on the received signals to produce a signal acceptable for the input of the A/D converter. Signal conditioning includes functions such as amplification, filtering, and frequency translation (frequency conversion). Generally, analog amplification is required to make the received signal span the desired number of amplitude levels of the A/D converter, and filtering is required to satisfy the Nyquist criterion based on the A/D converter sample rate.

10 The use of a frequency down-down conversion stage can improve radio performance compared to using direct sampling of high frequency signals. As discussed in [Bad00], A/D converters may become more limited in dynamic range at higher frequencies.

40 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Antenna

Processor RF Signal A/D Data and Conditioning Conversion Sink Software

Analog Digital Conditioning Processing

Figure 3-1. Block diagram of the major components of a practical software radio receiver.

3.2.2 Division of Hardware and Software

While functions of a radio can be classified as hardware or software, a sharp boundary does not exist to determine whether a radio is truly a software radio. Radios whose functionality is weighted heavily in the direction of software implementation, and yet implement some of their functionality hardware, may arguably be classified as software radios. In [Mit99], the continuum of radio classifications is represented in a phase space plot, illustrating the subspace of software radio as a function of the digital access bandwidth and the type of programmable hardware used. In order to further mitigate the opacity caused by the loose definition of software radio, an alternative representation is presented in Figure 3-2, which shows a plot that depicts the relationship between the type of functionality used for a radio and the degree to which it is used. Functionality that is purely implemented in hardware, such as the reception of signals by the antenna, is represented on the left side of the plot. Functionality that is purely software is represented on the right side of the plot. Many radio functions, such as filtering, fall in the center of the plot because the filtering operations performed in a particular radio might be performed in both hardware and software. This plot of radio functionality distribution can be viewed to aid in determining (albeit subjectively) the degree to which a radio is software-defined. Software- defined radios will be heavily weighted to the right of the plot, and legacy hardware radios will be heavily weighted to the left side of the plot.

41 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Legacy Radio

Software Radio Degree of Functionality

Pure Pure Hardware Digital Control Digital Processing Software Type of Functionality Antennas Adaptive processing Hardware Filters Software filters Mixers RF Sampling

Figure 3-2. Functionality distribution of software radios versus legacy radio methodology.

3.2.3 Benefits of the Methodology

While the favorable implications of software radio are often included in the definition, they often depend upon the application of the system and are therefore not truly inherent to software radio design; the implications are, however, worth noting ([Bur00], [Mit95], [Wol00], [Jon00]):

· Flexible operation of the radio and its subcomponents · Downloadable air interface (over-the-air or otherwise) · Multiple mode and air interface standard support · Programmable parameters at all protocol layers (e.g., RF bandwidth, modulation and coding scheme, radio resource and mobility management) · Reduction of hardware size, weight, and power consumption

These benefits form the foundation for the movement toward the use of software radio in user terminals and base stations alike. Technologists envisage the universal radio that will operate on any standard using any modulation and will be entirely defined by the software load. The

42 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

wideband measurement receiver developed for the research described here was designed using software radio methodology to take advantage of these benefits and to further develop the methodology itself.

3.3 The Measurement Receiver Concept

In order to provide an unambiguous vocabulary for the development of the receiver presented here, the term measurement receiver is defined. A measurement receiver is a radio receiver whose purpose is to measure the characteristics of received signals and the channels through which the signals propagate. A real-time measurement receiver produces signal data and channel results as measurements are performed and at a rate sufficient to characterize the time- varying nature of the signals and channels, specific to the characterization parameters used.

Unlike a communications receiver, which is typically required to receive and demodulate a continuous or regularly time-slotted signal, the processing in a measurement receiver may tolerate gaps in received signals without corrupting the desired measurement results. For example, while a communications receiver (operating on a continuously transmitted signal) is required to sample signals continuously at a rate that satisfies the Nyquist criterion in order to maintain a communications link, a measurement receiver designed to measure multipath delay characteristics only needs to acquire signal data at a rate determined by the change of channel conditions that affect multipath delay (the actual sampling instants would depend upon factors such as the coherence time of the channel and the physical propagation environment).

3.3.1 Processing Tradeoffs

The processing objectives of the measurement receiver allow the sampling continuity and timing requirements to be relaxed compared to that of the communications receiver, thereby permitting a tradeoff in resources that let the measurement receiver outperform the communications receiver in several regards.

Bandwidth: Because a measurement receiver may tolerate gaps in received signal data, the sample rate and bandwidth can generally be higher than that of a communications receiver employing the same processing platform. By buffering necessary data and

43 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

ignoring redundant data, a measurement receiver can allow bottleneck processing to perform at a rate slower than the sample rate.

Algorithm complexity: By retaining only the signal data that a processing algorithm needs and ignoring other signal data, a measurement receiver can devote more processing resources to accommodate algorithms with increased complexity.

Data storage requirements: The omission of unnecessary signal data reduces the capacity needed to store measurement data. Data often can be stored in its rawest, unprocessed form, while doing this with a communications receiver would require prohibitively large storage capacity.

Processing platform: For a software radio application of a given complexity, the processing speed and available resources of a processing platform can be reduced compared to that required for a communications receiver. This means that processing platform that is less powerful but more versatile and easier to program can be selected, in important consideration for measurement receiver test bed systems.

3.3.2 Examples and Applications

A simple example of a measurement receiver is a receiver that logs narrowband received signal strength data in order to gather fading statistics. At the expense of losing waveform shape and frequency spectrum data, the receiver can log data at a slower rate; instead of continuously sampling the signal faster than the Nyquist rate, the receiver can sample received power at a rate sufficient to compute the signal envelope for detailing fading characteristics.

Measurement receivers can also be well suited to act as test beds for new algorithms. Instead of computing received signal strength from a signal, a measurement receiver can be used to compute the performance gains resulting from algorithms programmed into the receiver. For example, the output of a measurement receiver could be diversity gain, computed from an antenna combining algorithm programmed into the receiver.

44 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

A measurement receiver exhibits high utility for testing new wideband measurement techniques or processing algorithms, where historically the wide bandwidth of the new measurements or the complexity of the new algorithms prohibits full-scale implementation on a real-time communications receiver. For example, in the early- to mid-1990s multipath characterization measurements were performed using bandwidths greater than 10 MHz [Bod97][Dev95][New97], resulting from the rule of thumb that wideband measurements are performed using a bandwidth of greater than ten times the communications signal bandwidth of the system for which the measurements are being performed; in the early 1990s, the frequency channel bandwidth of the IS-95-A cellular and J-STD-008 PCS systems was 1.25 MHz [IS95A][JSTD8]. This “ten-times- bandwidth” rule results in the need to measure channels using a bandwidth much wider than the radio test beds designed for the target communications system.

The concept of the measurement receiver is the basis for the receiver developed for this research. Wide bandwidth, raw data storage, and an easily programmed processing platform are characteristics of this receiver designed to accommodate testing of measurement and processing algorithms.

3.4 System Specifications and Analysis

In this section, the specifications for the measurement receiver are discussed, and link-budget and noise analyses are presented. The specifications are based on meeting the requirements of a wideband measurement receiver for propagation research and test bed for smart antenna array experiments.

3.4.1 Target Applications

Table 3-1 lists the target applications of the measurement receiver. The applications shown in the table require the RF section of the receiver to be multi-channel and wideband. Also, the variety of processing required for the applications suggest that a software-defined architecture should be used, enabling the receiver to execute multiple signal processing applications. The use of MATLAB and C++ interfaces is specified for the software radio test bed applications because high-level languages provide a more structured and easier way for designers to program radio algorithms; DSP development tools and software radio designers have moved in the direction of

45 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

using high-level programming languages over assembly language for software radio applications [Dix01].

Table 3-1. Target applications of measurement receiver. Application Category Specific Applications Channel measurement and modeling support · Multi-element antenna channel modeling · Power-delay profile measurements · Multipath delay statistics · Wideband signal envelope measurements Smart antenna research · Antenna diversity · Adaptive combining · Direction of arrival Wideband data collection · Multi-channel raw received signal samples · Processed data logging Software radio test bed · MATLAB interface for use with m-files · C code interface using C++ base class

3.4.2 Design Goals

Table 3-2 summarizes the high-level design goals for the overall system and its hardware and software. The hardware goals include minimizing the amount of RF and non-configurable components to give the receiver the greatest amount of flexibility. The bandwidth of the system is maximized to give the best time-domain resolution for multipath power-delay profile measurements with which multipath radio channels are characterized. Although the maximization of bandwidth results in higher noise power at the A/D converter input, it affords the largest flexibility in bandwidth control by allowing the software to control and implement filtering and channelization of the spectrum. The software goals include maximizing the radio processing functions performed in software to accommodate the minimization of functions performed in dedicated hardware. To take advantage of organized and maintainable programming techniques and parallel processing, the software uses an object-oriented and

46 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

multithreaded design methodology, described further in sections 3.6 and 3.7. The interface between the radio hardware and signal processing software of the measurement receiver is simplified by encapsulating the hardware interface software in classes to enable standard interface methods, also described further in section 3.6.

Table 3-2. High-level design goals for measurement receiver Overall design goal · Develop a multi-channel, wideband receiver whose functionality is primarily implemented in software Hardware design goals · Minimize functions performed by hardware · Minimize amount of RF hardware · Maximize bandwidth of sampled spectrum Software design goals · Maximize receiver functions performed by software · Apply an object-oriented, multithreaded approach to receiver design · Encapsulate hardware functionality so that software processes are largely independent of specific hardware receiver

3.4.3 RF Specifications

Table 3-3 lists the RF specifications for the measurement receiver. The center frequency of 2050 MHz was used to be able to compare measurements with other measurements performed by Virginia Tech at this frequency11. A bandwidth of 100 MHz is required to perform power-delay profile measurements with a multipath time delay resolution of 10 ns, an acceptable resolution for both indoor and outdoor channel sounding [New97]. The IF bandwidth was designed wider than the initially chosen RF bandwidth so that other RF filters could be used to select a wider

11 Virginia Tech has performed multiple narrowband experiments and measurements at 2050 MHz. Results from measurements and experiments at this frequency can be extended to nearby bands, such as the 1900 MHz U.S. PCS band and the 2.4 GHz unlicensed band.

47 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

bandwidth. Also, the wide IF bandwidth of 400 MHz allows the RF spectrum to be down- converted to a wide range of center frequencies selectable by the signal processing software. Four RF channels serve to acquire signals from a four element array; at the time of development, a four-channel, high speed A/D converter was available.

Table 3-3. Radio frequency (RF) specifications for measurement receiver. RF Parameter Value Primary center frequency 2050 MHz RF Bandwidth 100 MHz IF bandwidth accommodated (max RF BW) 400 MHz Number of RF channels 4 Dynamic range > 40 dB RF section input/output impedance 50 ohms

3.4.4 System Specifications

Table 3-4 shows the system specifications for the measurement receiver. The single-stage down- conversion architecture was chosen because it requires a minimal amount of RF hardware compared to down-conversion using more stages. Direct RF sampling was not specified because of bandwidth limitations of the A/D converter12, which would not sample frequency bands above 1 GHz. The four-channel A/D converter that was selected was used to sample each 400 MHz- wide channel at 1 Gsps. The A/D converter stored in memory continuous sequences of signal samples taken simultaneously from the four channels. These sequences of signal samples are defined to be snapshots of the received signal.

12 The A/D converter had a bandwidth of 1 GHz and a sample rate of 1 Gsample/sec per channel. The A/D converter could have been used for bandpass sampling for bands up to 1 GHz, but the band of interest for this measurement system was 2.05 GHz.

48 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Table 3-4. System specifications for measurement receiver. System Parameter Specification Frequency translation Single-stage down-conversion Sampling type IF sampling Intermediate Frequency 0.2 MHz to 400 MHz (selected by software) Sample rate 1 Gsample/sec per channel A/D converter resolution 8 bit Number of A/D converter channels 4 Signal snapshot record length (buffer size) 2 Msamples per channel

3.4.5 Link Analysis

A link analysis for the measurement system is shown in Table 3-5, in which the path loss and received power are computed for an outdoor channel. A line-of-sight (LOS) channel was used to determine the upper bound on the range of the measurement system. The log-distance path loss model was used with a path loss exponent of 2 to determine the LOS path loss. The link analysis results in the received power at the antenna ports of the receiver.

Table 3-5. Measurement system link analysis for outdoor radio channel (1 mile, line-of-sight).

Parameter Sub-Param Sub-P Sym Sub-P Val Symbol Value Units Comments Transmit Power Pt 28 dBm TX Amp ZHL-4240W Transmit Antenna Gain Gt 0 dB Receive Antenna Gain Gr 0 dB Path Loss (Log-Distance) Ref Dist do 1 m Frequency fo 2.05E+09 Hz Center of channel Ref Loss Lp(do) 38.7 dB Calculated for free space at ref distance PL Exponent n 2 2=free space, ~3.5 outdoor obs, ~5 indoor ofc Distance d 1610 m 1610m = 1mi Path Loss PL 102.81 dBm Receive Power (Ant Port) Pr -74.81 dBm

3.4.6 RF Section Analysis

Table 3-6 shows an analysis for the RF section of the measurement receiver. RF component specifications were used to determine the power at the input to the A/D converter block. The A/D converter block includes an internal, variable-gain amplifier that is not included in this table

49 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

because the amplifier is part of the automatic gain control (AGC) loop, which is assumed to be in a maximum gain state for the maximum range computations. This AGC loop is discussed in section 3.7. The A/D converter block required a sinusoid with a magnitude of approximately -30 dBm (into 50 ohms) to have all levels of the A/D converter spanned.

Table 3-6. Measurement receiver RF section analysis for outdoor radio channel.

Parameter Sub-Param Sub-P Sym Sub-P Val Symbol Value Units Comments Receive Power (Ant Port) Pr -74.81 dBm From Link Budget Antenna Cable Loss Lc1 2 dB RF Filter Loss Lrf 4.4 dB LARK SM-Series 0.2G-3G (fo=2.05G, 5%BW) RF Amp Gain Grf 25 dB ZHL-1042J, 10M-4.2G Mixer Loss Lm 6.7 dB ZEM-4300, L-R 300M-4.3G, I DC-1G IF Filter Loss Lif 0.6 dB LARK LHP-Series 60M-700M (fc=200M) IF Amp 1 Gain Gif 20 dB ZFL-500, 50K-500M IF Amp 2 Gain Gif 20 dB ZFL-500, 50K-500M Connector Loss Lcn 3 dB SMA A/D Input Power Pad -26.51 dBm

3.4.7 Noise Analysis

An analysis of system noise is shown in Table 3-7. The noise figure specifications for each component were used to compute an overall system noise temperature. The system noise power, referenced to the input of the RF amplifier, is approximately –88 dBm; this noise power is considerably higher than that of a conventional narrowband receiver because of the wide bandwidth of the measurement receiver. When using the measurement receiver to perform channel sounding measurements, a direct-sequence spread-spectrum signal is used, benefiting the receiver with a large amount of processing gain. For the case of a 2047-chip sequence run at a chip rate of 100 MHz and integrated over the entire sequence period at the receiver, a 33 dB processing gain is realized. The resulting signal to noise ratio, accounting for processing gain, is approximately 40 dB. The resulting power-delay profile would have a maximum theoretical signal-to-correlation-noise ratio (interval of discrimination) of approximately 66 dB.

50 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Table 3-7. System noise analysis and noise results for outdoor radio channel.

Parameter Sub-Param Sub-P Sym Sub-P Val Symbol Value Units Comments RF Amp NF NFrf 6 dB ZHL-1042J, 10M-4.2G IF Amp 1 NF NFif1 5.3 dB ZFL-500, 50K-500M IF Amp 2 NF NFif2 5.3 dB ZFL-500, 50K-500M Oscilloscope NF Nfo N/A dB Spec by accuracy, N/A since high RF/IFgain Receiver Noise Bandwidth B 1.00E+08 Hz 100MHz RF Filter, Filter 100 MHz IF in software System Noise Temperature Antenna Noise Temp Ta 100 K Estimate Ant Cable Noise Temp Tc 107 K Calc from loss RF Filter Noise Temp Tfrf 185 K Calc from loss RF Amp Noise Temp Trf 865 K 290(10^NFrf/10 - 1) Mixer Noise Temp Tm 228 K ZEM-4300, Calc from conv loss IF Amp 1 Noise Temp Tif1 693 K ZFL-500, 50K-500M, Calc from NF IF Amp 2 Noise Temp Tif2 693 K ZFL-500, 50K-500M, Calc from NF IF Filter Noise Temp Tfif 37 K Calc from loss O-scope Noise Temp To N/A K Spec by accuracy, N/A since high RF/IFgain Equ. T into RF Amp Tin 246 K Eq noise temp at input to RF Amp System Noise Temp Ts 1122 K At input to RF Amp Total Noise Power N -88.1 dBm At input to RF Amp (kTB*1000) Signal Power S -81.21 dBm At input to RF Amp (Pr-Lc1-Lrf) Signal to Noise Ratio SNR 6.89 dB Signal to thermal noise ratio Processing Gain PN Sequence Length l 2047 chips 11 bit shift reg Chip Rate Rc 1.00E+08 chips/sec Integration Period Ti 2.05E-05 sec 20.5us = 1 seq period for 2047 chips Chip Period Tc 1.00E-08 sec Processing Gain P 33.1 dB Int Period / Chip Period Despread Sig to Therm Noise SNRt 40.0 dB SNR + Proc Gain Despread Sig to Corr Noise SNRc 66.2 dB 20*log10(chip length)

Through this analysis, the maximum range for the system in an outdoor, LOS channel was determined to be approximately one mile (1.6 km). Other analyses were performed to demonstrate the performance of the system in an outdoor obstructed channel (n=3.5) and an indoor, non-LOS channel (n=5). These analyses assumed a path loss reference distance of one meter, indicating obstructions in close proximity to the antennas, and demonstrated the system to be usable to approximately 100 m in an obstructed outdoor channel and approximately 25 m in a severely obstructed indoor channel.

The specifications presented above were developed through an iterative process, with consideration placed on the measurement requirements, equipment availability, equipment cost, development time, and usability of the system (including portability and maintainability). The analysis demonstrates the theoretical feasibility of constructing the measurement receiver.

3.5 Measurement Receiver Hardware

The measurement receiver hardware consists of three sections: an RF front end, a sampling section, and a processing platform. Figure 3-3 illustrates a block diagram of the hardware. The purpose of the RF front end is to condition the signals for sampling by the sampling section. The

51 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

sampling section samples and stores snapshots of signals from the four RF front end channels simultaneously. A personal computer (PC) is used as the processing platform to acquire the samples from the sampling section and perform all of the software processing. The PC also logs signal data and displays processed results.

Antenna

ZEM-4300 L=6.7 dB RF IF Ch 1 Signal BPF LPF Acquisition LARK SM ZHL1042J (2) ZFL-500 LARK LHP Fo=2050MHz G=25dB G=20dB fc=400MHz Brf=100MHz NF=6dB NF=5.3dB L=0.6dB L=4.4dB Ch 2 . Multi-

. High-Speed Channel RAM PC ADC Vector Channel Antenna Ch 3 Data

ZEM-4300 L=6.7 dB RF IF Ch 4 Receiver BPF LPF Control LARK SM ZHL1042J (2) ZFL-500 LARK LHP Fo=2050MHz G=25dB G=20dB fc=400MHz TDS 580D Brf=100MHz NF=6dB NF=5.3dB L=0.6dB L=4.4dB

Figure 3-3. Block diagram of the measurement receiver hardware, including the RF hardware that performs a frequency translation to a band that can be sampled by the 1 gigasample/sec sampling section.

3.5.1 RF Front End

Each channel of the four-channel RF front end translates the 2000 MHz to 2100 MHz spectrum down to an IF below 400 MHz. The RF front end uses an RF filter with a 100 MHz bandwidth to select the desired reception band and reject the image band. The RF filter is intentionally located at the input of the RF amplifier, which is wide band and could be saturated if strong out- of-band signals exist at the measurement site. The mixer is driven by a 1900 MHz local oscillator, translating the 2050 MHz RF center frequency down to the 150 MHz IF center frequency. Two IF amplifiers are used to provide sufficient gain for the sampling section. The IF filter is a low pass filter with a 400 MHz cutoff frequency. The use of these wide low pass

52 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

filters allows the software algorithm designer to choose IF center frequencies other than 150 MHz (between approximately 0.2 MHz and 400 MHz)13, and only tuning of the local oscillator is then necessary.

3.5.2 Sampling Section

The four IF signals at the output of the RF front end are sampled at 1 gigasample per second. A Tektronix TDS 580 digital oscilloscope with extended memory serves as the sampling section. The sampled IF signals are stored in high-speed RAM buffer until acquired by the PC for processing. The data transfer rate between the sampling section and the PC is a maximum of 8 Mbyte/sec. This transfer rate necessitates the use of signal snapshots, which are acquired by the sampling section at each channel simultaneously and buffered before delivery to the PC. When the sampling section buffer is full and the PC is acquiring the signal data from the sampling section, the sampling section ignores subsequent incoming signals. This process allows the sampling bandwidth to be extremely high while using a practical data transfer rate and realizable processing platform. The RAM can buffer up to 8 Msamples of signal data (2 Msamples per channel).

All raw IF samples are acquired and logged by the PC. The PC uses an IEEE 488 GPIB (general purpose interface bus) card to communicate with the sampling section. More information about signal processing and communication between the PC and the sampling section are presented in section 3.7.

Performing IF sampling versus using in-phase and quadrature (I/Q) sampling allows the greatest flexibility in software processing while minimizing hardware requirements. When using IF sampling for the four channels, only four IF channels need to be sampled instead of eight quadrature baseband channels. This reduction in sampling channels is at the cost of a higher sampling rate and places the responsibility of a down-conversion stage on the software. Software modules perform the final filtering, automatic gain control (control of the final hardware amplification stage), and complex baseband down-conversion.

13 The 0.2 MHz restriction is due to the AC coupling cutoff of the sampling section and not the low pass filter frequency response.

53 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

3.5.3 Complete System

Figure 3-4 illustrates the RF front end assembly and the entire measurement receiver system. As shown in Figure 3-4 (a), eight-section tubular filters perform the hardware filtering operations. Wideband RF amplifiers allow the RF filters to be exchanged for filters covering other bands for future measurements. The mixers are driven by a common local oscillator through a signal splitter to maintain phase coherence among the channels. The amplifiers in the RF front end are powered by a 15 volt power bus supplied from a single point on the assembly. Figure 3-4 (b) shows the entire measurement receiver and a signal generator used to produce a test signal.

(a) (b)

Figure 3-4. (a) The RF front end of the four-channel receiver, showing the tubular filters and connectorized RF components. (b) The complete system, showing the oscilloscope used for sampling, a signal generator used for the local oscillator, and another signal generator used to generate a test signal.

The measurement system hardware provides a versatile channel measurement and test bed system. While most of the functionality of the measurement receiver is performed by software, and is therefore configurable, the RF components are connectorized and can be exchanged for other components to accommodate other center frequencies and bandwidths (up to 400 MHz wide).

3.6 Theory and Application of Object Orientation

In this section, a foundation for the object-orientated design of the measurement system software is presented. A knowledge of the concepts and terminology of object oriented programming is very helpful for understanding the measurement receiver software. The theory of object oriented

54 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

programming relevant to the development of the measurement receiver software and its processing modules is discussed.

3.6.1 Objects

Object-oriented programming is an organized approach to large-scale software development based on abstract data types, encapsulation, hierarchical organization, polymorphism, and a generic activation mechanism for message passing [p.21 Kri96]. In object-oriented programming, data members and functional methods are packaged into groups known as objects [p.2 Sul94]. An object is a metaphorical representation of entities that need to be abstracted into a programmatic context. Objects give programmers a way of defining the characteristics and actions of entities (physical or conceptual) using data members and methods, respectively. Stated similarly, “an object is a meaningful group of process requirements and data requirements.” [p.27 Sul94]

Objects consist of two components that allow them to store data and perform actions [p.22 Kri96]. Attributes form the static component of an object to store the object’s data, which describes the characteristics and state of that object. Attributes are the object’s variables, which are contextually sensitive. Methods form the dynamic component of an object, defining the behavioral and functional characteristics of the object. Methods are the functions belonging to the object that comprise all that an object can do. The data type of an object is called a class. A class combines the attributes and methods of an object into one package [p.21 Ent90]. Classes are used to define the attributes and methods of the objects they describe.

3.6.2 Object Orientation Concepts

The following five concepts of object-oriented programming are important to understanding the significance of applying object orientation to software radio applications:

Encapsulation: The hiding of the internal structure of an object, including its internal data and functions, is known as encapsulation [p.24 Kri96]. Encapsulation allows the designer to purposefully determine which components of the object should be exposed and which components should be hidden as the integral workings of the object.

55 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Programming can be greatly simplified and protected using encapsulation; for example, a large set of low level commands can be encapsulated by an object, and access to functional groups of those commands can be given to the programmer in the form of methods. In this way, a specific set and order of low level commands can be predefined and provided to the programmer, relieving the programmer of the responsibility of determining the correct set and order of commands to perform a particular task. Encapsulating benefits the programmer at the cost of reduced freedom to prod at low level operations, but transparent interfaces can be developed for objects where low level command manipulation is warranted.

Abstract data types: Abstraction is the act of representing something without including background or inessential detail [p.10 Gra94]. An abstract data type is an abstraction that encapsulates the components of a set of objects. Abstract data types are defined by the programmer rather than being specified in the particular programming language. The abstract data type defines both attributes and methods for objects, and hence the programmer can completely define the behavior of objects.

Hierarchical Organization (Inheritance): Classes of objects are organized in a hierarchical fashion, where one class can inherit the methods and attributes from other classes. If Class D (a derived class) is derived from Class B (a base class), then some or all of the methods and attributes of Class B can be made available for use by Class D. This allows derived classes to become more specific in their abstraction while maintaining commonality with the base class and other classes derived from the same base class. Inheritance provides a method of distinction between the general properties of an entity and the properties of a specific entity [p.21 Str91].

Polymorphism: Polymorphism allows selection between redundant methods or attributes using the context in which the methods or attributes are referred [p.70 Sul94]. This concept allows software modules to be developed separately and provides a mechanism for forward compatibility software. With polymorphism, calls to methods that do not yet exist can be handled, and those methods can be added or modified in the

56 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

future. Polymorphic references are resolved within a particular class hierarchy, allowing a base class to handle references that are not resolved in the derived classes, and permitting derived classes to override the methods and attributes in their own base classes.

Message-passing mechanism: Generically defined in the context of object-oriented programming, a message is a query given to an object that requests execution of one of the members of that object [p.23 Kri96]. A message consists of a selector and arguments, which specify which method should be called and the parameters to be passed to the method. Objects can use messages to perform an operation or to transfer information, between two objects or among multiple objects.14

3.6.3 Application of Object-Oriented Methods to Software Radios

The overhead of object-oriented design and programming makes object orientation appropriate only for large software systems. Because of the multifaceted complexity of software radio programming, it is a probable candidate for object orientation, especially if the software is developed by a group of programmers, or if the software is intended to be reusable and have a long life with multiple revisions. The following list summarizes the more important benefits of using object-oriented programming for software radio projects, adapted from the generic object orientation benefits [p.31 Gra94]:

· Classes designed for object-oriented software radios form a library of reusable modules that can be used by future projects, resulting in a reduction of redundant effort and an increase in development productivity. · As reusable software modules become mature through use, the quality and reliability of the modules increases, resulting in fewer software deficiencies and a more useable library of software radio blocks.

14 For generic object-oriented design, it is implied in [Kri96] that passing messages is the only method of communication among objects. However, in practice, programming languages such as C++ and development environments such as those using Microsoft Foundation Classes distinguish between calling of methods and passing of messages. Methods of an object can be called directly using the function name and associated parameters, while messages are received by an object’s message handler methods, which may call other methods of the object.

57 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

· Using object-oriented programming allows software radio modules to be developed independently or in parallel through inheritance. Developers can interface with functionally incomplete classes until such time in development or testing where the objects need to perform a required operation or provide required data. · The message passing mechanism of object orientation provides a straightforward interface to software modules and defines a clean break between modules for minimal coupling and interdependency. · Encapsulation inherent in object orientation naturally divides a complex programming task into manageable subtasks, increasing the likelihood of successful completion and yielding modules that are scalable for other projects of more or less complexity.

The benefits of object orientation come at the cost of planning time, development speed, and software overhead:

· Variable referencing and function calling are context-sensitive, requiring overhead embedded in the program [p.5 Sul94]. · Reliance on a compiler to be efficient in minimizing processor instruction cycles and occupied code space. · Increased effort required for planning, organization, and preparation at the beginning of the software development cycle. · Reduction in upfront development speed when attention is devoted to the architecture rather than signal processing functionality [p.5 Sul94].

As more functionality is integrated in to the software of radios, and as additional radio communication standards need to be handled by a single device, the size and complexity of software radio projects will continue to increase. Because of this trend, the benefits of object- oriented programming techniques will progressively outweigh the costs, an assertion supported by case studies of other large scale software applications and their migration to object technology [p.50 Gra94].

58 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

The applicability of object technology to the growing complexity of wireless communications is evidenced by emerging wireless architectures. In [Moe99], the network entities rather than internal radio entities are abstracted to objects. The same methodology applies, however, in that the functionality of a network object is encapsulated, and external entities are separated from the object’s workings and behavior. An interface is defined for use by outside objects and is the means by which communications occur. While [Moe99] defines objects to be wireless network nodes between which network traffic is passed, the measurement receiver described here defines objects to be radio modules between which signal data is passed. In another reference [Dav99], concepts of abstraction, encapsulation, messaging, and object-orientation in general are used in the communication architecture of a software radio to allow portability of software radio applications and dynamic instantiation of objects. In both references cited, object orientation is aimed at organizing the components of complex radio systems and facilitating scalable and maintainable architectures.

3.7 Measurement Receiver Software

The architecture of the measurement receiver software was designed in such a way as to allow implementation of a variety of radio applications. The functionality of the software can be broken into several stages as shown in Figure 3-1. This figure shows a data flow representation of the measurement receiver, where signal data is distributed and processed successively through the software modules, beginning at the hardware receiver object and ending at the user interface that displays processed results. In this section the following topics are covered to explain the measurement receiver software:

· Signal acquisition with the hardware-specific receiver object · Radio receiver and processing functions · Display/file interface functions · Multithreading and inter-object communications · Automatic gain control · Example of measurement receiver software application

59 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

The architecture described here, including the logical division of functionality into objects and the method of inter-object communications within a software radio, was originally developed for the research presented in this dissertation.

Receiver Hardware SW Receiver 1 SW Processor 1 Interface 1

Hardware- SW Receiver 2 SW Processor 1 Interface 2 . .

Specific . Receiver Object SW Receiver n SW Processor m Interface k

Signal Radio Receiver Processing Display/File Acquisition Hardware Software Functions Functions Functions

• DS-SS receiver • Narrowband receiver • Impulse responses • Diversity metrics • DOA displays • Channel characterization • Oscilloscope-based acquisition • Wideband diversity • Multi-channel PC acquisition card • Narrowband diversity • DOA algorithms

Figure 3-5. Flow of signal data through the processing of the measurement receiver software.

3.7.1 Signal Acquisition with the Hardware-Specific Receiver Object

The hardware-specific receiver object is responsible for communications between the external hardware and the measurement receiver software. Hardware configuration routines and signal acquisition functions are encapsulated by the receiver object in order to sever coupling between the radio processing objects and the RF hardware. This means that the processing objects can work independently and without knowledge of the type of RF hardware to which they are connected. To exploit the benefits of polymorphism, the hardware object is defined in a hierarchical class structure, and a standard set of interface methods are defined. These standard methods allow new hardware to replace old hardware without breaking code downstream in the data flow.

60 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Table 3-8. Description of the generic hardware-specific receiver object interface functions. Receiver · CReceiver(.) – This constructor (and derived-class constructors) sets up the Object initial state of the object and the hardware to which it is connected. Interface · Configure(.) – Sets the state of the receiver object based on the user’s Functions input. This method defines which configuration options are presented to the user based on the hardware type with which the class is associated. · Initialize(.) – Prepares the hardware by setting up the hardware with the desired configuration and confirming that hardware has been set up successfully. · GetSignal(.) – Retrieves raw signal data from the hardware, scales the data with calibration constants, and obtains the sample rate of the data snapshot.

The hierarchical relationships among the receiver object classes are illustrated in Figure 3-6. The CReceiver class handles the generic methods for all classes that are derived from CReceiver. CReceiver and CGpibDevice are abstract classes and therefore cannot be instantiated alone. The CGpibDevice class handles GPIB (IEEE-488) interface functions; the GPIB interface is used for communications with the oscilloscope that samples the IF channels. The CGpibDevice class handles opening the connection to the GPIB device, checking for errors, and managing GPIB addresses. Any GPIB device can use an object derived from this class for communications. The CTekScope class is derived from the CGpibDevice class and provides methods specific to interface with a Tektronix oscilloscope. The CTekScope class has been tested with the Tektronix TDS 580 and TDS 520 oscilloscopes. Specific routines for communicating with the TDS oscilloscopes are encapsulated in the CTekScope object and are far removed from the software radio processing code, relieving the signal processing programmer from the need to fully understand the hardware interface software. The measurement receiver software uses a pointer to a CReceiver object, so that through polymorphism any object of a class derived from CReceiver can be used transparently, and the correct methods for the appropriate class will be called.

61 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

CReceiver Handles generic methods for all receiver objects.

CGpibDevice Handles methods for GPIB devices.

CTekScope Handles methods for Tektronix devices.

Figure 3-6. Class hierarchy of hardware-specific receiver objects.

3.7.2 Radio Receiver and Processing Functions

The radio receiver and processing modules perform all of the signal processing on the acquired signal data. The modules exist in the form of objects in the measurement receiver, and multiple processing objects can be instantiated simultaneously to operate on data in parallel. Radio receiver functions are classified as operations that are performed on raw signal data at the modulation or waveform level. Processing functions are categorized as operations that require processed data to perform statistical characterization or symbol-level decoding. These objects together implement both simple and complex operations such as narrowband receivers, direct- sequence spread-spectrum receivers, channel characterization algorithms, and antenna diversity algorithms. Radio receiver functions and processing functions can be combined into a single object depending upon the complexity of the operations. Generally, functionally complex algorithms should be compartmentalized to facilitate design and maintenance of the software.

3.7.3 Display/File Interface Functions

After processing, the data generally needs to be displayed or stored to disk. The interface objects are responsible for this task, and multiple objects can operate on the same processed data. The interface objects take the processed data and display it on a graph or table, or alternatively the processed data can be stored to disk. Existing display interfaces include plots of power-delay profiles, histograms, cumulative distribution functions (CDFs), and frequency spectra. Displays also include tables of computed signal data (for example, received power). A data logging object has also been developed that stores raw IF samples, sample rates, time stamps, and calibration parameters to disk continuously as the measurement receiver is running.

62 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

3.7.4 Multithreading and Inter-Object Communications

Objects in the measurement receiver communicate through messaging and shared memory space. An illustration of the communication paths within the receiver software is shown in Figure 3-7. The RF hardware of the measurement receiver is represented by the box on the left side of the figure, and the display and storage media is represented by the boxes on the right side of the figure. In between these components is the software of the measurement receiver, with each oval representing an object or module of the system.

The operations of the entire system are either controlled or launched by the System Exe object at the top of the diagram. This object is responsible for accepting instructions from the user for configuring the receiver, launching processing objects, logging data to disk, and overall control of the measurement receiver. The System Exe object is the central point in the software through which all objects can communicate.

System Exe Display Hardware Channel Sounding Receiver Frequency Spectrum Hard Disk Playback Asynchronous Data Logging Messaging Matlab Applications

MATLAB

Figure 3-7. Relationships among the measurement system software modules and external interfaces.

63 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Each of the objects represented by the ovals in Figure 3-7 operates on signal data in an independent thread15. The usage of multiple threads offers several advantages [Coh98], namely,

Maximization of parallel processing: When a process needs to execute tasks that are independent activities, performance of the overall process can be improved by assigning tasks to different threads and executing the threads in parallel. This is especially true for tasks that involve a user interface or tasks that wait for events to occur.

Reduction of overall idle time: Separating tasks that consume idle time into separate threads reduces the amount of idle time consumed by the entire process. For example, a separate thread that waits for data due to relatively slow I/O (input/output) can be designed so that the whole process does not need to wait for the I/O to complete, as might be the case with a single-threaded process performing the same task.

Responsiveness: Separating the interface functions and processing functions yields a more responsive user interface. By doing this, a processing function that takes a long time to complete will not freeze user input functions or output displays.

Simplified design: A design can be simplified using multiple threads by assigning unique threads to independent and well defined tasks. The use of separate threads naturally modularizes the software into manageable portions.

Communication between the System Exe object and other objects shown in Figure 3-7 is performed using asynchronous messaging. Each object has message handler methods that respond to messages posted into the message queue of the measurement receiver software. These messages start and stop processing, alert objects new data that new data is ready, and send indexing parameters used as references for each processing object. Communications between the measurement receiver user interface and the objects is also performed using messaging.

15 A thread is a path of execution through software code. Each thread has its own call stack and register state independent from the rest, but all exist within the code and address space defined by the process that has launched the threads [Coh98].

64 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Before the measurement receiver is started, the Receiver object in Figure 3-7 is sent configuration information to set up the hardware. The receiver object configures the hardware and alerts the System Exe object that the hardware is ready to perform. While the measurement receiver is running, the Receiver object executes its primary responsibility of acquiring signal data from the receiver hardware. Signal data is acquired in snapshots up to two megasamples in length per channel, and the data is placed in memory space that is shared with the processing objects.

Synchronization of data reading and writing is an important consideration when shared memory space is used among multiple threads. A technique must be used in order to eliminate the possibility of one thread overwriting data space while another thread is reading the same data space. The measurement receiver software uses synchronization objects to handle data reading and writing by multiple objects (each managing an independent thread). The receiver object and the playback object are the source of the received signal data, and the processing objects are the recipients of the data. When the source objects are writing data, they first check the synchronization object to see if any processing object is reading data. If no object is reading data, then the source object locks out the common memory space from the processing objects using the synchronization object, and then the source object writes data to the memory space. Once done writing, the source object unlocks the memory. Processing objects follow a similar process, using the synchronization object to check if a source object is writing to the common memory space and only reading if no source object is writing. Processing objects that implement time-intensive algorithms can copy the data to local memory space to free the synchronization lock in a minimum amount of time.

3.7.5 Automatic Gain Control

Automatic gain control (AGC) is accomplished using a combination of hardware and software components. Figure 3-8 illustrates a block diagram of the AGC components, distributed between hardware and software sections. The AGC for each of the four measurement receiver channels is independent of those of the other channels.

65 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Final Amp Software Stage – Sampling Hardware Device Communications Adjustable AGC Radio From RF Gain Signal Level Signal Processing Front ADC Detection End RAM

Gain Adjustment Gain Factor Controller

Figure 3-8. Block diagram of hardware and software components of automatic gain control.

The Sampling Hardware block represents the digital oscilloscope in the current measurement receiver implementation. The oscilloscope has an internal amplifier that is used as the final gain stage in the analog signal path. This amplifier has an adjustable gain and is controllable from the communications port of the oscilloscope. While the hardware is responsible for the actual signal gain, the entire AGC algorithm is implemented in software (illustrated within the Software block in Figure 3-8).

The AGC signal level detection can respond to any computed value of the signal; for example, it can operate using values of signal power or peak amplitude. The gain adjustment factor is then used to scale the absolute gain of the final analog amplifier stage. The AGC software includes the option of throwing out snapshots that are far out of range before signal data is passed to the radio processing objects.

3.7.6 Example of Measurement Receiver Software Application

Presented here is an example radio application developed for the measurement receiver. The application is designed to measure multipath channel characteristics using the measurement receiver and a separate transmitter (see section 3.8 for information on the transmitter).

To detect individual multipath components, the measurement system transmitter transmits a BPSK-modulated PN sequence through the radio channel. The autocorrelation function of an m- length PN sequence produces a sharp peak having a width of two PN chips and an amplitude of

66 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

20log10(m) above the correlation noise (see [Jer92]). The receiver can implement a correlator to detect relative delays and amplitudes of individual multipath components that arrive at the receiver16.

Figure 3-9 illustrates a block diagram of the software algorithm used to measure power-delay profiles, which are plots of amplitude versus delay that represent channel impulse responses. This design improves upon analog sliding correlator measurement systems, which are limited in their ability to measure rapidly changing channels because of non-instantaneous sliding of PN codes [New97]. A problem arises when measuring dynamic channels where channel impulse responses change rapidly. Such is the case when the receiver or transmitter is moving quickly, when objects in the environment are in motion, or when the transmitter or receiver are moved through regions of intermittent shadowing. Errors in measurements result when the channel changes during a sweep of the analog sliding correlator, producing a power-delay profile that represents one channel at the beginning of the power-delay profile (short delays) and another channel at the end of that same profile (long delays). The system illustrated in Figure 3-9 performs a correlation on very short snapshots of signals (15 microseconds or less), and therefore does not suffer from this problem.

For each of the four receiver channels, the signal acquired from the ADC is filtered in software and split into two signals. Both signals are translated in frequency using a 150 MHz local oscillator (LO), with one of the LO signals shifted by 90 degrees. The translated signals are low- pass filtered and decimated to produce I and Q channel (quadrature) signals. The correlator correlates the received I and Q signals with the known PN sequence. From these two quadrature signals, profiles of the magnitude and phase representing the channel impulse response are produced. An example power-delay profile plot is shown in Figure 3-10. The phase plot must be interpreted to be valid only at points where multipath components exist17, and the phase values represent the phase of the multipath carrier relative to other arriving multipath components.

16 For detailed information on multipath channel measurements and channel measurement systems, see [New97]. 17 The phase values indicated on the plot between the multipath components is simply the phase of the composite noise between the components.

67 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Lowpass X Decimate Correlator IF in Filter I Power from IF 2 2) Delay LO Sqrt(I +Q Ch n Filter Profile 150 PN Sequence 90o Generator MHz Multipath ATAN2(Q,I) Component Q Lowpass Phase X Decimate Correlator Filter

Figure 3-9. Block diagram of the software module that measures the strength, delay, and phase of multipath components arriving at the receiver.

Figure 3-10. Power-delay profile (amplitude and phase) computed by measurement receiver.

The channel characterization software can run simultaneously with other processing modules, allowing comparison of receiver performance with radio channel conditions. By having a power-delay profile recorded at the time of an algorithm anomaly or failure (running in another processing object), the offending channel conditions that caused the failure can be observed.

68 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

3.8 FPGA-Based Transmitter

The measurement system transmitter produces a programmable test signal appropriate for the wideband propagation experiment being performed. The transmitter information source is based on a PLD (programmable logic device), and the transmitted data signal is programming on a PC and downloaded to the PLD. The output of the PLD modulates a 2050 MHz carrier; the amplified signal is transmitted by a single antenna. The transmitter transmits symbol at rates up to 80 Mbps.

3.8.1 Transmitter Hardware

The transmitter configuration illustrated in Figure 3-11 and Figure 3-12 produces a BPSK signal for channel characterization. The modulating signal is a pseudorandom binary sequence (PN sequence) having autocorrelation properties suitable for detection of individual multipath components occurring in radio channels [Jer92].

Monopole/ G = 30 dB Dipole Pout = 28 dBm

Oscillator X G BPF Signal Generator fo = 2050 MHz fc = 2050 MHz BW = 100 MHz Baseband Data PLD/FPGA

80 Mbps (Mcps)

Figure 3-11. Block diagram of the measurement system transmitter, including a PLD that is programmable to produce the data required for the particular experiment.

69 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Figure 3-12. Wideband transmitter used for generating BPSK-modulated signal.

3.8.2 Transmitter Verification

The plots in Figure 3-13 show a processed snapshot of the signal produced by the wideband transmitter; this plot is used to verify the modulation and data sequence content of the signal. The snapshot was acquired and demodulated using the measurement receiver. To produce the plots of in-phase and quadrature components, the measurement receiver performed a complex baseband down-conversion on the received signal. The plot of phase was produced using the I and Q components.

Symbol timing was acquired by detecting the edge transitions of the baseband signals. The constellation plot in Figure 3-14 shows the symbols and the decision boundary. The amplitudes of the I and Q channels were normalized using the same multiplier for each channel. The plot clearly shows that the transmitter is producing a BPSK signal. The phase rotation is simply due to the offset in phase between the transmitter local oscillator and the software receiver local oscillator and is of no significant consequence because that phase rotation can be detected and applied to either the decision boundary or the symbols. The plot in Figure 3-15 shows the received signal after symbol decisions have been made; the phase offset was applied to the decision boundary in this case.

70 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

I Component Relative Magnitude 1

0.5

0 Mag (V) -0.5

-1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -6 Q Component Relative Magnitude x 10 1

0.5

0 Mag (V) -0.5

-1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -6 Relative Phase of Received Signal x 10 4

2

0

Phase (rad) -2

-4 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) -6 x 10

Figure 3-13. Output of transmitter acquired with measurement receiver (in-phase component, quadrature component, and relative phase shown).

Received Symbol Constellation 1

0.8

0.6

0.4

0.2

0

Q component -0.2

-0.4

-0.6

-0.8

-1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 I component

Figure 3-14. Signal constellation as demodulated by measurement receiver (phase rotation of constellation has not been applied for illustration purposes; the diagonal dashed line indicates the decision boundary).

71 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

Regenerated Signal Produced by Transmitter 2

1.5

1

0.5

0

Symbol Value -0.5

-1

-1.5

-2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time (sec) -6 x 10

Figure 3-15. Transmitter signal acquired with measurement receiver after symbol decisions have been made.

The transmitter discussed here has been used for several channel measurement campaigns. A variety of PN sequences and chip rates in addition to those employed here for validation have been programmed into the transmitter during measurements. Chapter 5 presents a description and results of measurements.

3.9 Summary

This chapter has described the design and development of a wideband, multi-channel, real-time, software-defined measurement receiver. The measurement receiver has been successfully built, demonstrated, and used in the field for RF channel measurements. The measurement receiver has also served as a test bed for smart antenna algorithms and a wideband signal data collection system.

The measurement receiver can be programmed using MATLAB or C++. Since MATLAB is a widely used tool for simulating communication systems, the MATLAB interface capability of the measurement receiver provides a way to turn simulated processing algorithms into functional software radio modules to process actual received radio signals in real time. The modularity of the software facilitates managing the code for expansion to future software radio applications.

72 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

The minimization of functionality performed by the RF hardware permits the measurement receiver to be alterable for other frequency bands of interest. The receiver can process RF bandwidths up to 400 MHz, and center frequencies can be processed by modifying the mixer and RF filter in the single down-conversion stage.

The successful development and use of this measurement receiver validates its architecture for propagation measurement and radio test bed applications. The actual implementation of new software modules beyond the original design of the receiver and created by researchers in addition to the original developer supports the motivation for using an object-oriented, multi- threaded methodology.

73 CHAPTER 3 – A MULTI-CHANNEL, SOFTWARE-DEFINED MEASUREMENT RECEIVER

This page intentionally left blank.

74 Chapter 4

Multipath Channel Models for Antenna Arrays

This chapter presents research in the area of channel models for use in antenna array simulation and analysis. The chapter first reviews the purpose and methods of existing channel models, and then presents the development of new channel models. The channel models considered here provide information on delay, strength, and direction of multipath components. Sections 4.1 and 4.2 review the purpose and classification of channel models. Section 4.3 describes selected channel models that are widely accepted. In section 4.4, the general form of an ellipsoidal channel model is described.

Section 4.5 describes a new air-to-ground channel model in detail. First, equations that specify the air-to-ground model geometry are derived. Next, a theoretical probability density function for direction of arrival of multipath components is analytically derived. Finally, joint DOA- propagation time delay probability density functions are presented, and their implications are discussed.

75 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

4.1 The Purpose of Radio Channel Models

Channel models provide a means of simulating and analyzing radio channels. A channel model may perform the function of producing raw channel output, such as multipath strengths and delays, narrowband fading envelopes, and signal direction of arrival. A channel model may also be used as a component of a system simulation. In this case, statistics of the channel itself are not necessarily of interest, but a measure of the impact on the output of the system simulation is desired. Figure 4-1 illustrates the use of radio channel models.

Functional View Mean path loss, Measurements, Fading envelope, Geometry, Channel Multipath delays, Statistics, Model Direction of arrival, … Analytical expression, … System View Channel simulator

Transmitter Channel Model Receiver N M

Figure 4-1. Uses for channel models shown from the standpoints of functionality and system implementation.

As shown in Figure 4-1, the input to the channel model may consist of measurement results, geometry specifications, or signal statistics. The model may actually represent multiple, statistically correlated radio channels consisting of N channel inputs and M channel outputs. Such a channel model is called a vector channel model and describes the spatial and temporal characteristics of the radio channel [Ree02].

76 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

Table 4-1. Requirements of channel models versus radio access technology. Received Multipath Direction … power delay of Arrival

Narrowband Systems (e.g., AMPS)

Wideband Systems (e.g., IS-95)

Antenna Array Systems (e.g., GSM with antenna array)

Wideband Antenna Array Systems (e.g., IS-2000 with ant. array) Multiple-Input Multiple-Output Systems Other technologies, New receiver architectures (4G+)

Since the deployment of the analog AMPS cellular phone network in the early 1980s, modulation and signal processing techniques have become increasingly complex, and the transmitted bandpass signals have become wider in bandwidth. In addition, antenna array technology is finding its way into commercial wireless communications networks. Channel models need to accommodate these changes in radio access technologies. Table 4-1 lists a set of wireless technologies and the associated requirements placed on channel models. In the early days of cellular, modeling a received power using fading envelope provided much of the information required to simulate the 25 KHz-wide radio channel. With the introduction of IS-95 CDMA networks, which used rake receivers in base stations and mobile stations, channel models needed to provide information on the strength and delay of multipath components (temporal characteristics). As antenna arrays are incorporated into wireless systems, models must provide direction of arrival information (spatial characteristics). In order to simulate spatial filtering systems, a multipath radio channel model must not only produce multipath channel parameters18 but also direction of arrival information [Lib95]. Although an assumption can be made that

18 Multipath channel parameters include the strengths and delays of the individual multipath components that form a channel impulse response.

77 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS multipath components arrive along paths that are uniformly distributed in angle from 0 to 2p around the receiver [Par92], a model that accounts for the physical environment will produce more realistic results because the model is tied to the physical propagation processes in the environment. It is historically evident, through decades of publications, that the evolution of wireless systems requires the evolution of radio channel models.

4.2 Channel Model Classification

Channel models can be developed based on factors of measured data, propagation environment geometry, and analytical electromagnetic theory. Channel models can be placed into classifications of geometric and statistical [Ert99]:

· Geometric channel models are developed by characterizing a propagation environment with a particular geometrical layout. Geometric channel models define a particular region within which objects act as scatterers, causing multipath within the channel. Time delay and strength of multipath components are derived using the distances that multipath signals travel through the environment; properties of the scattering objects may also be considered. Geometric models may begin based entirely on geometry, and they may be tuned with measured data so that the models more accurately represent a particular environment.

· Statistical channel models use a statistical distribution of channel characteristics to represent the radio channel rather than using the physical geometry of the environment. Measurements may be used to characterize received power, propagation delay, and direction of arrival in order to produce the statistical distributions. Measurements can be made in new environments and frequency bands to determine the statistical characteristics of signal propagation, or else measurements in similar environments or nearby frequency bands may be used. In the absence of measurement data, statistical distributions are sometimes estimated or assumed.

Geometric channel models have the advantage of a physical tie to the channel environment; because of this, it may be easier to verify and understand the results and implications of channel

78 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS simulations. Geometric channel models are beneficial for producing results that do not tie the channel to any actual physical environment; for example, measurements made in an urban region to produce a statistical model may bind the results to the particular region in which the measurements were performed. Statistical models based on measurements are good if this environmental binding is desired, and measurements can be performed in multiple sub- environments to more accurately represent the entire propagation channel.

4.3 Existing Geometric Channel Models

This research focuses on geometric channel models because of their ability to produce spatial channel characteristics that are tied to the physical propagation environment. Simulations that represent the physical environment and that implement the geometry of the channel models are used to verify some of the analytical results derived in this chapter.

4.3.1 Multipath Channel Impulse Response

Multipath channels can be represented by the impulse response h(t) given in ( 4.1 ). The impulse response represents multiple paths within the radio channel with d(t) functions, and each multipath has an associated amplitude ai and delay ti. The parameter L is the number of signal components, including the LOS component (if one exists), in a given impulse response.

L-1 h(t) = åa id (t -t i ) ( 4.1 ) i=0

Equation ( 4.1 ) is a bandpass model, which accounts for multipath delays solely in terms of absolute time. Although phases shifts are in fact minute time delays, a more appropriate model that explicitly accounts for phase shifts and that is used as a complex baseband model is given in equation ( 4.2 ). In ( 4.2 ), the parameter fi represents the phase shift of individual multipath components due to the channel.

L-1 jfi h(t) = åa i e d (t -t i ) ( 4.2 ) i=0

79 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

The effect of direction of arrival of signal components and the receiving antenna radiation pattern can be taken into account with a slight variation of this model. In [Lu97], the radiation pattern is multiplied by the signal component amplitude coefficient, yielding

L-1 jfi h(t) = åai e d (t -t i )Fr (q i ,fi ) ( 4.3 ) i=0

where the signal component amplitude coefficients ai are the strengths that would be received if an isotropic antenna were used. The normalized field strength of the receiver antenna in the direction of qi and fi (azimuth and elevation angles) is specified by Fr (q i ,fi ). The relationship between the amplitude coefficients is given by

a i = ai Fr (q i ,fi ) ( 4.4 )

However, it must be understood that this expression implies that the antenna is part of the radio channel. In general, it is probably less confusing to separate channel effects from antenna effects.

Directionality of multipath components can also be taken into account using the following form of the baseband multipath channel impulse response (taken from [Oda00] with phase term

fi appended),

L-1 jfi h(t,q ) = åa i e d (q -q i )d (t -t i ) ( 4.5 ) i=0

th where q i represents the direction of arrival of the i signal component.

The impulse response accurately models a wireless channel but gives no means to statistically or analytically compute the parameters that determine the strengths, delays, and number of multipath components. Models discussed in the following sections are used to produce values for these channel defining parameters.

80 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

4.3.2 Geometrically Based Single-Bounce Elliptical Model

The geometrically based single-bounce elliptical (GBSBE) model is based entirely on geometry and provides a method of producing values of propagation delay, strength, and direction of arrival of multipath components [Lib95]. The model assumes that all multipath components arriving at the receiver undergo a single bounce between the transmitter and receiver. An object in the environment that caused the bounce is generically called a scatterer19. Because direction of arrival and direction of departure are modeled using GBSBE, the model can account for antenna radiation patterns at the transmitter and receiver.

The geometry for the GBSBE model is shown in Figure 4-2. In terrestrial wireless networks with relatively large transmitter-receiver separations, the vertical distribution of direction of arrival shows that multipath components arrive primarily along a horizontal plane oriented with the horizon [Par92]. As such, the GBSBE model uses a planar surface to model the propagation environment. The transmitter and receiver are located at points T(-f,0) and R(f,0), respectively.

The transmitter-receiver separation is therefore do = 2f, and the line-of-sight propagation delay is 8 to = do/c where c is the speed of light (3x10 m/s). A multipath component that arrives with propagation delay ti equal to a constant value (greater than the LOS delay) and resulting from a single bounce must have been produced by a scatterer S(xs,ys) located on an ellipse [Par89]. The defining parameters of the ellipse are

ct a = i ( 4.6 ) 2

b = a 2 - f 2 ( 4.7 )

where a defines the major axis of the ellipse and b defines the minor axis, and the scatterer

S(xs,ys) lies on the ellipse defined by

x 2 y 2 s + s = 1 ( 4.8 ) a 2 b 2

19 Although the object that caused the multipath is called a scatterer, the actual mechanism causing the multipath may be reflection, refraction, or scattering.

81 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

y b S(xs,ys)

T(-f,0) R(f,0) x -a -f f a

do = 2f

-b

Figure 4-2. Physical layout of the geometrically based single-bounce model.

If scatterers are uniformly distributed in space around the transmitter and receiver, then the single-bounce scatterers that induce a multipath delay between t and t + Dt would be bounded

by the ellipses E1 and E2 defined by

ct a = ( 4.9 ) 1 2

2 2 b1 = a1 - f ( 4.10 )

for ellipse E1, and

c(t + Dt ) a = ( 4.11 ) 2 2

2 2 b2 = a1 - f ( 4.12 )

for ellipse E2. The terms scattering region and scattering surface are herein used to describe the locus of scatterers that induce multipath components for a particular condition or constraint. In the case of GBSBE, the scattering surface for delays between t and t + Dt is the two- dimensional region outside of E1 and inside of E2. Note for a later discussion that both ellipses

82 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

E1 and E2 used in the derivation of the GBSBE model share common foci at x = ± f . Figure 4-3 illustrates these two ellipses.

y b2

b1

T(-f,0) R(f,0) f x -a2 -a1 -f f a1 a2

do = 2f

E t: -b1 1

Scattering Region E :t + Dt -b 2 2

Figure 4-3. Ellipses E1 and E2 that define scattering region between delays t and t+Dt for the GBSBE model.

As shown in Figure 4-3, the angle represented by f is defined such that f = 0 is in the direction from the receiver to the transmitter, and clockwise rotation about the receiver is a positive angle change. The range of f is defined to be -p £ f £ p . To simplify expressions, a parameter for

normalized multipath delay is introduced, ri, given by

ct i t i ri = = ( 4.13 ) d o t o

where to is the LOS propagation delay over distance do. For a particular multipath component i,

the parameter ri is the ratio of the propagation time for that multipath component to the line-of- sight propagation time.

Using the geometry described by equations ( 4.6 ) through ( 4.12 ), the cumulative distribution

function (CDF) for fi conditioned on the normalized multipath delay ri was shown in [Lib95] to be

83 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

ì 1 æ1- r cosf ö r 2 -1sin (- f )(1- r cosf ) ï cos-1 ç i ÷ - i i ç ÷ 2 2 -p £ f £ 0 ï 2p ri - cosf 2p r -1 (r - cosf ) ï è ø ( i ) i Ff r (f ri ) = í ( 4.14 ) ï 1 æ1- r cosf ö r 2 -1sin F(1- r cosf ) 0 £ f £ p ï1- cos-1ç i ÷ + i i ï 2p ç r - cosf ÷ 2 2 î è i ø 2p (ri -1)(ri - cosf )

Equation ( 4.14 ) gives the probability that a multipath component i arrives along direction of arrival between 0 and f .

By differentiating ( 4.14 ) with respect to f , the conditional probability density function (PDF) for direction of arrival was shown to be

3/ 2 (r 2 -1) (r 2 - 2r cosf +1) f f r = i i i -p £ f £ p ( 4.15 ) f r ( i ) 2 3 p (2ri -1)(ri - cosf )

The PDF for the normalized multipath delay is

2r 2 -1 f r (r) = 1 £ r < rm ( 4.16 ) b r 2 -1

where the parameter b is given by

2 b = rm rm -1 ( 4.17 )

and the parameter rm is the maximum value of the normalized multipath component delay given by

t m rm = ( 4.18 ) t o

The parameter tm is chosen to be the largest expected detectable multipath delay. The marginal PDF for the direction of arrival, without regard to time delay or multipath component strength, is given by

2 2 1 (rm -1) ff (f ) = 2 -p £ f £ p ( 4.19 ) 2pb (rm - cosf )

84 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

Finally, the joint PDF for direction of arrival and normalized multipath delay is

2(r 2 -1)(r 2 - 2r cosf +1) -p £ f £ p ff ,r (f,r) = 3 ( 4.20 ) pb(r - cosf ) 1 £ r < rm

To simulate the impulse response of a multipath channel using the GBSBE model, the CDF for r is calculated by integrating equation ( 4.16 ), resulting in

r r 2 -1 F (r) = 1 £ r < r ( 4.21 ) r b m

In order to use a uniformly distributed random variable u to produce values of r, the random

value u is set equal to Fr (r) , and the equation is solved for r. The result is

1 1 r = + 1+ 4b 2u 2 0 £ u £ 1 ( 4.22 ) i 2 2 i i

Using a uniformly distributed random number generator U(0,1) to produce ui , values of the normalized multipath delay ri can be produced with ( 4.22 ).

Given ri, the CDF for angle of arrival in equation ( 4.14 ) can be used to calculate a value for fi .

A uniformly distributed random variable u is set equal to Ff r (f ri ), and f is determined as a function of u. Unlike equation ( 4.21 ), whose functional inverse was easily obtainable, the functional inverse of ( 4.14 ) needs to be computed numerically. In [Lib95], numerical values were computed using a lookup table and linear interpolation.

In summary, the GBSBE model provides a way to produce channel impulse responses based on the geometry of the transmitter, receiver, and statistical location and number of scatterers in the propagation environment. As discussed in section 4.4, this model can be shown to be a special case of a constrained ellipsoidal model.

85 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

4.3.3 Geometrically Based Single-Bounce Circular Model

The geometrically based single-bounce circular (GBSBC) model was developed for application to the reverse link (mobile transmitter to base station receiver) of macro-cellular systems [Pet97]. It is assumed that plane waves arrive in the horizontal direction from scatterers in the cellular environment, and therefore DOA statistics are calculated only in azimuth. The scatterers in the environment are assumed to surround the mobile station within a circular boundary as shown in Figure 4-4.

S

d R T (MS) (BS) qmax r Scattering Region

Figure 4-4. Geometry for the geometrically based single-bounce circular model.

In Figure 4-4, the transmitter T (a mobile station) and receiver R (a base station) are separated by distance d. The circle of radius r defines the scattering region, which circumscribes all of the uniformly distributed scatterers. Each scatterer is assumed to be an omnidirectional re-radiating element, and each re-radiated plane wave is only influenced by one scatterer (i.e., single bounce).

The parameter qmax defines the largest deviation of direction of arrival from the line-of-sight

direction; therefore, the spread of direction of arrival is confined to a range of 2qmax, and qmax is given by

-1 æ r ö q max = sin ç ÷ ( 4.23 ) è d ø

The probability density function was derived in [Pet97] to be

86 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

2 2 2 2 ì2d cos(q ) d cos (q ) - d + r -1 æ r ö -1 æ r ö ï - sin ç ÷ £ q £ sin ç ÷ ï pr 2 è d ø è d ø fq (q ) = í , ( 4.24 ) ï 0 otherwise ï î

Figure 4-5 illustrates the probability density function for direction of arrival for three different radii of the scattering region.

Probability density function for DOA for GBSB macrocell model 0.7

0.6

0.5 r = 100 m T-R Separation d = 5 km 0.4 pdf 0.3 r = 300 m 0.2 r = 1000 m 0.1

0 -15 -10 -5 0 5 10 15 Direction of Arrival (deg)

Figure 4-5. Probability density function for direction of arrival for the GBSB macrocell model with d=5 km and r=100, 300, 1000 m.

Because this model is applied to macro-cellular environments, the distance d is typically large. For d >> r , where scatterers surround the mobile in close proximity, the spread of angles about the LOS direction (whether or not an actual propagation path exists) is confined to small angles. For small scattering regions, when the scattering region is only 2% of the T-R separation, multipath arrives along directions within a few degrees of the LOS direction. For scattering regions with a radius of 20% of the T-R separation, which is large for a macro-cellular environment, the spread of DOA is still within approximately 12 degrees of the LOS direction.

87 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

To simulate a channel with the GBSBC macrocell model, the location of L scatterers is generated within the scattering region. The power of the LOS component is computed using the log- distance path loss formula given by

æ d ö P = P -10nlogç o ÷ + G 0 + G (0) o ref ç ÷ r ( ) t ( 4.25 ) è d ref ø

where Pref is the reference power at distance do, n is the path loss exponent, and Gr and Gt are the receiver and transmitter antenna gains, which are a function of directions of arrival and departure, respectively. For each multipath component, the excess propagation delay is calculated based on the excess distance traveled compared to the LOS component. The path loss for each multipath component is computed using

æ d ö ç i ÷ Pi = Po -10nlogç ÷ - Lr + Gr (q a ) - Gr (0)+ Gt (q d )- Gt (0) ( 4.26 ) è d o ø

th where di is the distance traveled by the i multipath component, Lr is the reflection loss of each scatterer, and qa and qd are the directions of arrival and departure of each multipath component, respectively. Using this technique, the propagation delay, path loss, and DOA for multipath components between the mobile station transmitter and the base station receiver can be computed for each channel, and the process can be repeated for a plurality of multipath channels.

4.3.4 Elliptical Sub-Regions Model

Like the GBSBE model, the elliptical sub-regions model was developed based on physical propagation processes for testing and validating antenna array systems in multipath environments [Lu97]. The model is used to simulate multipath vector channels and accounts for large-scale and small-scale fading.

The elliptical sub-regions model uses the single-bounce assumption for scatterers, implying that each multipath component arriving at the receiver is reflected by a single scatterer. Instead of randomly distributing scatterers throughout a single bounding ellipse, where the transmitter and receiver are located at the foci, this model uses several, co-focused elliptical regions that correspond to intervals of excess delay. A maximum multipath excess delay tm is defined, and

88 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS the corresponding maximum-delay ellipse is formed. The area is then delimited into M sub- regions, and the ith sub-region corresponds to excess delays in the intervals of

éi -1 i ù t m , t m , i Î{1,2,L,M} ( 4.27 ) ëê M M ûú

The excess delay of each interval is given by

1 Dt = t ( 4.28 ) s M m

Figure 4-6 illustrates the model geometry. The transmitter and receiver are located at points T (- f ,0) and R( f ,0), respectively. The outermost ellipse is the boundary within which all scatterers must lie. A compound Poisson distribution is used to determine the number of scatterers within each of the M elliptical sub-regions. If pi is defined to be the probability that a multipath component results from a scatterer in the ith sub-region, causing an excess delay

between t = (i -1)Dt s and t = iDt s , then pi is given by

iDt s p = p(t )dt ( 4.29 ) i ò i-1 Dt ( ) s

where p(t ) is the probability density function for excess delay. If L is the Poisson parameter for the total number of scatterers, then the Poisson parameter for the ith sub-region is given by

L i = pi L ( 4.30 )

Once the number of scatterers is determined for each sub-region, the scatterers are uniformly distributed within each sub-region.

The arrival times of signal components are computed in [Lu97] using position vectors for the transmitter, receiver, and scatterers. The position vectors for the transmitter and receiver are xT th th and x R , and the position vector for the i scatterer is xi . The propagation delay due to the i scatterer is then given by

1 t = (x - x + x - x ) ( 4.31 ) i c R i i T

89 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

y b i=M

…

i=1 x -a T(-f,0) R(f,0) a

do = 2f

-b

Figure 4-6. Geometry for the elliptical sub-regions channel model.

If each scatterer is assumed to be a cluster of Ki reflecting points, then the composite signal component arriving at the receiver from the scatterer will be a sum of reflected signals. This provision allows a receiver to experience fading signal components in a mobile channel, which would be the case if the scattering cluster consists of reflecting points that produce signal components within the multipath delay resolution of the receiver. The delay time of the kth reflection within the ith scattering cluster is described by the inter-arrival exponential probability density function, given by

1 æ t -t ö ç i,k i,(k -1) ÷ , k Î 1,2,K, K p(t i,k t i,(k -1) ) = expç- ÷ { i } ( 4.32 ) t è t ø where t is the mean inter-arrival time, which is estimated using the spatial extent of the

reflections within the scattering cluster. The value t i,0 = t i is given by equation ( 4.31 ).

The CDF for direction of arrival q i (for the center of each cluster) is dependent upon the ellipticity of each bounding ellipse, given by

d e = , i Î{0,1,L, M} ( 4.33 ) i d + icDt

The CDF is expressed in [Lu97] as

90 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

2 q 1 i 1- e 2 F(q i e) = 1- 2ecost + e dt ( 4.34 ) C(e) ò-p 2e(1- ecost)2

The factor C(e) is chosen so that F(q i e) = 1 when q i = p .

Large-scale fading of multipath components is determined using the location of each scatterer. The total received power of the multipath component caused by the ith scatterer is given by

r G G l2 P P = h i R T t i i 2 n ( 4.35 ) (4p ) (x R - xi + xi - xT )

where hi is the effect of shadowing, GT and GR are the transmitter and receiver antenna gains, Pt is the transmit power, l is the wavelength, n is the path loss exponent (for the log-distance path

loss model), and ri is the scattering coefficient (r i = 1 for an ideal, lossless reflection). The

shadowing factor hi and the scattering coefficient ri are assumed to follow log-normal distributions.

Small-scale fading of multipath is determined by summing the signal components arriving from the ith cluster. In [Lu97], the components from all reflectors within a cluster are assumed to have the same amplitude. In this case, the (corrected) expression for each reflected component’s amplitude is

Pi a i,k = , k Î{1,2,K, K i } ( 4.36 ) K i

Finally, the impulse response of the channel as represented by the elliptical sub-regions model is given by

L Ki (T ) h(t;to ) = å FT (q i )åa k ,i exp(- j(2pf i,k to + fi,k ))d (t -t i,k )FR (q i ) ( 4.37 ) i=1 k =0

(T ) Note that this impulse response includes antenna pattern effects of the transmitter FT (q i ) and

(T ) th the receiver FR (q i ) , and q i is the angle from the transmitter to the i scattering cluster. The

91 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

frequency f i,k provides for any Doppler frequency due to the motion of the scatterers,

transmitter, or receiver; with a Doppler frequency given, the observation time is specified by to.

In conclusion, the elliptical sub-regions model provides another way to simulate multipath radio channels in a cluttered, micro-cellular environment where the transmitter and receiver are surrounded by multipath-causing scatterers.

4.3.5 Other Channel Models

Some geometric channel models that have been designed to fulfill a particular purpose are worth mentioning. Lee’s channel model was used to predict signal component correlation at an antenna array in a macro-cellular environment [Lee82]. The model uses N effective scatterers uniformly spaced around a ring about a mobile station (see Figure 4-7). Each effective scatterer represents the effect of several reflections from that scatterer.

BS MS

Figure 4-7. Base station and mobile station orientation for Lee's geometric model.

The signals reflected by each effective scatterer are summed at the base station and the correlation coefficient of signal envelopes is determined at pairs of antenna elements. Extensions to this model have been made, such as the one placing the ring of scatterers in angular motion about the mobile station to account for Doppler effects [Sta94].

Other models have been developed for the purpose of simulating urban environments, including the typical urban (TU) model and the bad urban (BU) model [Ert99]. The TU model simulates scatterers surrounding a mobile station as shown in Figure 4-8. Within 1 km of the mobile station, 120 scatterers are randomly distributed, and the mobile is moved along a distance of five

92 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS meters. Then the scatterers are oriented back in their initial position about the mobile, and a random phase is defined for each scatterer. The process repeats to simulate a mobile moving throughout an urban environment. Path loss is computed using the log-distance path loss model, and shadowing is computed using a log-normal distribution with standard deviations between 5 dB and 10 dB.

MS S Motion S d 5 m MS BS qmax S 1 km Scattering Region

Figure 4-8. Geometry of base station, mobile station, and scatterers for the typical urban model.

S S S

S Secondary Scattering Region MS S Motion

5 m S MS BS S 1 km Scattering Region

Figure 4-9. Geometry of base station, mobile station, and two scattering regions for the bad urban model.

93 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

The bad urban model augments a secondary scattering region to the typical urban model. The secondary scattering region is offset from the first by 45 degrees as shown in Figure 4-9. This secondary region provides for a harsher propagation environment: increased delay spread, wider angle spread, and lower signal covariance among antenna array elements.

Another urban channel model is presented in [Oda00] that adds the layout of streets and structures to a geometric channel model. The mobile is assumed to be at street level in an urban environment, as shown in Figure 4-10, and the model is used to analyze time of arrival and direction of arrival of multipath components. The model accounts for three types of propagation characteristics: 1) street-microcell propagation in the vicinity of the mobile station; 2) reflection and scattering in isolated areas; 3) macrocell propagation between the reflection areas and the base station.

Urban Streets Reflection Area

Street Microcell MS Propagation

Macrocell

Propagation

BS

Figure 4-10. Orientation of mobile station and base station among city streets for the urban street geometric model, indicating types of propagation.

The path loss for each type of propagation is computed and summed to obtain a composite path loss. Between the mobile station and the reflection area, LOS or non-LOS propagation may

occur, and the loss is represented by Lp1. The reflection loss experienced in the reflection area is

assigned Lp2; this is the difference in power that leaves the reflection area compared to that which

entered the reflection area. Along the macrocell propagation leg, Lp3 may be calculated using a model such as the early Hata model [Hat80]. Then, the overall path loss between the mobile station and base station is computed with

94 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

L p = L p1 + Lp2 + L p3 (dB) ( 4.38 )

The requirement for street geometry is both an advantage and a disadvantage. If the specific locations of stations are specified, the model will more accurately account for the physical propagation environment compared to the GBSBE model. If a more statistical result is desired, rather than results based on specific station locations, then the use of this model becomes more cumbersome because of the requirements of defining street geometry and specifying characteristics of the three types of propagation.

4.4 Three-Dimensional Ellipsoidal Channel Model

In macro-cellular systems, multipath components arrive primarily in the direction of the horizon [Par92] as stated earlier. However, for smaller cell sizes (micro- or pico-cellular systems) or for communication geometries other than terrestrial communications, a three-dimensional model provides results based on a more accurate representation of the physical environment. The GBSBE model relies on the fact that single-bounce multipath components with delays of a particular value must be caused by scatterers located on an ellipse. This premise, however, is valid when the transmitter, receiver, and scatterers lie on a common plane.

4.4.1 The Ellipsoidal Scattering Region

Now consider the general case where scatterers can lie anywhere in space around the transmitter and receiver. The geometric shape that describes the location of scatterers producing a constant multipath delay is now defined by an ellipsoid. A general ellipsoid surface, centered at the origin of a Cartesian axis, is defined by

z 2 y 2 x 2 + + = 1 ( 4.39 ) a 2 b 2 c 2

The general ellipsoid has axis lengths of 2a, 2b, and 2c. The ellipsoid that defines a constant- delay surface for multipath components has two equal axis lengths because of rotational symmetry about a line between the transmitter and receiver. Therefore, the ellipsoid equation becomes

95 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

z 2 y 2 x 2 + + = 1 ( 4.40 ) a 2 b 2 b 2 with a and b completely defining the ellipsoid. This ellipsoid is oriented so that the major axis on which the transmitter and receiver lie is oriented on the z-axis. The coordinates z = ± f where the transmitter and receiver are located are defined by

f = a 2 - b 2 ( 4.41 )

The geometry is illustrated in Figure 4-11. Because of the two common axis lengths, the cross section of the ellipsoid in the x-y plane is exactly circular.

In the simplest form, the ellipsoidal surface can be used as a boundary within which all scatterers that produce multipath components less than a particular delay must lie. In the absence of other scatterer location information, scatterers may be uniformly distributed within the ellipsoidal scattering volume and around the transmitter and receiver, as shown in Figure 4-12. The scatter locations can be assumed to be individual scatterers or clusters of scatterers, and signal component delay, strength, and direction of arrival at the receiver can be computed.

Without further refinement, the utility of this model is questionable because scatterers typically do not exist uniformly throughout all space surrounding a transmitter and receiver. However, by placing constraints on the allowable locations of scatterers within the ellipsoid, the model has the ability to represent real-world propagation geometries more accurately than two-dimensional geometric models.

4.4.2 Applications of the Bounded Ellipsoid

One application of this model is the simulation of air-to-ground radio channels, discussed in depth in section 4.5. For this case, the ellipsoid would be oriented such that one focus is located at the ground station, and the other focus is located at the airborne station. Clearly, the entire ellipsoid would not be filled with scatterers. Instead, the scatterers would lie on the intersection of the ground plane (on which the ground station is located) with the ellipsoidal volume. In the real world, the height of buildings may be considered negligible compared to the altitude of the

96 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS airborne station, and hence scatterers are located on a two-dimensional planar surface20. (Note that for low-altitude operations, building height could be taken into account by applying a finite thickness.)

x

y (b) z

z

x x (c) y (a)

Figure 4-11. Geometry of the ellipsoid (a=2, b=1) bounding surface for maximum multipath delay: (a) three- dimensional view, (b) top view, (c) side view.

Another application is the modeling of a cluttered urban environment consisting of tall structures, a street-level station, and an elevated base station. Consider Figure 4-13, where a base station antenna is located on a building or other structure. To model this case, the ellipsoidal scattering volume is truncated by upper and lower planar boundaries. The lower planar boundary is defined by the street level, and the upper planar boundary is defined by the

20 This planar assumption would be appropriate, for example, for aircraft flying at 7,500 feet when the tallest buildings are 500 feet. One could conceive of situations where the urban ellipsoidal model, discussed shortly, is more appropriate, such as when an aircraft flying along a low-altitude VFR corridor near an urban center at approximately building-top altitudes.

97 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS maximum building height (which may be higher or lower than the height of the elevated station). In this case, signal component direction of arrival at the receiver cannot be described simply by an azimuth angle; an elevation angle must also be used. The truncated ellipsoid model provides for this by allowing scatterers to lie throughout all possible locations of true scattering objects. This model would be useful for building-mounted, pole-top, or distributed antenna transceivers used in urban environments, where benefits of smart antennas could be used to solve the concerns of achieving large capacity, high data rates, and wide bandwidths in an environment cluttered in three dimensions.

1.5

1

0.5

z 0

-0.5

-1

-1.5 1 0.5 1 0 0 x -0.5 -1 -1 y

Figure 4-12. Locations of uniformly distributed scatterers throughout the ellipsoide bounding surface; transmitter and receiver are located at foci.

98 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

Maximum Building Height (Upper Planar Boundary)

Elevated Station

Ellipsoid Boundary Buildings, etc. Buildings, etc.

Street-Level Station

Street Level (Lower Planar Boundary)

Figure 4-13. An urban model based on the ellipsoidal geometry useful for three-dimensional direction of arrival simulation and analysis.

4.4.3 Axis Lengths and Normalized Excess Delay

The elliptical axis dimensions define the elliptical (two-dimensional) and ellipsoidal (three- dimensional) boundaries for the geometric channel models that use them, and they have a significant effect on the probability density function for direction of arrival. For example, if the axis dimensions are specified such that the ellipse or ellipsoid is largely circular or spherical, respectively, then the probability of components arriving from any particular direction is roughly equal when the bounding shape itself is very large. Such would be the case when the maximum excess delay is very large compared to the LOS propagation time between the transmitter and receiver.

A quantity called normalized excess delay is now defined to be the ratio of excess delay Dt to theoretical transmitter-receiver LOS propagation time t TR . The values of Dt/t TR range from 0 (corresponding to the LOS path) to infinity (or the maximum value detectable by the receiver

99 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

due to path loss over the excess propagation distance). A Dt/t TR value of 0.25 approximately corresponds to an excess delay of 1300 ns for a transmitter-receiver separation of 1 mile; values of this order were observed during the measurements presented in Chapter 5. Larger or smaller

Dt/t TR values may be used for more sensitive or less sensitive receivers, respectively. Ellipses for Dt/t TR equal to 0.05, 0.30, and 0.90 are shown in Figure 4-14. Note that larger Dt/t TR values correspond to more circular ellipses.

Ellipses for excess delay ratios 0.05, 0.3, and 0.9 2

1.5 Dt = 0.90 t TR 1 0.30 0.5 0.05

0 T R Minor Axis -0.5

-1

-1.5

-2 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Major axis

Figure 4-14. Scatterer distribution boundaries around transmitter and receiver for normalized excess delay of 0.05, 0.3, and 0.9.

The ratio of minor axis length to major axis length is related to normalized excess delay by

2 æ Dt ö ç +1÷ -1 b èt TR ø = ( 4.42 ) a Dt +1 t TR

This relationship is plotted in Figure 4-15 for Dt/t TR ranging from 0 to 1. As Dt/t TR approaches and exceeds unity (excess delay equal to LOS delay), the minor axis length

100 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

approaches the major axis length and the ellipse approaches circular. As Dt/t TR further increases, the receiver approaches the center of the ellipse (relative to the size of the ellipse) and the probability of components arriving in any sector around the receiver becomes approximately equal.

Ellipse minor/major axis ratio versus excess/absolute delay ratio 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1 Minor axis length / major (b/a) (meters/meter)

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Excess delay / absolute delay (Dt/t ) (sec/sec) TR

Figure 4-15. Ratio of minor to major axis of elliptical scatterer boundary versus normalized excess delay.

This ellipsoidal channel model may be applied to a variety of three-dimensional, single-bounce propagation environments. Two scenarios have been demonstrated here, but others can be conceived, possibly involving indoor channels which have attenuation functions that vary depending upon the direction vector of multipath component propagation. A specific case of the ellipsoidal channel model is presented in the next section, where the development of an air-to- ground channel model using the ellipsoidal geometry is discussed.

4.5 Geometric Air-to-Ground Ellipsoidal Channel Model

In this section a geometric, single-bounce, air-to-ground multipath channel model is developed. As described earlier, the geometry for the scattering region is the intersection of an ellipsoidal volume and a horizontal plane. The scatterers lie on the ground surface within this scattering

101 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS region, and all propagation legs between the airborne station and the ground station must be considered.

Figure 4-16 illustrates the air-to-ground model geometry. The ellipsoid is defined by the normalized excess delay, and all ground scatterers have negligible height compared to the aircraft altitude. The elevation angle from the horizon up to the aircraft is El, and the complementary angle down from the vertical direction is y. The distance from the ground station to a ground point directly under the airborne station is the range (the distance from the ground station to the airborne station is commonly called the slant range).

Airborne Station

Aircraft Ellipsoid Boundary Altitude (AGL) Slant Range y El

Ground Station

Scattering Region Ground Level (Planar Intersection) Range

Figure 4-16. Geometry, distance, and angle definitions for the geometric air-to-ground ellipsoidal model.

The air-to-ground geometry produces some challenges in modeling the channel. Note that existing channel models do not accurately represent the air-to-ground propagation environment:

· GBSBE model accounts for a planar scattering region but does not account for the shape of the scattering region or additional distance caused by airborne transmitter.

102 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

· GBSBC model accounts for the fact that the transmitter is not within the scattering region, but does not correctly model the scattering region for the air-to-ground environment. Also, excess distance caused by the airborne transmitter is not considered.

As such, this air-to-ground channel model was developed. First, the scattering region is derived and discussed. Then, computation of the model geometry and scattering points for simulation is presented. Finally, direction of arrival and time of arrival statistics are presented.

4.5.1 Analytical Specification of Scattering Region

The expression for a three-dimensional ellipsoid with a circular cross section in the x'-y' plane and elliptical cross sections in the x'-z' and y'-z' planes is given by equation ( 4.43 ),

(z¢ - z )2 (x¢)2 (y¢)2 o + + = 1 ( 4.43 ) a 2 b 2 b 2

where zo is the distance by which the ellipsoid is offset along the z'-axis (see Figure 4-11). The equation for a plane through the axis origin at an angle y to the x'-z' plane is given by

z¢ = mx¢ ( 4.44 )

where m is the slope of the plane given by

m = tan -1 (y ) ( 4.45 )

By setting zo = f in ( 4.43 ) where f is the focus distance of the ellipse, the plane given in ( 4.44 ) intercepts the ellipsoid through the focus and at angle y with respect to the major axis of the ellipsoid. The intersection of the plane and the ellipsoid projected onto the x-y axis can be expressed as

(mx¢ - f )2 (x¢)2 (y¢)2 + + = 1 ( 4.46 ) a 2 b 2 b 2

This equation can be expressed as a function of x' with

2 æ (mx¢ - f ) ö 2 y¢ = ± b 2 ç1- ÷ - (x¢) ( 4.47 ) ç 2 ÷ è a ø

103 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

Now an axis transformation is introduced to facilitate formation of the equation for the surface of ( 4.46 ) projected onto the plane of ( 4.44 ). The z'-axis and x'-axis are rotated about the y'-axis by angle y so that the new x-axis and y-axis lie in the plane of ( 4.44 ). A new y-axis is named but is equivalent to the old y'-axis. The x-coordinates are transformed to x'-coordinates through

x¢ = x cos(y ) ( 4.48 )

The new surface, which exactly represents the intersection surface of the ellipsoid and the plane, is given by

æ (xsiny - f )2 ö y = ± b 2 ç1- ÷ - x 2 cos2 (y ) ( 4.49 ) ç 2 ÷ è a ø

where a, b, and f are the parameters of the original ellipsoid. The domain of x for the ellipsoid on the original set of axes was - a £ x¢ £ a , but the domain of the x-coordinate for the surface described by ( 4.49 ) is bounded by

a 2 - f 2 a 2 - f 2 f - a 1+ f + a 1+ b 2 tan 2 (y ) b 2 tan 2 (y ) £ x £ ( 4.50 ) a 2 cos2 (y ) a 2 cos2 (y ) sin(y )+ sin (y )+ b 2 sin (y ) b 2 sin (y )

To simplify the analysis of the problem, the surface in ( 4.49 ) is shown to be an ellipse by expressing ( 4.49 ) in a form similar to that of ( 4.46 ), given by

(mxx - f )2 (xx)2 y 2 + + = 1 ( 4.51 ) a 2 b 2 b 2

where the parameter x = cos(y ) is introduced for simplification. Equation ( 4.51 ) can then be rearranged and equivalently expressed as

b 2 fm b 2 f 2 x 2 - 2 x + x (a 2 + b 2 m 2 ) x 2 (a 2 + b 2m 2 ) y 2 + = 1 ( 4.52 ) a 2b 2 b 2 x 2 (a 2 + b 2m 2 )

It is now desirable to equate the polynomial of x in the numerator of ( 4.52 ) with form shown in ( 4.53 ) to solve for the terms K and R,

104 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

b 2 fm b 2 f 2 x 2 - 2 x + = x 2 - 2Kx + K 2 + R ( 4.53 ) x(a 2 + b 2 m 2 ) x 2 (a 2 + b 2m 2 )

By equating polynomial coefficients, it can be shown that

b 2 fm K = ( 4.54 ) x (a 2 + b 2 m 2 ) and

b 2 f 2 R = - K 2 ( 4.55 ) x 2 (a 2 + b 2m 2 )

The denominator in ( 4.52 ) is then equated with

a 2b 2 D = ( 4.56 ) x 2 (a 2 + b 2 m 2 )

Using the parameters K, R, and D, the expression in ( 4.52 ) can be written as

x 2 - 2Kx + K 2 + R y 2 (x - K )2 + R y 2 + = + = 1 ( 4.57 ) D b 2 D b 2

Equation ( 4.57 ) can be rearranged into the form of an offset ellipse, given by

(x - K )2 y 2 + = 1 D - R æ R ö ( 4.58 ) b 2 ç1- ÷ è D ø

This ellipse must now be expressed with the defining terms of the original ellipsoid (a and b) and the major axis angle y. To do this, the terms K, R, and D are also expressed in terms of a, b, and y, given by

b 2 sin (y ) a 2 - b 2 K = ( 4.59 ) a 2 cos2 (y ) + b 2 sin 2 (y ) and

b 2 (a 2 - b 2 ) æ b 2 sin (y ) ö R = ç1- ÷ 2 2 2 2 ç 2 2 2 2 ÷ ( 4.60 ) a cos (y ) + b sin (y )è a cos (y )+ b sin (y )ø

105 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS and

a 2b 2 D = ( 4.61 ) a 2 cos2 (y )+ b 2 sin 2 (y )

With these parameters defined, the desired results are shown in Table 4-2, giving expressions for the surface over which randomly distributed scatterers are placed for the geometric air-to-ground ellipsoidal channel model.

Table 4-2. Equations that describe the intersection of a tilted, three-dimensional excess delay bounding volume and a planar surface containing scatterers.

Expressions for the Scattering Surface

2 2 (x - x p ) y Surface Equation 2 + 2 = 1 ( 4.62 ) a p b p

4 2 2 2 2 b æ (a - b )sin (y ) ö a = ç1+ ÷ Major Axis p 2 2 2 2 ç 2 2 2 2 ÷ ( 4.63 ) a cos (y )+ b sin (y )è a cos (y )+ b sin (y )ø

4 2 2 2 2 b æ (a - b )sin (y ) ö b = ç1+ ÷ Minor Axis p 2 ç 2 2 2 2 ÷ ( 4.64 ) a è a cos (y ) + b sin (y )ø

b 2 sin(y ) a 2 - b 2 Major Axis Offset x = ( 4.65 ) p a 2 cos2 (y ) + b 2 sin 2 (y )

2 2 Focus f p = a p - b p = x p ( 4.66 )

It is notable that one focus of the elliptical scattering surface lies on the axis origin; that is,

x p = f p . This can be shown by using the elliptical focus equation to find fp from ap and bp,

2 2 2 f p = a p - bp ( 4.67 )

and performing a substitution of ap and bp with equations ( 4.63 ) and ( 4.64 ). Simplifying the resulting expression demonstrates that

106 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

4 2 2 2 4 2 2 2 2 b æ (a - b )sin (y ) ö b æ (a - b )sin (y ) ö f = ç1+ ÷ - ç1+ ÷ p 2 2 2 2 ç 2 2 2 2 ÷ 2 ç 2 2 2 2 ÷ a cos (y )+ b sin (y )è a cos (y ) + b sin (y )ø a è a cos (y )+ b sin (y )ø

2 æ b 2 sin (y ) a 2 - b 2 ö = ç ÷ = x 2 ( 4.68 ) ç 2 2 2 2 ÷ p è a cos (y ) + b sin (y )ø

This equality has the important implication that ellipses that represent the scattering regions for arbitrary excess delays do not share a common center but do share one common focus. In contrast, for the GBSBE model, the scattering regions for arbitrary excess delays do share a common center and two common foci. This makes sense intuitively because for the GBSBE model, the foci of the planar ellipse correspond to the actual locations of the transmitter and receiver; however, for the geometric air-to-ground ellipsoidal model, one focus is the location of the ground station, but the other focus depends upon the shape of the ellipsoid.

4.5.2 Generating the Ellipsoid and Scatterers on the Rotated Axes

It is useful to have the ability to generate the oblique ellipsoidal surface and points on the surface for simulation of ellipsoidal-based channel models. Numerically producing the surface aids in generating scatterers for simulation and assists in verification of channel model geometry.

Consider an ellipsoidal surface for a particular normalized multipath delay ri. A given normalized multipath delay uniquely defines an ellipsoid in three dimensional space whose major and minor axes are determined using equations ( 4.13 ), ( 4.9 ), and ( 4.10 ). An equation for that ellipsoid is given by ( 4.43 ), where the ellipsoid is oriented along the z'-axis and whose one focus lies on the axis origin so that zo '= f . N number of points with coordinates xn ', yn ' , and z n ' can be generated for this ellipsoid and represented by matrix E x'y'z' given by

é x1 ' y1 ' z1 ' ù ê x ' y ' z 'ú E (r ) = ê 2 2 2 ú ( 4.69 ) x' y'z' i ê M M M ú ê ú ëxN ' y N ' z N 'û

107 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

In order to represent the oblique ellipsoid for the ellipsoid-planar intersection model, the ellipsoid is effectively rotated about the y'-axis such that (90o-y) is the elevation angle for the ellipsoid major axis. The rotation is used to place the transmitter and receiver in their respective positions on the x-z plane for the model. The rotation is performed by defining the unit vectors for a new coordinate system given by

uˆ x = cosyuˆ x' + sin yuˆ z' ( 4.70 )

uˆ y = uˆ y' ( 4.71 )

uˆ z = -sinyuˆ x' + cosyuˆ z' ( 4.72 )

where y defines the angle between the x-axis and the major axis of the ellipsoid, and uˆ x' , uˆ y' , and uˆ z' are the orthonormal unit vectors that define the x'-y'-z' coordinate system (before rotation). The vectors uˆ x , uˆ y , and uˆ z are the orthonormal unit vectors for the coordinate system rotated by y about the y'-axis. Figure 4-17 illustrates the orientation of the axes.

1

uˆ z' 0.5 uˆ z uˆ x

uˆ y' 0 y uˆ x' uˆ y

1 1 0.5 0.5 0 0

Figure 4-17. Unit vectors that define the axes for the ellipsoid model geometry.

108 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

For convenience, the unit vectors are represented in a matrix form expressed by

éu x,(x) u y,(x) u z,( x) ù écosy 0 - sin y ù ê ú U = u u u = ê 0 1 0 ú ê x,( y) y,( y) z,( y) ú ê ú ( 4.73 ) ê ú ê ú ëu x,( z) u y,( z) u z,(z) û ësiny 0 cosy û

In this form, the unit vectors can be used to transform the points of given by ( 4.69 ) into the

points on the oblique ellipsoidal surface E xyz using

é x1 y1 z1 ù é x1 ' y1 ' z1 ' ù ê ú ê úéu x,( x) u y,( x) u z,(x) ù x2 y2 z2 x2 ' y2 ' z 2 ' ê ú E (r ) = ê ú = ê ú u u u ( 4.74 ) xyz i ê M M M ú ê M M M úê x,( y) y,( y) z,( y) ú ê ú ê ú ê úëu x,(z) u y,(z) u z,( z) û ëxN y N z N û ëx N ' y N ' z N 'û

Simply expressed, this rotation of the is performed with

E xyz (ri ) = E x'y'z' (ri )U ( 4.75 )

Using equation ( 4.13 ), a set of points uniformly spaced along the z'-axis was generated to

represent scatterers falling on an ellipsoid defined by a normalized multipath delays ri = 1.15. The elevation angle was set to 30o so that y = 60o. Using ( 4.73 ) and ( 4.75 ), the constant-delay scattering points were rotated to produce the ellipsoidal surface illustrated in Figure 4-18. A z=0 plane is also illustrated to show the horizontal ground scattering constraint. The theoretical scattering region boundary derived in the previous section and expressed by equations ( 4.62 ) through ( 4.66 ) is shown by the dark line on the horizontal plane. The figure demonstrates the accurate representation of the scattering surface calculated using ( 4.62 ) through ( 4.66 ).

Equations ( 4.70 ) through ( 4.75 ) are useful for transforming scattering regions or simulated scatterers into locations that fit the configuration of the physical environment. Also, for other ellipsoidal model applications other than the air-to-ground model, these equations will prove useful where the scattering region is a volume rather than a planar surface.

109 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

(a) (b)

(c) (d)

(e)

Figure 4-18. Views of the ellipsoid, ground plane, and scattering region: (a) The oblique view shows the overall geometry of the model and the ellipse outlining the scattering region, (b) The end view shows the y- axis width of the scattering region, (c) The side view shows the x-length of the scattering region which is clearly dependent upon the major axis elevation angle, (d) The top view shows the perfectly elliptical shape of the scattering region, (e) The ground-bounded view limits the ellipsoid to z<0 to show that the analytical scattering region exactly matches the ground-ellipsoid intersection.

110 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

4.5.3 Direction-of-Arrival Statistics

Using the equations derived in section 4.5.1, expressions that statistically describe the direction of arrival (DOA) can be derived. One would suspect that since the scattering surface is exactly elliptical, the results would mimic those derived for the GBSBE model in [Lib95]. Although some of the elliptical channel model work in [Lib95] can be advantageously used, the overall geometry of the three-dimensional environment described here is fundamentally different in that the transmitter and receiver do not lie on the foci of the scattering surface as required by the GBSBE model. For the GBSBE model to apply directly, the ellipses corresponding to the same transmitter/receiver locations but different delays must have the same foci locations.

Since the scatterers for this model are uniformly distributed throughout an elliptical, planar region, the marginal probability density function for direction of arrival will take the same functional form as that of the GBSBE model21. However, rather than a direct dependency on the

maximum normalized multipath delay rm, the probability density function will be dependent

upon the scattering region parameters, namely ap and bp. The function of ap and bp, defined to be g(ap,bp), must be determined so that the following equation, which has the form of equation ( 4.19 ), is satisfied:

2 2 1 (g (a p ,bp )-1) ff (f ) = 2 -p £ f £ p ( 4.76 ) 2pb (g(a p ,bp )- cosf )

To solve for g(a,b), the maximum normalized multipath delay must be expressed in terms of ap

and bp, as shown in ( 4.77 ).

ct m t o + Dt m d o + Dd m a p rm = = = = ( 4.77 ) d t d 2 2 o o o a p - bp

Therefore, g(ap,bp) is given by

21 This equivalence between the GBSBE model and the air-to-ground model is only true for direction of arrival since the distance traveled from the transmitter to the receiver does not affect the DOA PDF. Only the locations of the scatterers around the receiver affect the DOA PDF, and given the same dimensions of a ground-level ellipse, the distribution of scatterers around a receiver for the GBSBE model is the same as that for the air-to-ground model.

111 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

a p g(a p ,b p ) = 2 2 ( 4.78 ) a p - b p

and from ( 4.17 ) and ( 4.77 ), an expression that relates b to ap and bp is shown to be

1 é 2 ù 2 2 a p a p b = g(a p ,bp ) g (a p ,bp )-1 = ê -1ú ( 4.79 ) 2 2 a 2 - b 2 a p - bp ëê p p ûú

By combining ( 4.76 ) and ( 4.78 ), the marginal probability density function for the distribution of direction of arrival around the ground-based receiver is shown to be

æ a 2 ö ç p -1÷ ç 2 2 ÷ 1 a p - b p f (f ) = è ø f 2pb 2 ( 4.80 ) æ a ö ç p - cosf ÷ ç 2 2 ÷ ç a - b ÷ è p p ø

Using ( 4.62 ) through ( 4.66 ), ap and bp can be derived for the particular model geometry and used as parameters of ( 4.80 ).

This probability density function has been verified using simulation. The receiver is defined to be the ground station on the intersecting plane and on the lower focus of the tilted ellipsoid, and the transmitter is defined to be the airborne station on the elevated focus of the ellipsoid. For the simulation, scatterers were uniformly distributed on the scattering surface, and the direction of arrival for signals inbound to the receiver was computed for each scatterer. The scattering

surface was calculated using a maximum normalized multipath value of rm = 1.15. A histogram for direction of arrival was created, and the bin values were normalized so that histogram contained unit area over angles of –180o to 180o DOA. The points for the normalized histogram and the probability density function given in ( 4.80 ) computed over angles of –180o to 180o were both plotted as shown in Figure 4-19.

112 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

Marginal PDF of DOA for Ellipsoidal-Plane Intersection Model

1 y = 80o (El = 10o) f 0.8

0.6

y = 30o 0.4 (El = 60o)

Probability Density Function f 0.2

0 -150 -100 -50 0 50 100 150 Direction of arrival f (deg)

Figure 4-19. Marginal probability density function of direction of arrival for y=30 and y=80.

The “x” symbols in Figure 4-19 are the normalized histogram points, and the solid lines represent the analytically derived marginal PDF for DOA. The PDF was computed for the cases where the ellipsoid tilt angle y was 30o and 80o. An elevation angle for the ellipsoid is also tagged to each curve, where elevation angle is defined by

El = 90o -y 0o £ El £ 90o , 0o £ y £ 90o ( 4.81 )

The simulation shows the results of ten-thousand scatterers distributed on the scattering surface. The results show that the analytical expression in ( 4.80 ) accurately follows the results of the simulation.

The direction of arrival statistics derived from the model yield insight into the physical channel. Specific trends are still being investigated, but the following general statements should be noted:

· As tilt angle y decreases (or equivalently as elevation angle El increases), the distribution of DOA approaches a uniform distribution.

113 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

· As tilt angle y increases (or equivalently as elevation angle El decreases), the distribution of DOA shows that significantly more multipath components arrive in the direction of the transmitter (f = 0). · At tilt angle y = 90o (or equivalently El = 0o), the marginal PDF for DOA equals that of the two-dimensional GBSBE model using the same major and minor axis dimensions. This is an expected result since the GBSBE model is a special case of this ellipsoidal model with y = 90o.

Although the physical geometry and interpretation of results is different, this simulation result mathematically validates the marginal probability density function for DOA given by the

GBSBE model presented in [Lib95] when ap and bp are used as dimensions of a and b for the GBSBE input parameters.

4.5.4 Joint Direction-of-Arrival and Time-Delay Statistics

In this section the direction of arrival and propagation time delay joint probability density function is investigated. Simulation results for the DOA and time delay marginal probability density functions are also presented. Of particular interest are the trends of DOA and time delay as elevation angle is varied. In order to begin, the following points in three-dimensional space have been defined. These definitions facilitate representing the system in simulation.

T = location of transmitter = (xT, 0, zT) = xT uˆ x + zT uˆ z ( 4.82 )

R = location of receiver = (0, 0, 0) = 0 ( 4.83 )

th Si = location of i scatterer = (xS, yS, 0) = xS uˆ x + y S uˆ y ( 4.84 )

T is the location of the transmitter and R is the location of the receiver; the transmitter is located on the x-z plane and the receiver is located at the origin of the coordinate system. Each scatterer has coordinates Si and is located on the x-y plane within the scattering surface (i.e., within the ellipse in the x-y plane). Coordinates of Si, namely xS and yS, are uniformly distributed within

114 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS the bounds of the scattering surface. Using these points, the following spatial vectors are defined to represent the relative positions of the transmitter, receiver, and scatterer.

v TSi = S i - T ( 4.85 )

v SiR = R - Si ( 4.86 )

The vector v TSi points from the transmitter to scatter i, and the vector v SiR points from scatterer i to the receiver. Using these vectors, the relative delay of each multipath component can be calculated using

v TSi + v SiR v TSi + v SiR ri = = ( 4.87 ) 2 2 d o 2 a - b and the direction of arrival can be calculated using

fi = arctan2 (Si ×uˆ y , S i × uˆ x) ( 4.88 )

Where arctan2(y, x) is the inverse tangent function that returns the angle in the appropriate quadrant given the signs of x and y parameter, where the angle ranges from – p to p radians.

Sample joint probability density functions for ri and fi are shown in Figure 4-20. These joint PDFs were computed for elevation angles El of 0o (transmitter rotated down to x-axis, on the x-y plane with the receiver), 12o, 20o, 30o, 60o, and 90o (transmitter rotated up to z-axis, directly above the receiver). These PDFs correspond to a maximum relative multipath delay of 1.15.

· Low elevation angles – The plots for El = 0o and El = 12o demonstrate the multipath characteristics for an airborne transmitter on the ground or barely above the horizon in angle. The joint PDF plots show a spike at low normalized delay and small DOA angles. This spike indicates that multipath arrives primarily from the direction of the transmitter and with relatively low normalized multipath delay. For increasing normalized delays, the distribution shows a tendency for multipath components to arrive along directions on either side of line-of-sight from the transmitter. As delay increases to the maximum delay, the distribution flattens in the DOA dimension, indicating that the spread of

115 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

multipath DOA widens and off-LOS angles are more probable. The results for El = 0o correspond to the special case when the ellipsoid axes a and b are equal to the scattering

surface axes ap and bp, and these results corroborate the analytical results for the joint DOA-delay statistics plotted in [Lib95].

· Moderate elevation angles – The plots for El = 20o, El = 30o, and El = 60o demonstrate multipath characteristics from a transmitter at elevation angles significantly above the horizon and significantly down from vertical. The joint PDF plots show broadening in the DOA dimension indicating a wider spread of DOA at the receiver. As elevation angle increases, the probability of longer multipath delays increases relative to that of shorter delays. This shift of probability corresponds to the scattering surface becoming more circular as the elevation angle increases for a constant normalized multipath delay.

· High elevation angles – The plot for El = 90o is representative of DOA-delay distributions when the transmitter is nearly directly overhead the receiver. The flattening in the DOA dimension indicates that multipath components arrive from all directions around the receiver with equal probability. The steady increase in the distribution in the delay dimension is caused by the circular shape of the scattering surface which grows in all directions with increasing normalized delay for El = 90o.

For further clarity on the multipath component direction and delay statistics, Figure 4-21 illustrates the marginal probability density functions for direction of arrival and time delay of arrival.

116 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

El = 0o El = 12o

Normalized Delay r Normalized Delay r

DOA (deg) DOA (deg)

o El = 20 El = 30o

Normalized Delay r Normalized Delay r

DOA (deg) DOA (deg)

El = 60o

El = 90o

Normalized Delay r Normalized Delay r

DOA (deg) DOA (deg)

Figure 4-20. Joint probability density functions for direction of arrival and normalized multipath delay for several elevation angles El.

117 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

Direction of Arrival Marginal PDF Direction of Arrival Marginal PDF

1 1 0.8 o 0.8 El = 0o El = 12 0.6 0.6 0.4 0.4 0.2 0.2 0 0 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 DOA (deg) DOA (deg) Propagation Delay Marginal PDF Propagation Delay Marginal PDF 8 25

20 6 o 15 o El = 12 El = 0 4 10 2 5

0 0 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.02 1.04 1.06 1.08 1.1 1.12 1.14 Normalized Multipath Delay r Normalized Multipath Delay r

Direction of Arrival Marginal PDF Direction of Arrival Marginal PDF

0.15 0.6 El = 30o

0.1 0.4 El = 90o

0.2 0.05

0 0 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 DOA (deg) DOA (deg) Propagation Delay Marginal PDF Propagation Delay Marginal PDF 8 10 6 o El = 30 8 4 6 4 2 El = 90o 2 0 1.02 1.04 1.06 1.08 1.1 1.12 1.14 0 Normalized Multipath Delay r 1.02 1.04 1.06 1.08 1.1 1.12 1.14 Normalized Multipath Delay r

Figure 4-21. Marginal DOA and delay PDFs for the air-to-ground model.

118 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

4.6 Summary

In this chapter, several existing channel models have been reviewed and new channel models have been developed. The new channel models were developed based on geometric principals used by the existing models. The general ellipsoidal channel model provides a framework to develop three-dimensional, single-bounce, channel models to represent channel environments in which the transmitter and receiver are surrounded by scatterers in three-dimensions. The general ellipsoidal model was refined and constrained to form an air-to-ground channel model useful for airborne vehicle communications. These models assist in developing wireless systems that employ smart antennas by providing multipath strength, delay, and direction of arrival information.

119 CHAPTER 4 – MULTIPATH CHANNEL MODELS FOR ANTENNA ARRAYS

This page intentionally left blank.

120 Chapter 5

Channel Measurements

This chapter investigates past results and new developments in radio channel measurements. First, a survey of terrestrial and air-to-ground measurements is presented. The results of the survey demonstrate direction of and the interest in various types of radio channel measurements. Next, measurement campaigns performed at Virginia Tech are discussed, including descriptions of measurement sites, system configurations, and propagation characteristic results relevant to antenna arrays and channel modeling. New measurement results presented in this chapter serve as input to channel simulation and channel model evaluation described later

5.1 Survey of Radio Channel Measurements

Section 5.1 provides an overview of results from measurement campaigns reported in propagation research literature. This section gives examples of measurement results that are of interest to propagation researchers and outlines the measurement campaigns performed to obtain the results.

121 CHAPTER 5 – CHANNEL MEASUREMENTS

5.1.1 Terrestrial Measurements

Numerous terrestrial measurements have been performed by researchers to characterize propagation between base stations and mobile stations. Measurements were performed as early as 1972 [Cox72] to characterize multipath properties and wideband propagation for digital communications in a mobile environment. Measurements continue to be performed today to characterize radio channels in specific ways for new applications of wireless technology (e.g., antenna array applications). Measurements performed by Wilson [Wil01] characterized wideband propagation at 1920 MHz using a four-element antenna array. A mobile transmitting antenna and a roof-mounted receiving antenna array were used to measure radio channels throughout a suburban environment. The receiver antenna array used nonlinear inter-element separations of 2l, 5l, and 10l. A direct-sequence, spread-spectrum measurement system was used to log power-delay profiles. Table 5-1 summarizes the measurement results.

Table 5-1. Results of a wideband measurement campaign in a suburban environment [Wil01]. Measurement Parameter Result Site Suburban (Boulder, CO). Mobile transmitter; roof-mounted receiver 14 m above predominant elevation. Multipath characteristics RMS delay spread: CDF 90%: <1.38 ms and <0.65 ms throughout two sectors CDF 99%: <3.14 ms and <1.35 ms throughout two sectors Path loss exponent 4.1 and 4.9 throughout two sectors. Diversity Gain Maximal ratio combining 19.6 KHz BW (4-channels) CDF 90%: 11.2 dB (max) CDF 99%: 18.3 dB (max) Maximal ratio combining 10 MHz BW (4-channels) CDF 90%: 6.9 dB (max) CDF 99%: 7.8 dB (max) Observations · Fade depths decrease for increasing bandwidth. · Increasing bandwidth reduces computed diversity gain.

122 CHAPTER 5 – CHANNEL MEASUREMENTS

Received power within particular bandwidths was determined by integrating the normalized power spectral density (NPSD) over the desired bandwidth. Using the notation in [Wil01], The NPSD normalized to a calibration profile was defined to be

DFT (DP)2 NPSD = ( 5.1 ) DFT (CAL _ DP)2

where DP is the delay profile, DFT(.) is the discrete Fourier transform (DFT), and CAL_PD is the DFT of the system response delay profile. Delay profiles are related to power-delay profiles using

2 PDP(ti ) = DP(ti ) ( 5.2 )

where PDP(ti ) is the power-delay profile curve (showing received power versus propagation delay). The power-delay profiles used for the results in [Wil01] were a subset (approximately 60%) of the total collected. An acceptance criterion was applied to all power-delay profiles in order to keep poorly measured profiles (low interval of discrimination, noisy, etc.) from corrupting measurement results.

Measurements in [Lar99] provided results on spatial and temporal characteristics of radio channels in urban and suburban environments. Wideband measurements were performed using an antenna array to produce azimuth-delay spectra showing power versus angle and propagation delay. Results for delay spread, azimuth spread, and coherence bandwidth were reported; results are summarized in Table 5-2.

Propagation delay results showed a decrease in RMS delay spread as antenna beamwidth was narrowed. Rician K-factors in the suburban environments were shown to be higher than those in urban environments, suggesting that stronger LOS components existed in suburban environments (K = 0 corresponds to Rayleigh fading).

123 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-2. Results of a spatial-temporal measurement campaign [Lar99]. Measurement Parameter Result Site Dense urban and suburban environments. Multipath characteristics RMS delay spread: CDF 50%: <70 ns (15 degree antenna beamwidth) CDF 50%: <90 ns (120 degree antenna beamwidth) CDF 90%: <200 ns (15 degree antenna beamwidth) CDF 90%: <230ns (120 degree antenna beamwidth) Rician K factors Urban environment CDF 70%: K = 2 Suburban environment CDF 70%: K = 10 Coherence bandwidth CDF 50%: 6 MHz (15 degree antenna beamwidth) CDF 50%: 4 MHz (120 degree antenna beamwidth) CDF 80%: 23 MHz (15 degree antenna beamwidth) CDF 80%: 10 MHz (120 degree antenna beamwidth) Observations · Approximately 20% of measured channels showed K<1 and coherence bandwidth > 4 MHz. · Approximately 50% of measured channels showed K<1 and coherence bandwidth > 1 MHz.

Receivers that employ rakes can combine resolvable multipath components, and the number of useful rake fingers l for an ideal rake receiver is expressed in [Lar99] by

æ B ö l = ç ss ÷ +1 ( 5.3 ) è CBW ø where Bss is the system bandwidth and CBW is the coherence bandwidth of the channel. For example, if a 4.096 MHz W-CDMA receiver is used in a channel with a coherence bandwidth exceeding 4.096 MHz, then less than two rake fingers are active. If multipath components cannot be resolved, then a rake finger will experience fading because of combining of signal components within the resolution of the system. Therefore, as shown by the measurement results, in 20% of the measured channels where K<1 (indicating significant multipath content) and coherence bandwidth greater than 4 MHz (indicating short relative multipath delays), a W-

124 CHAPTER 5 – CHANNEL MEASUREMENTS

CDMA receiver employing a rake receiver would experience severe fading on a single useful rake finger. For a 1.25 MHz IS-95 receiver employing a rake, a single finger would experience severe fading more than approximately 50% of the time due to K<1 and CBW>1 MHz more than 50% of the time.

Results for spatial signatures measured in outdoor environments at 1.88 GHz are presented in [Kav00]. Variations of spatial signatures due to a dynamic propagation environment can be quantified using a correlation coefficient given by

H ai a j r i, j = i ¹ j ( 5.4 ) ai a j

th th where ai and aj are column vectors representing the i and j spatial signatures measured for an array at two different locations. Measurements were performed in a suburban environment using a mobile transmitter and a base station array consisting of seven elements in a circular pattern with a radius of 10 cm. The transmitter antenna was a half-wavelength, vertically polarized dipole.

Table 5-3. Summary of results of campaign to measure correlation of spatial signatures [Kav00]. Measurement Parameter Result Site Suburban environment; LOS and NLOS channels. Spatial signature correlation Pedestrian measurement runs: coefficients CCDF 90%: 0.41 (min) – 0.98 (max) CCDF 50%: 0.82 (min) – 0.99 (max) Car measurement runs: CCDF 90%: 0.21 (min) – 0.69 (max) CCDF 50%: 0.61 (min) – 0.92 (max) Observations · For NLOS propagation, spatial signatures become less correlated with small movements due to varying complex path attenuation.

125 CHAPTER 5 – CHANNEL MEASUREMENTS

An empirical model that best fit the probability density functions of spatial signature correlation coefficients was found using the beta function given by

G(y + b + 2) b f (ry , b ) = ry (1- r) , 0 £ r £ 1, y > -1, b > -1 ( 5.5 ) G(y +1)G(b +1)

where G(×) is the gamma function defined by

¥ G(t) = ò x t-1e -x dx = (t -1)!. ( 5.6 ) 0

Values for the parameters of this model and measured PDFs are presented in [Kav00]. The results for this measurement campaign showed that spatial signatures in LOS environments exhibited high correlation between pairs of spatial signature vectors when a the transmitter antenna was moved through the environment. However, the rich multipath environments of NLOS channels caused lower values of correlation coefficients computed for pairs of spatial signature vectors.

To summarize, the following observations have been made regarding the reviewed terrestrial measurements:

· Increasing signal bandwidth reduces fade depth and reduces potential antenna diversity gain. · Narrower antenna beamwidth reduces RMS delay spread and increases coherence bandwidth because of attenuation of multipath components separated in angle. · Measurements of coherence bandwidth and Rician K-factors show conditions where rake receivers can become ineffective because of short multipath delays but strong multipath content. Rakes become more effective where small K-factors and narrow coherence bandwidths exist simultaneously. · Spatial signatures vary more rapidly over shorter distances in shadowed, multipath-rich environments; conversely, spatial signature vectors remain highly correlated in predominantly LOS channels.

126 CHAPTER 5 – CHANNEL MEASUREMENTS

5.1.2 Air-to-Ground Measurements

Measurements between low-altitude (below 10,000 feet) airborne vehicles and ground stations can be found in literature for measurement campaigns intended to emulate satellite-to-ground communications. Measurements at 1636 MHz are presented in [Smi91] were performed using a transmitter in a light aircraft and a receiver on the ground. The measurement system was a sliding correlator system that measured power-delay profiles using a 1023-chip PN sequence clocked at 10.23 Mcps; the plots presented in [Smi91] indicate that the system had an interval of discrimination of approximately 28 dB. Data was collected for elevation angles between 60 degrees and 80 degrees above the horizon in suburban environments. The results in primarily LOS channels indicate low delay spread. When the mobile vehicle was located in a canyon of tall buildings, sample power-delay profiles indicated excess delay at the 25 dB level to be between 1 ms and 1.5 ms.

Table 5-4. Results of a measurement campaign using a light aircraft to study land mobile satellite communications [Smi91]. Measurement Parameter Result Site Suburban and rural environments; 60o to 80o elevation angles. Multipath characteristics Obstructed channel: Excess delay (25-dB level): 1.0 ms to 1.25 ms (building obstruction) LOS channel Excess delay: minimal Observations · LOS channels in suburban and urban environments showed low delay spread for elevation angles of 60o to 80o. · Transition from LOS condition to shadowing behind building obstruction showed sharp increase in multipath components reflected from nearby buildings.

127 CHAPTER 5 – CHANNEL MEASUREMENTS

Measurements in [Jah96] also used an airborne transmitter to characterize multipath propagation at 1820 MHz for spread-spectrum satellite communications. The measurement data indicated that multipath components could be divided among three regions in the power-delay profiles: direct path, near echoes, and far echoes. Note that this division of the delay axis corresponds to an approach similar to that of the elliptical sub-regions channel model presented in Chapter 4. The amplitude of the direct-path component was shown to be Rician distributed in LOS conditions and Rayleigh distributed in shadowed regions22. In the near-echo region, the amplitude of components decreased exponentially with delay, and the delay of the components was exponentially distributed. A majority of the multipath components appeared in the near- echo region. The components that appeared in the far-echo region were distributed uniformly in delay and showed Rayleigh-distributed amplitude. Detailed results for various elevation angles are presented in [Jah96].

The measurement system used for the measurements described in [Jah96] is described in [Jah94]. A sliding correlator system used a chip rates of 10 MHz and 30 MHz and PN sequence lengths of 127, 255, and 511 chips. A maximum transmit power of 44 dBm was available, and an omnidirectional transmitter antenna was mounted on the skin of an aircraft. The receiver used an experimental antenna for an INMARSAT-P handheld terminal.

In an air-to-ground channel sounding campaign [Dye98] designed to study aircraft communications, a narrowband measurement system and a sliding correlator system was used to measure narrowband and wideband channel characteristics in the VHF communications band23 at 135 MHz. The sliding correlator channel sounder was operated at 5 Mcps, resulting in a multipath time delay resolution of approximately 0.4 ms. The measurements were performed between the airport terminal area and an airborne aircraft flying standard departure and arrival procedures. Table 5-6 summarizes the results of the measurement campaign. Because of the large K factors, indicating a strong LOS component during measurements, the effect of small scale fading was reported to be insignificant.

22 Strictly speaking, a completely resolved, direct-path component would not fade. The fading of the “direct-path” component in [Jah96] was caused by the combination of signal components that could not be resolved by the measurement system. 23 The aviation communications band in use by civil aircraft in the United States exists between 118 MHz and 136 MHz. For voice communications, amplitude modulation is used.

128 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-5. Summary of results for a campaign that measured land mobile satellite channels [Jah96]. Measurement Parameter Result Site Open, rural, suburban, urban, highway. Multipath characteristics Direct path Rician amplitude in LOS conditions (3.2-11.8 dB carrier to multipath ratio) Rayleigh/log-normal in shadowed conditions Near echoes Exponentially decreasing mean amplitude with delay Rayleigh-distributed amplitude around mean Exponentially-distributed delay of components Poisson-distributed number of components (l=0.5- 4.0) Maximum excess delay 400 ns - 600 ns Far echoes Rayleigh-distributed amplitude Poisson-distributed number of components (l=0.3- 4.1) Uniformly-distributed delay of components Maximum excess delay 5 ms - 15 ms Observations · Multipath components typically attenuated 10 – 30 dB relative to LOS component. · Most multipath components lie in 0 – 600 ns delay region.

129 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-6. Results of an air-to-ground measurement campaign [Dye98]. Measurement Parameter Result Site Airport environment Small scale fading distribution Predominantly Rician with large K factors Range of Rician K factors 2.6 dB to 19.7 dB Average Rician K factor 16 dB

Multipath characteristics RMS delay spread: mean st = 4.0 ms (variance = 1.4 ms) Delay spread: mean Dt = 2.9 ms (variance = 1.3 ms) Path loss exponent 2 to 4 at large T-R separations Observations · Surface and low altitude operations resulted in larger standard deviation of large scale fading (shadowing) · Small scale fading was insignificant for this particular measurement setup

In summary, these observations have been made with respect to measurements performed in the air-to-ground propagation environment:

· The existence of multipath in the air-to-ground channel is dependent upon the environment surrounding the ground-based receiver. For the flat, non-obstructed airport environment, weak multipath resulted in Rician fading with large K-factors. · Small elevation angles resulted in richer multipath content. · Although large excess delay values may be apparent (over 1 ms), the air-to-ground channel may remain Rician with large K-factors. · Rician fading of direct-path components indicates multipath caused by scatterers in close proximity to receiver (since airborne transmitter is not near any scatterers). · Large excess delays can be expected in air-to-ground channels; up to 15 ms has been recorded.

130 CHAPTER 5 – CHANNEL MEASUREMENTS

5.2 Rooftop-Level Measurement Campaign

Rooftop measurements were performed in a manner that emulated radio channels between tower- mounted and ground-level transceivers. Measurements were processed to produce results appropriate for geometric channel model simulation and channel characterization.

5.2.1 Measurement Overview

Wideband measurements were performed at Virginia Tech to record experimental data for a receiver antenna height of approximately 25 meters above ground level and a receiver approximately 1.5 meters above ground level. The wideband, multi-channel measurement system described in Chapter 3 was mounted on the roof of Whittemore, a six-story academic building on the Virginia Tech campus. The transmitter antenna was mounted on the roof of a vehicle and driven through the parking lots and streets adjacent to the building on which the receiver was located. Figure 5-1 shows the measurement system location on the roof and the orientation of the antenna array relative to the surroundings.

Figure 5-1. The measurement system was positioned on the roof of Whittemore near the corner of the building, and the receiver array was mounted on a stand approximately six feet above roof level.

The antenna array used at the receiver was a four-element linear array, using quarter-wavelength monopole antenna elements with half-wavelength spacing. The antenna array was mounted with the ground plane above the antenna elements so that the antennas would receive signals from below the horizontal plane (where the transmitter was located throughout the measurements).

131 CHAPTER 5 – CHANNEL MEASUREMENTS

The automobile with the transmitter was driven at slow speeds (less than 5 MPH) while the receiver logged signal data. Table 5-7 summarizes the system configuration and site details.

Table 5-7. Details of the measurement system setup and transmitter/receiver locations for the Whittemore roof measurements. Measurement Parameter Value / Description Transmit power +26 dBm Transmitted signal 80 Mcps PN sequence, 1023 chips, register taps (3,10) Transmit frequency 2050 MHz (center) Transmitter antenna Dipole, vertically-polarized Transmitter antenna height 1.5 m AGL Receiver antennas Four-element monopole array, half- wavelength spacing Receiver antenna array height Approximately 25 m AGL Receiver location Whittemore Hall, roof Drive test areas (transmitter driven) 1) Parking lots north of Whittemore (LOS) 2) Parking lots behind Durham (NLOS) 3) Suburban neighborhood north of Whittemore(LOS/NLOS)

5.2.2 Multipath RMS Delay Spread

Multipath characteristics were computed from measured power-delay profiles. Sample power- delay profiles from the Whittemore roof measurements are shown in Figure 5-2. Relative axes units are typically acceptable for producing meaningful multipath delay characterization results. For example, RMS delay spread statistics rely only on the relative (as opposed to absolute) strength and delay of multipath components contained in a power-delay profile. Figure 5-2 illustrates power-delay profiles that were recorded simultaneously at two of the four antenna

132 CHAPTER 5 – CHANNEL MEASUREMENTS

elements. Both power-delay profiles were normalized using the same factor. Differences in signal component strengths due to uncorrelated multipath fading across the antenna array are noticeable.

Figure 5-2. Sample power-delay profiles recorded at elements 2 and 3 of the antenna array. The solid line is the channel 2 PDP, and the dotted line is the channel 3 PDP.

RMS delay spread is used to quantify the relative time dispersion of a signal due to multipath. For TDMA systems, a large delay spread may add the requirement for an equalizer in the receiver to mitigate frequency selected fading caused by the channel. For CDMA systems, a large delay spread means that a rake receiver may be used to combine multipath components of different delays to form a more reliable composite signal. Mean multipath delay is computed using

N 2 åa nt n n=1 t = N ( 5.7 ) 2 åa n n=1

133 CHAPTER 5 – CHANNEL MEASUREMENTS

2 where a n is the relative power of each signal component and t n is the corresponding delay of each component. Note that mean delay is a function of absolute propagation delay between the transmitter and receiver, not simply a function of relative delay. RMS delay spread is the second central moment of the power delay profile computed with

N 2 2 åa n (t n -t ) n=1 s t = N . ( 5.8 ) 2 åa n n=1

Because the computation involves subtracting the mean delay from individual multipath delays, RMS delay spread is not a function of absolute propagation delay.

Table 5-8 shows the RMS delay spread results for the Whittemore roof/Whittemore parking lot measurements. Mean, standard deviation, minimum, and maximum RMS delay spread values are given for each element of the antenna array. Figure 5-3 shows the complimentary CDF for RMS delay spread computed for each antenna element. Results shown on the plot indicate similar RMS delay spread characteristics across all four elements of the array. This is expected since all antenna elements received signals through channels in the same propagation environment.

Table 5-8. RMS delay spread statistics. Channel 1 Channel 2 Channel 3 Channel 4 Mean RMS Delay 137.2 ns 106.9 ns 115.1 ns 117.4 ns Spread Standard Deviation 186.1 ns 91.6 ns 109.9 ns 107.6 ns RMS Delay Spread Minimum RMS 3.2 ns 4.3 ns 14.3 ns 2.4 ns Delay Spread Maximum RMS 1186.7 ns 507.0 ns 614.5 ns 633.9 ns Delay Spread

134 CHAPTER 5 – CHANNEL MEASUREMENTS

RMS Delay Spread Based On Measurements 1

0.9

0.8 Channel 1 Channel 2 0.7 Channel 3 Channel 4 0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 50 100 150 200 250 300 350 400 RMS Delay Spread

Figure 5-3. Complementary CDF for RMS delay spread based on measurements.

5.2.3 Distribution of Multipath Components

The histogram in Figure 5-4 was produced to show the distribution of multipath components across delay in the measured power-delay profiles. All detectable multipath components are included in the histogram. The results show a decrease in numbers of multipath components with delay. The specific values of component count can serve as input for simulations using geometric channel models. The average number of components in each delay bin and for the entire profile are tabulated in Table 5-9.

135 CHAPTER 5 – CHANNEL MEASUREMENTS

Average number of signal components per delay bin 5

4

3

2

1 Average number of components

0 0 500 1000 1500 2000 2500 Excess delay (ns)

Figure 5-4. Number of signal components versus excess propagation delay.

Table 5-9. Distribution of multipath components among delay bins of power-delay profiles. Bin # Delay Bin (ns) # Components per Profile 1 0 – 150 4.69 2 150 – 300 3.03 3 300 – 450 2.29 4 450 – 600 2.16 5 600 – 750 1.84 6 750 – 900 1.50 7 900 – 1050 1.34 8 1050 – 1200 1.08 9 1200 – 1350 0.582 10 1350 – 1500 0.310 11 1500 – 1650 0.172 12 1650 – 1800 0.138 13 1800 – 1950 0.0776 14 1950 – 2100 0.0647 15 2100 – 2250 0.0172 16 2250 – 2400 0.0690 ALL 0 – 2400 19.4

136 CHAPTER 5 – CHANNEL MEASUREMENTS

5.2.4 Multipath Strength Correlation Coefficients Versus Delay

This section provides a method of computing correlation coefficients for signal component magnitude across an antenna array. The purpose of the method and the associated results is to investigate behavior of signal component fading across the array and for varying ranges of excess propagation delay.

It is well known that performance gain provided by antenna diversity is dependent upon the signal envelope correlation among the elements of an antenna array [Jan02]. Traditionally, the signals are measured using a continuous-wave transmitted signal and a narrowband receiver to record the fading envelope at each antenna element simultaneously. When fading envelopes are highly correlated, improvement of system performance through antenna diversity is low compared to the case when fading envelopes exhibit low correlation coefficients.

For a narrowband system, a fading envelopes are caused by the constructive and destructive combination of signal components at the receiving antenna when the receiver or transmitter is in motion24. These signal components are caused by two or more propagation paths of electromagnetic energy between the transmitter and receiver. Narrowband systems generally cannot resolve signal components, and the fading envelopes are a result of the summation of all signal components arriving at the receiver antenna.

Certain wideband systems, such as direct-sequence spread spectrum systems, have the ability to resolve individual or groups of signal components at the receiver. A rake receiver can demodulate signal components that are delayed in time with respect to one another. When signal components are mutually separated in delay by more than a chip period, those signal components can be uniquely resolved with unfading magnitude. However, when multiple signal components arrive at the receiver with relative delays less than one chip period, those signal components combine and appear as a single signal component25 that fades with time as the receiver or transmitter moves. It is the correlation coefficient of these fading envelopes, caused by signal components with irresolvable delays, across elements of an antenna array that is of interest here.

24 Fading envelopes are also caused by relative motion of scatterers in the propagation environment. 25 The composite signal component may appear wider in delay, and the shape may not be that of an ideal PN sequence autocorrelation function observed for single-component peaks.

137 CHAPTER 5 – CHANNEL MEASUREMENTS

The measurements reported here are relevant to a receiver that uses a rake receiver at each antenna element and combines the output of the rake fingers to form a composite received signal. Similar to the case of combining multiple narrowband signals directly from antenna elements, the performance of combining signal components with particular delays from multiple antenna elements will be affected by the correlation coefficient of the envelopes of the signal components.

A signal component magnitude for a power-delay profile (PDP) is defined to be the maximum magnitude value detected for a particular cross-correlation peak that exists in the profile. Figure 5-5 illustrates a sample set of power-delay profiles used for the signal component magnitude correlation processing. The continuous trace (blue) shown for each channel is a plot of all samples of the power-delay profile. The straight horizontal (yellow) line indicates the noise threshold below which all PDP samples are considered noise. The circles (red) around each peak represent the discrete magnitude and delay pairs that were detected for signal components in the power-delay profiles.

The correlation coefficients for multipath magnitude across an array are defined as follows. A power-delay profile P(t), which may be interpreted as relative received power versus relative propagation delay, can be represented as a set of Ns samples given by

P(t n ) = P(nTs ) ( 5.9 )

where Ts is the sample period with which the power-delay profile is sampled, and t n = nTs is the

discrete time value (in seconds) of the propagation delay for sample n Î{0,1,2,L, N s -1}. A measured power-delay profile represents received signal components as a channel impulse response convolved with the pulse shape determined by the measurement system response. For the measurements processed here, the pulse shape is approximately triangular and corresponds to the autocorrelation function of the PN sequence transmitted for the measurements (see [New97]).

138 CHAPTER 5 – CHANNEL MEASUREMENTS

Figure 5-5. One set of power-delay profiles acquired simultaneously at each antenna element for multipath magnitude correlation processing.

139 CHAPTER 5 – CHANNEL MEASUREMENTS

The samples at the peaks of the signal components, as shown in Figure 5-5, are the relative signal component strengths ak in the impulse response given by

N c -1 h(t ) = åa k exp( jfk )d (t -t k ) ( 5.10 ) k =0

26 th where Nc is the number of signal components , fk is the phase of the k signal component, and th tk is the delay of the k signal component corresponding to strength ak. If we consider only the peaks of P(t n ), occurring at times tk where k Î{0,1,2,L, N c -1}, then the discrete magnitudes and phases of the impulse response in equation ( 5.10 ) are related to the power-delay profile

P(t n ) by

a k = P(t k ) ( 5.11 ) and

fk = ÐP(t k ). ( 5.12 )

Power-delay profiles were identified for this measurement campaign with a snapshot number and a channel number. A channel number i Î{1,2,3,4} identifies which of the four elements was

used to receive the power-delay profile, and each snapshot number j Î{0,1,2,L, N snap -1} identifies a set of four power-delay profiles recorded simultaneously at the four antenna elements, where Nsnap is the total number of snapshots recorded. Within each power-delay

( j ) profile, individual signal component magnitudes are assigned an index k Î{0,1,2,L, N c -1},

( j ) where N c is the number of signal components in each power-delay profile recorded during the jth snapshot. With this notation defined, individual multipath components can be identified by

26 Technically, Nc is the number of discrete paths between the transmitter and receiver, but if Nc paths exist, then Nc signal components will also exist at a receiver.

140 CHAPTER 5 – CHANNEL MEASUREMENTS

a i, j,k

i = channel (antenna element) number where i Î{1,2,3,4}

j = power-delay profile snapshot number where j Î{0,1,2,L, N snap -1} ( 5.13 ) ( j ) k = signal component index where k Î{0,1,2,L, N c -1}

N snap = number of snapshots

( j ) th N c = number of signal components in each PDP for j snapshot

Since correlation coefficients versus delay are of interest, each power-delay profile is divided

into Mbins evenly spaced delay bins. Delay bins are identified with index m Î{1,2,3,L, M bins }. The width of each delay bin is determined by dividing the time between the first-arriving and last-arriving signal components by the number of delay bins M. Figure 5-6 illustrates delay bins for a measured power-delay profile.

Delay Bins 1 2 3 4

Figure 5-6. Delay bins evenly divide the delay between the first arriving signal component and the last arriving signal component.

141 CHAPTER 5 – CHANNEL MEASUREMENTS

In order to operate on all signal components in all power-delay profiles for each channel, the matrix A m was created. This matrix contains all signal component magnitudes found within delay bin m.

é a1,0,0 a2,0,0 a3,0,0 a 4,0,0 ù ê a a a a ú ê 1,0,1 2,0,1 3,0,1 4,0,1 ú ê a1,0,2 a2,0,2 a3,0,2 a 4,0,2 ú ê ú ê M M M M ú A m = . ( 5.14 ) ê a (0 ) a (0 ) a (0 ) a (0 ) ú ê 1,0,Nc -1 2,0,Nc -1 3,0,N c -1 4,0,Nc -1 ú ê a1,1,0 a 2,1,0 a3,1,0 a 4,1,0 ú ê M M M M ú ê ú

êa (Nsnap-1 ) a (Nsnap-1) a (Nsnap-1) a (Nsnap-1) ú ë 1,N snap -1,Nc -1 2,N snap -1,N c 3,N snap -1,Nc 4,N snap -1,Nc û

Each column of matrix A m contains the magnitudes of all of the multipath components received at a particular antenna element (column one corresponds to element one, etc.). Each row of matrix A m contains four multipath components received simultaneously at the antenna elements during one of the Nsnap power-delay profile snapshots. In order to simplify the notation for the elements of A m , and since further calculations only depend upon the column and row organization of the matrix, the matrix A m will be rewritten as

A m = [a1 a 2 a3 a 4 ] ( 5.15 )

where the column vectors ai represent the signal component magnitudes received by antenna element i.

The correlation coefficient matrix of A m can now be computed. The signal component

magnitude correlation coefficient matrix rc is defined as

ér11 r12 r13 r14 ù ê ú r 21 r 22 r 23 r 24 rc = ê ú . ( 5.16 ) êr 31 r 32 r 33 r 34 ú ê ú ër 41 r 42 r 43 r 44 û

142 CHAPTER 5 – CHANNEL MEASUREMENTS

The elements r mn of matrix rc, where m indicates row and n indicates the column of rc, are given by

T (am - am ) (an - an ) rmn = T T ( 5.17 ) (am - am ) (am - am ) (an - an ) (an - an )

where am and an are the means of column vectors a m and a n respectively.

Since rc is symmetric about the diagonal and rmn = 1 for m = n, which can be deduced from equation ( 5.17 ), there are six unique quantities that completely describe the correlation of signal component magnitudes among the four antenna elements. These quantities are the following

elements of rc: r12, r13, r14, r23, r24, and r34.

The data recorded during the Whittemore roof measurements was used for this processing. Measurements can be performed over a local area or a wide area. For example, measurements presented in [Kav00] use a local area approach, during which the transmitter or receiver is moved throughout an area of a few wavelengths to characterize small-scale changes in signal properties (in [Kav00], spatial signature correlation across local areas was investigated). The measurements discussed in this section were performed using a wide area approach, during which power-delay profiles were recorded while a transmitter was moved randomly throughout a very large area compared to a wavelength. The area was chosen such that the propagation environment remained similar at all points throughout the area (e.g., not mixing urban environments with rural environments throughout the wide area chosen).

Power-delay profiles used for processing were limited to those which had a large enough interval of discrimination so that signal components could be measured on a consistent basis. Power- delay profiles were normalized using a common factor. As such, an approximate index of discrimination was derived for each channel by comparing the strongest signal component across all channels with the noise floor of the power-delay profile for each channel. The minimum index of discrimination allowed was called the noise threshold. The noise threshold was chosen to be 3 dB above the peak power-delay profile sample in a delay region where no signal components were observed, defined to be the noise region. For the measurements described in

143 CHAPTER 5 – CHANNEL MEASUREMENTS

this section, the noise region was set to be the last 20 percent of each power-delay profile, as indicated by the straight vertical (yellow) line in the plots in Figure 5-5.

Multipath components were for each power-delay profile were detected by an iterative process whereby the maximum magnitude value is identified as a signal component and a window of samples, having a width equal to the resolution of the measurement system, is removed from the maximum magnitude check for the next iteration. In order to further assure that noise peaks were not falsely identified as signal components, a minimum signal component level was defined. Peaks within this dB level of the strongest signal component across all channels were used during processing. Table 5-10 summarizes the processing details.

Table 5-11, Table 5-12, and Table 5-13 summarize the results for three different delay bin sizes. The six correlation coefficients are shown for each delay bin, and the number of signal components that existed in those delay bins is listed. The delay range for each bin and element spacing is also shown.

Table 5-10. Processing details for signal component correlation processing. Processing Factor Details Noise threshold 30 dB below strongest component across all channels Noise region Last 20% of 4 ms power-delay profile Margin between peak noise region and noise 3 dB above peak sample in noise region threshold Number of delay bins 4, 8, and 16 bins Minimum signal component level 27 dB below strongest component across all channels Normalization factor All power-delay profiles normalized by subtracting same dB factor from dB-scale PDPs. Normalization factor set such that strongest component across all channels equaled 0 dB.

144 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-11. Correlation coefficients for signal component magnitude across antenna elements (4 delay bins). Delay Delay Correlation Coefficients Number of Bin Range Signal r12 r13 r14 r 23 r24 r 34 No. (ms) Components* 1 0-0.36 0.91748 0.89406 0.84693 0.92163 0.8629 0.89392 258 2 0.36-0.71 0.30562 0.26789 0.33806 0.63443 0.61436 0.63367 47 3 0.71-1.07 0.84732 0.70833 0.59953 0.65819 0.58294 0.68511 15 4 1.07-1.42 0.34766 0.24449 0.53386 -0.466 -0.5548 0.6808 7 Element Spacing l/2 l 3l/2 l/2 l l/2 * Signal components detected within 208 power-delay profiles.

Table 5-12. Correlation coefficients for signal component magnitude across antenna elements (8 delay bins). Delay Delay Correlation Coefficients Number of Bin Range Components r12 r13 r14 r 23 r24 r 34 No. (ms) Signal* 1 0-0.18 0.91495 0.90385 0.88074 0.93027 0.89583 0.92894 206 2 0.18-0.36 0.69605 0.46992 0.19446 0.623 0.30935 0.42116 52 3 0.36-0.53 0.23328 0.18571 0.31093 0.65197 0.54222 0.52036 35 4 0.53-0.71 0.51271 0.49939 0.43926 0.60896 0.73837 0.77877 12 5 0.71-0.89 0.84041 0.8304 0.86474 0.84828 0.93369 0.80717 7 6 0.89-1.07 0.86746 0.65001 0.38844 0.67706 0.44905 0.49309 8 7 1.07-1.25 0.11047 0.96931 0.71757 -0.097809 -0.5893 0.81005 4 8 1.25-1.42 0.91521 -0.39596 0.89873 -0.73242 0.64582 0.046811 3 Element Spacing l/2 l 3l/2 l/2 l l/2 * Signal components detected within 208 power-delay profiles.

145 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-13. Correlation coefficients for signal component magnitude across antenna elements (16 delay bins). Delay Delay Correlation Coefficients Number of Bin Range Components* r12 r13 r14 r 23 r24 r 34 No. (ms) 1 0-0.09 0.91996 0.93527 0.91201 0.95558 0.91642 0.94838 144 2 0.09-0.18 0.50385 0.35558 0.26853 0.64626 0.55205 0.66376 62 3 0.18-0.27 0.43866 0.31679 -0.07140 0.29552 0.1415 0.31201 26 4 0.27-0.36 0.84455 0.55788 0.63497 0.71643 0.61248 0.74363 26 5 0.36-0.45 0.25178 0.32238 0.49312 0.67144 0.61809 0.65301 28 6 0.45-0.53 0.22744 0.015498 0.1421 0.68934 0.49123 0.44003 27 7 0.53-0.62 0.58598 0.49731 0.46097 0.82369 0.89891 0.80876 8 8 0.62-0.71 -0.11005 0.94608 0.68587 0.12021 0.43351 0.88461 4 9 0.71-0.80 -0.56082 0.38164 -0.83668 0.37923 0.43101 -0.03374 4 10 0.80-0.89 0.99923 0.93717 0.99984 0.92277 0.99977 0.93079 3 11 0.89-0.98 0.94317 0.68902 0.435 0.87489 0.51255 0.72668 4 12 0.98-1.07 0.8719 0.77448 0.4975 0.47402 0.36116 0.85729 4 13 1.07-1.16 0.17749 0.96976 0.61127 -0.06807 -0.6704 0.78594 3 14 1.16-1.25 ** ** ** ** ** ** 1 15 1.25-1.34 ** ** ** ** ** ** 1 16 1.34-1.42 -1 1 1 -1 -1 1 2 Element Spacing l/2 l 3l/2 l/2 l l/2 * Signal components detected within 208 power-delay profiles. ** Only one component in delay bin; correlation coefficient undefined.

Several observations can be made using these results:

· The first bin of multipath components shows consistently high correlation coefficients (above 0.9). The presence of a dominant line-of-sight signal component would have this effect. A dominant line-of-sight component indicates that no significant multipath components exist near the LOS component (in delay) within the resolution of the measurement system.

146 CHAPTER 5 – CHANNEL MEASUREMENTS

· As the first bin is widened in delay, the correlation coefficients remain approximately the same for the l/2-spaced elements; and the correlation coefficients decrease for more widely spaced (l and 3l/2) elements. This makes sense since a larger number of multipath components with lower correlation is included in the bin as the bin is widened.

· Although significant multipath exists in the power-delay profiles, signal components in any delay bin can be highly correlated across the antenna elements.

· There is no obvious trend of monotonically increasing or decreasing values of correlation coefficient versus delay. Bins of signal components with high correlation coefficients can immediately follow or precede bins of signal components with low correlation coefficients.

· Additive noise must be considered when comparing correlation coefficients for signal component magnitudes. When correlation coefficients are low, additive noise may have caused highly correlated, weak signal components to appear uncorrelated. However, when signal components appear highly correlated because of large correlation coefficients, it can be reasoned that these components were impacted very little by noise and that these components in actuality were highly correlated. This of course relies upon the noise of the receiver channels being uncorrelated among the channels, which is a reasonable assumption since four independent receiver chains were used. The consequence of this observation is that highly correlated signal component magnitudes can be known to be highly correlated, but signal component strength relative to noise level must be considered before deeming signal components uncorrelated because of low correlation coefficients. The effect of noise on the results can be reduced by using a higher noise threshold when processing the measurements, but this results in fewer multipath components per power-delay profile in the sample set.

147 CHAPTER 5 – CHANNEL MEASUREMENTS

5.3 Dense Scatterer Measurement Campaign

Measurements were performed with a ground-level transmitter and a ground-level receiver in an environment with numerous scatterers to emulate channels experienced micro-cellular, LAN, and ad-hoc networks operated in outdoor, densely obstructed environments. These channels are appropriate for being modeled by the two-dimensional elliptical geometric channel models (GBSBE and elliptical sub-regions models). Processed measurements are used to evaluate these models in Chapter 7.

5.3.1 Measurement Overview

Wideband measurements were performed on the Virginia Tech campus in an plaza densely populated by outdoor structures. Figure 5-7 shows a map of the plaza, which is bordered by four buildings of stone construction reaching heights of two to four stories. Figure 5-8 shows a photo of the measurement environment. The obstructions within the plaza consist of vestibules and skylights constructed of concrete, metal, and glass. Pedestrian traffic in the area was very low during measurements.

Two receiver locations and ten transmitter locations were used. The locations were chosen such that six sets of non-line-of-sight (NLOS) and four sets of line-of-sight (LOS) measurements could be performed. For NLOS measurements, the path between the transmitter and receiver was blocked by multiple obstructions. For LOS measurements, the transmitter antenna was in view of each receiver antenna element. The receiver antenna was a four-element, linear array of vertical monopoles with half-wavelength spacing. The transmitter antenna was an end-fed dipole oriented vertically throughout the measurements. Transmitter-receiver separation for each location is shown in Table 5-14.

Measurements were performed with the receiver array was held stationary. While the receiver was logging signal data, the transmitter antenna was moved randomly throughout an extent of approximately five wavelengths around the defined transmitter location. This movement enabled recording of small-scale fading of multipath at the receiver while excluding large scale attenuation effects. A sample measured power-delay profile is shown in Figure 5-9. The profile

148 CHAPTER 5 – CHANNEL MEASUREMENTS shows relative multipath signal strength versus relative propagation delay. This profile was measured for the NLOS1 transmitter location and shows the typical multipath measurements taken at the site.

NLOS1 NLOS2 LOS1 NLOS3 NLOS4 TX TX TX TX TX

OBSTRUCTED PATH FOR NLOS1 MEASUREMENT NLOS5 TX

LOS2 NLOS6 TX TX

LOS3

TX

LOS4 TX BURRUSS HALL

LOS1-4 RX RX NLOS1-7 BURKE JOHNSTON STUDENT CENTER Figure 5-7. Map of the plaza where measurements were performed.

Figure 5-8. Photo of measurement site with transmitter in the foreground at the LOS1 location.

149 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-14. Transmitter-receiver separation for each transmitter location. Location T-R Separation NLOS1 205 feet 62.5 m NLOS2 193 feet 58.8 m NLOS3 190 feet 57.9 m NLOS4 195 feet 59.4 m NLOS5 165 feet 50.3 m NLOS6 135 feet 41.1 m LOS1 190 feet 57.9 m LOS2 145 feet 44.2 m LOS3 110 feet 33.5 m LOS4 75 feet 22.9 m

Power Delay Profile - Magnitude 5

0

-5

-10

-15

-20

-25

-30 Multipath Strength (dB) -35

-40

-45

-50 -0.2 0 0.2 0.4 0.6 0.8 1 Delay (us)

Figure 5-9. Sample power-delay profile from dense scatterer measurement site (NLOS1).

150 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-15 shows a link budget used for measurement planning purposes. All locations actually used for measurements fall within the 300 m range assumed in the link budget calculations. However, as shown later, the path loss exponent computed for the actual path loss experienced by multipath signal components was much higher than the path loss exponent used for the link budget.

Table 5-15. Link budget for terrestrial measurements on the VT campus. VT Campus Site Path Loss Data Range m 300 Freq Hz 2.05E+09 PL exp - 3 Ref dist m 10 Ref PL dB 58.7 Path Loss dB 102.99 System Gains and Losses Tx Power dBm 27 Tx Ant Gain dB 0 Tx Ant Gain dB 0.0 Total Losses dB 0.0 Rx Power dBm -76.0 Narrowband Received Power Margin Rx noise floor dBm -114.0 Margin dB 38.0

Over 7,500 power-delay profiles were measured and processed to produce discrete channel impulse response estimates (magnitude, delay, and phase of resolvable multipath components) and characterization results.

5.3.2 Multipath RMS Delay Spread

RMS delay spread was calculated for each power-delay profile on each channel for every NLOS location. Table 5-16 provides the mean, standard deviation, minimum, and maximum RMS delay spreads divided among channels and locations. Statistics for all channels combined are also provided for each location. Figure 5-10 through Figure 5-15 show complementary cumulative distribution functions (CCDF) for all NLOS locations. Results for each channel are shown on each plot.

151 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-16. RMS delay spread results for NLOS locations for the dense scatterer measurement campaign. Location Channel RMS Delay Spread (ns) Mean Std. Dev. Minimum Maximum NLOS1 1 67.4 10.2 40.2 99.5 2 68.6 9.12 47.0 108 3 70.7 9.78 48.5 97.9 4 63.3 9.67 44.2 94.1 All 67.5 10.1 40.2 108 NLOS2 1 58.5 9.09 34.4 85.3 2 61.7 10.0 34.1 89.0 3 59.1 10.2 35.0 87.1 4 64.1 9.88 0.00 91.0 All 60.9 10.0 0.00 91.0 NLOS3 1 71.0 10.1 45.7 96.7 2 65.2 12.7 35.9 99.3 3 70.0 11.5 39.8 99.4 4 74.7 12.0 42.1 151.9 All 70.2 12.1 35.9 151.9 NLOS4 1 81.2 11.1 57.2 112 2 79.5 10.6 51.6 103 3 74.8 10.2 55.6 108 4 79.3 9.95 54.5 110 All 78.6 10.7 51.6 112 NLOS5 1 74.4 7.38 50.5 95.3 2 68.8 7.30 51.3 89.0 3 71.3 6.74 55.3 87.2 4 68.2 7.85 49.3 89.8 All 70.7 7.70 49.3 95.3 NLOS6 1 73.6 11.1 40.3 106 2 68.3 9.39 41.1 93.9 3 69.2 13.0 45.4 260 4 66.6 17.5 31.3 368 All 69.4 13.3 31.3 368

152 CHAPTER 5 – CHANNEL MEASUREMENTS

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-10. RMS delay spread CCDF for NLOS1.

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-11. RMS delay spread CCDF for NLOS2.

153 CHAPTER 5 – CHANNEL MEASUREMENTS

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-12. RMS delay spread CCDF for NLOS3.

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-13. RMS delay spread CCDF for NLOS4.

154 CHAPTER 5 – CHANNEL MEASUREMENTS

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-14. RMS delay spread CCDF for NLOS5.

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-15. RMS delay spread CCDF for NLOS6.

155 CHAPTER 5 – CHANNEL MEASUREMENTS

Several observations were made for NLOS RMS delay spread results. Mean RMS delay spread values remain relatively constant throughout all NLOS measurements. RMS delay spread is typically expected to increase with increasing transmitter-receiver separation; however, separation only varied between 135 feet and 205 feet. This consistency of RMS delay spread suggests that the measured region is well characterized by a single RMS delay spread value (e.g., the mean value). Single, large RMS delay spread values occurred on a channel when the strongest, early-arriving multipath components faded simultaneously. Fading of the dominant components cause weaker, late-arriving components to contain a larger percentage of the composite signal energy. RMS delay spreads as large as 368 ns were measured, over five times the average RMS delay spread for NLOS locations.

RMS delay spread values were also computed for each power-delay profile on each channel for every LOS location. Table 5-18 provides the mean, standard deviation, minimum, and maximum RMS delay spreads for all channels and locations. Figure 5-16 through Figure 5-19 show CCDF plots of RMS delay spread for all LOS locations.

It was observed that RMS delay spread was smaller for LOS locations compared to NLOS locations, a result consistent with expectations. Unobstructed LOS signal components are typically strong compared to components with larger delays, resulting in relatively smaller RMS delay spreads. Table 5-17 summarizes RMS delay spread for the entire site. The mean LOS RMS delay spread was shown to be nearly half of that for NLOS locations.

Table 5-17. Summary of RMS delay spread results for dense-scatterer measurement site. Location Mean RMS Delay Spread NLOS locations 69.6 ns LOS locations 36.6 ns All dense-scatter site locations 53.1 ns

156 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-18. RMS delay spread results for LOS locations for the dense-scatterer measurement campaign. Location Channel RMS Delay Spread (ns) Mean Std. Dev. Minimum Maximum LOS1 1 34.5 5.13 23.5 48.8 2 32.7 4.66 21.4 42.0 3 33.2 3.82 24.0 43.9 4 37.4 4.11 28.2 51.2 All 34.4 4.81 21.4 51.2 LOS2 1 36.2 6.49 22.8 54.7 2 36.7 7.07 21.6 53.8 3 39.0 7.26 23.3 63.2 4 43.5 9.96 0.00 73.3 All 38.8 8.31 0.00 73.3 LOS3 1 37.8 10.9 22.2 73.9 2 36.7 12.3 20.1 91.8 3 39.2 12.7 22.5 84.3 4 42.3 12.0 25.7 86.1 All 39.0 12.1 20.1 91.8 LOS4 1 34.6 8.7 16.9 69.9 2 32.9 8.5 17.6 65.1 3 34.7 9.4 19.2 61.9 4 34.6 8.1 19.6 56.9 All 34.2 8.7 16.9 69.9

157 CHAPTER 5 – CHANNEL MEASUREMENTS

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-16. RMS delay spread CCDF for LOS1.

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-17. RMS delay spread CCDF for LOS2.

158 CHAPTER 5 – CHANNEL MEASUREMENTS

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-18. RMS delay spread CCDF for LOS3.

RMS Delay Spread Based On Measurements 1 Channel 1 0.9 Channel 2 Channel 3 0.8 Channel 4

0.7

0.6

0.5

0.4

0.3

0.2

Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 20 40 60 80 100 120 RMS Delay Spread (ns)

Figure 5-19. RMS delay spread CCDF for LOS4.

159 CHAPTER 5 – CHANNEL MEASUREMENTS

5.3.3 Multipath Excess Delay Spread

Excess delay spread is defined to be the largest difference in delay between multipath components that are within a particular dB level below the strongest received multipath component. Excess delay spread gives insight into the largest excess delay associated with strong multipath components. Excess delay spread was calculated from the measured power- delay profiles recorded at NLOS and LOS locations. Table 5-19 and Table 5-20 give excess delay spread values for NLOS and NLOS measurements for 10 dB, 20 dB, 25 dB, and 30 dB levels. The means of the values of excess delay spread for NLOS and LOS groups are also shown.

Table 5-19. Excess delay spread values for NLOS locations. Excess Delay Spread (ns) Level 10 dB 20 dB 25 dB 30 dB Mean Max Mean Max Mean Max Mean Max NLOS1 200 480 390 1300 549 1300 682 1500 NLOS2 204 447 328 697 440 811 601 1510 NLOS3 272 580 435 775 581 1250 693 1450 NLOS4 252 572 499 776 615 888 712 1380 NLOS5 243 493 380 747 503 909 637 1210 NLOS6 207 478 367 758 471 1365 620 1450 Mean 230 508 400 842 527 1087 658 1417

Table 5-20. Excess delay values for LOS locations. Excess Delay Spread (ns) Level 10 dB 20 dB 25 dB 30 dB Mean Max Mean Max Mean Max Mean Max LOS1 115 335 196 533 230 725 313 751 LOS2 131 501 233 790 300 790 408 791 LOS3 123 509 222 651 315 835 432 868 LOS4 89.1 421 162 586 263 786 390 861 Mean 115 442 203 640 277 784 386 818

160 CHAPTER 5 – CHANNEL MEASUREMENTS

5.3.4 Distribution of Multipath Components

Distribution of multipath components over excess propagation delay is illustrated in the following normalized histograms and tables. These results are useful for implementing and evaluating geometric channel models based on scatterer sub-regions. Results showing average number of signal components per channel are useful for wideband channel modeling in general.

Figure 5-20 through Figure 5-25 show normalized histograms of the number of multipath signal components for NLOS locations. The first histogram bin begins at 0 ns excess delay, and the last bin ends at the largest measured multipath excess delay measured for each location. Each bin width is approximately 100 ns. The first bar (leftmost bar) in each bin represents the average number of multipath components per profile in that bin. The following four bars in each bin correspond to the average number of multipath components per profile for each channel. The count of multipath components in each bin includes all detectable components above the power- delay profile noise threshold. Figure 5-26 through Figure 5-29 show normalized histograms of measured multipath components for LOS locations.

Average number of signal components per delay bin 3.5 All Channels 3 Channel 1 Channel 2 Channel 3 2.5 Channel 4

2

1.5

1

Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-20. Average number of signal components using 16 delay bins for NLOS1.

161 CHAPTER 5 – CHANNEL MEASUREMENTS

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-21. Average number of signal components using 16 delay bins for NLOS2.

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-22. Average number of signal components using 16 delay bins for NLOS3.

162 CHAPTER 5 – CHANNEL MEASUREMENTS

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-23. Average number of signal components using 16 delay bins for NLOS4.

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-24. Average number of signal components using 16 delay bins for NLOS5.

163 CHAPTER 5 – CHANNEL MEASUREMENTS

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-25. Average number of signal components using 16 delay bins for NLOS6.

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-26. Average number of signal components using 16 delay bins for LOS1.

164 CHAPTER 5 – CHANNEL MEASUREMENTS

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-27. Average number of signal components using 16 delay bins for LOS2.

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-28. Average number of signal components using 16 delay bins for LOS3.

165 CHAPTER 5 – CHANNEL MEASUREMENTS

Average number of signal components per delay bin 4 All Channels 3.5 Channel 1 Channel 2 3 Channel 3 Channel 4 2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-29. Average number of signal components using 16 delay bins for LOS4.

NLOS Measurements - Average number of signal components per delay bin 4 All Channels (1 through 4) 3.5

3

2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-30. Average number of signal components using 16 delay bins for all NLOS measurements.

166 CHAPTER 5 – CHANNEL MEASUREMENTS

LOS Measurements - Average number of signal components per delay bin 4 All Channels (1 through 4) 3.5

3

2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-31. Average number of signal components using 16 delay bins for all LOS measurements.

Table 5-21. Average number of signal components per delay bin per profile for NLOS measurements. Delay Range (ns) Average number of signal components per delay bin per profile 0 – 99 3.54 99 – 199 2.96 199 – 298 2.99 298 – 397 2.90 397 – 496 2.76 496 – 596 2.63 596 – 695 2.07 695 – 794 0.937 794 – 893 0.337 893 – 993 0.259 993 – 1092 0.193 1092 – 1191 0.104 1191 –1290 0.0560 1290 – 1390 0.0480 1390 – 1489 0.0407 1489 – 1588 0.00803

167 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-22. Average number of signal components per delay bin per profile for LOS measurements. Delay Range (ns) Average number of signal components per delay bin per profile 0 – 97 3.59 97 – 194 2.87 194 – 292 2.67 292 – 389 2.39 389 – 487 1.21 487 – 584 1.65 584 – 681 0.430 681 – 779 0.0569 779 – 876 0.0997 876 – 973 0.0596 973 – 1070 0.0401 1070 – 1168 0.0218 1168 –1265 0.0101 1265 – 1363 0.220 1363 – 1460 0.0187 1460 – 1557 0.00312

Measurements for all NLOS locations were combined to form the histogram shown in Figure 5-30 and the results shown in Table 5-21. Figure 5-31 and Table 5-22 show the combined results for LOS locations. Results for both NLOS and LOS locations suggest a non-uniform distribution of measurable multipath components that must be handled by channel models. While an appropriate channel model may still use a uniform distribution of scatterers over a region, the resulting simulated channel impulse responses must show a decrease of significant components with increasing delay. Compared to measured NLOS power-delay profiles, LOS power-delay profiles have the same number of detectable multipath components in the first bin but generally fewer components in bins representing longer delays. Given the resolution of the measurement system and the processing technique used, approximately four components is the maximum number of detectable multipath components in each bin.

168 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-23 shows the average number of measured signal components per power-delay profile over the entire excess delay range. Results for NLOS locations, LOS locations, and the entire dense-scatterer site are shown.

Table 5-23. Average number of signal components per power-delay profile for LOS and NLOS measurements. Measurement Type Average number of signal components per profile NLOS 21.8 LOS 15.3 NLOS and LOS combined 19.6

5.3.5 Strength of Multipath Components Versus Delay

The strengths of multipath components propagating along a path in a geometric channel model can be related using the log-distance path loss model [Lib95]. In this section, a method of computing the path loss exponent given measured power-delay profiles is derived.

Using the log-distance path loss model, the received power in dB-units (e.g., dBm or dBW) of a signal propagating over distance d is given by

æ d ö P = P -10nlog ç ÷ - L r ref 10 ç ÷ ( 5.18 ) è dref ø where Pref is a reference power measured at distance dref. The factor L is a fixed loss not experienced during the Pref measurement, such as a reflection loss if the signal is a single-bounce multipath component,. Distance can be replaced by absolute (not relative) propagation delay using

æ ct ö P = P -10nlog ç ÷ - L r ref 10 ç ÷ ( 5.19 ) è ct ref ø

yielding the expression for a log-time model given by

169 CHAPTER 5 – CHANNEL MEASUREMENTS

æ t ö P = P -10nlog ç ÷ - L . r ref 10 ç ÷ ( 5.20 ) èt ref ø

This expression is equivalently expressed as

Pr = Pref -10nlog10 (t ) +10nlog10 (t ref )- L . ( 5.21 )

Let Pr1 and Pr 2 be the power of multipath components arriving at a receiver with absolute

propagation delays t 1 and t 2 , respectively, where t 2 > t 1 . The power of each component is given by

Pr1 = Pref -10nlog10 (t1 ) +10nlog10 (t ref )- L ( 5.22 )

and

Pr 2 = Pref -10nlog10 (t 2 ) +10nlog10 (t ref )- L . ( 5.23 )

The difference in power in dB is given by

Pr 2 - Pr1 = -10nlog10 (t 2 ) +10nlog10 (t 1 ) ( 5.24 ) simplifying to

Pr 2 - Pr1 = -(10n log10 (t 2 )-10nlog10 (t 1 )) ( 5.25 ) and

Pr 2 - Pr1 = -10n(log10 (t 2 ) - log10 (t 1 )). ( 5.26 )

The ratio of power differences (in dB) to log-delay differences is given by

P - P r 2 r1 = -10n ( 5.27 ) log10 (t 2 ) - log10 (t 1 )

The path loss exponent can be isolated in the equation by expressing the relationship as

1 æ Pr 2 - Pr1 ö n = - ç ÷ . ( 5.28 ) 10 è log10 (t 2 ) - log10 (t 1 )ø

170 CHAPTER 5 – CHANNEL MEASUREMENTS

As shown in Figure 5-32, the expression in parentheses is actually the slope of the line connecting the components on a power (dB) versus log10 (t ) plot.

P - P slope = m = r 2 r1 log10 (t 2 )- log10 (t1 )

Pr1

Pr 2 Relative Power [dB]

t1 t 2 Log (Absolute Propagation Delay [sec]) 10

Figure 5-32. Relationship between two multipath components arriving with different delays with all other factors held constant.

This slope, defined as m, is given explicitly by

P - P m = r 2 r1 . ( 5.29 ) log10 (t 2 )- log10 (t 1 )

Therefore, in the ideal case, the path loss exponent n can be related to the slope m of the power

(dB) versus log10 (t ) using the equation

1 n = - m . ( 5.30 ) 10

Since a constant dB value can be added to both multipath components without affecting the slope, the power axis of the plot can be relative power units (e.g., dB) rather than absolute power units (e.g., dBm or dBW).

The power versus log-delay line must also be characterized by an intercept point in addition to a slope. A convenient intercept point to use is the value of the line where log10 (t ) = 0. If units of seconds are used, then the intercept point occurs at 1-second (where log10 (t ) = 0). The value B

171 CHAPTER 5 – CHANNEL MEASUREMENTS

is defined to be the power value at the 1-second intercept. Using this definition, the equation of the power versus log-delay line is given by

P(t ) = mlog10 (t )+ B . ( 5.31 )

In actual propagation environments, factors such as shadowing, reflection loss differences, and fading of resolvable components will cause multipath component strengths to deviate from the theoretical power versus log-delay line. Each factor may impose its own statistical distribution on signal strength. For example, shadowing may follow a log-normal distribution, and fading may follow a Rayleigh or Rician distribution. Here, the composite deviation is modeled by a

2 zero-mean, log-normal random variable Gs with variance s P (or standard deviation s P ). Assuming this distribution, the power (in dB-units) of measured multipath components is given by

P(t ) = mlog10 (t )+ B + Gs . ( 5.32 )

For each location, the slope m and intercept B of the best-fit line (in the least-squares sense) through signal component powers of each power-delay profile were computed. The standard deviation s P of the component strengths about the corresponding line values was also computed. Figure 5-33 through Figure 5-44 show three plots for each location NLOS1 through NLOS6. The first plot in each set shows a scatter plot of magnitudes of all of the detected multipath components and the best-fit line on a power versus log-delay plot. The second plot shows a histogram of the deviation of multipath component power from the best-fit line. The third plot shows a normalized histogram overlaid on a theoretical Gaussian probability density function, where the zero-mean Gaussian PDF was calculated using the variance computed from the corresponding measurements of deviation from the best-fit line.

172 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 700

600

500

400

300 Occurences

200

100

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-33. NLOS1 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.09 Measured 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-34. NLOS1: PDF created using data points and corresponding theoretical Gaussian distribution.

173 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 600

500

400

300 Occurences 200

100

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-35. NLOS2 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.09 Measured 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-36. NLOS2: PDF created using data points and corresponding theoretical Gaussian distribution.

174 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 600

500

400

300 Occurences 200

100

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-37. NLOS3 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.08 Measured Gaussian 0.07

0.06

0.05

0.04 PDF

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-38. NLOS3: PDF created using data points and corresponding theoretical Gaussian distribution.

175 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 600

500

400

300 Occurences 200

100

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-39. NLOS4 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.09 Measured 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-40. NLOS4: PDF created using data points and corresponding theoretical Gaussian distribution.

176 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 800

700

600

500

400

Occurences 300

200

100

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-41. NLOS5 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.12 Measured Gaussian 0.1

0.08

0.06 PDF

0.04

0.02

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-42. NLOS5: PDF created using data points and corresponding theoretical Gaussian distribution.

177 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 2500

2000

1500

Occurences 1000

500

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-43. NLOS6 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.1 Measured 0.09 Gaussian

0.08

0.07

0.06

0.05 PDF

0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-44. NLOS6: PDF created using data points and corresponding theoretical Gaussian distribution.

178 CHAPTER 5 – CHANNEL MEASUREMENTS

Normalized histogram results for all NLOS measurements visually show a similarity to the associated Gaussian PDFs. The NLOS measurement location where the largest number of power-delay profiles were logged, NLOS6, shows the best fit to the Gaussian PDF. Scatter plots for NLOS1 through NLOS4 show a nonlinear trend of signal component magnitude that deviates from the best-fit lines for early delays. This trend may be caused by non-uniform distribution of scatterers or dissimilar distributions of factors such as reflection coefficients among scatterers. NLOS5 and NLOS6 show a more linear trend of multipath component power versus log-delay.

Table 5-24 shows path loss exponent, standard deviation, and 1-second intercept points calculated from the measured multipath components at NLOS locations. The path loss exponents computed from the multipath strengths are large compared to path loss exponents expected for narrowband measurements in the same environment. A fundamental difference is that traditional path loss exponents are based on local averages of composite signals comprising many multipath components. For the case here, however, magnitude measurements at a particular delay on the plot correspond to a single or possibly small number of multipath components, which is a different physical scenario.

Table 5-24. Path loss exponent, standard deviation of multipath strength about best-fit line, and intercept of best-fit line for NLOS measurements. Location Path Loss Exponent Standard deviation 1-second t intercept n about best-fit line point B (dB)

s P (dB) NLOS1 5.10 4.72 -341 NLOS2 5.22 5.42 -350 NLOS3 4.79 5.46 -320 NLOS4 4.30 5.46 -287 NLOS5 5.01 4.20 -337 NLOS6 4.55 4.41 -309

179 CHAPTER 5 – CHANNEL MEASUREMENTS

Figure 5-45 through Figure 5-52 show the scatter plots, histograms, and probability density functions for the LOS measurements. The scatter plots show dense areas of signal components at discrete times, suggesting that a few multipath components dominated the power delay profiles throughout the measurements at each location. The LOS histograms follow the Gaussian distribution less closely than those for the NLOS measurements, but in general the assumption of a Gaussian distribution still appears valid.

180 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 350

300

250

200

150 Occurences

100

50

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-45. LOS1 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.08 Measured Gaussian 0.07

0.06

0.05

0.04 PDF

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-46. LOS1: PDF created using data points and corresponding theoretical Gaussian distribution.

181 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 400

350

300

250

200

Occurences 150

100

50

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-47. LOS2 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.09 Measured 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-48. LOS2: PDF created using data points and corresponding theoretical Gaussian distribution.

182 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 400

350

300

250

200 Occurences 150

100

50

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-49. LOS3 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.08 Measured Gaussian 0.07

0.06

0.05

0.04 PDF

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-50. LOS3: PDF created using data points and corresponding theoretical Gaussian distribution.

183 CHAPTER 5 – CHANNEL MEASUREMENTS

Histogram of differences between measured multipath strength and best-fit line 500

450

400

350

300

250

Occurences 200

150

100

50

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 5-51. LOS4 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

PDF of differences between measured multipath strength and best-fit line 0.09 Measured 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB)

Figure 5-52. LOS4: PDF created using data points and corresponding theoretical Gaussian distribution.

184 CHAPTER 5 – CHANNEL MEASUREMENTS

The best-fit line for each location was computed by removing the first-arriving component, which was assumed to be the LOS component. In order to relate the strength of the LOS component to the strength of the later-arriving components (for LOS locations), the power of the LOS component relative to the value of the best-fit line at the LOS delay was calculated. This parameter can be used in modeling LOS channels based on this measurement data.

Table 5-25 shows the path loss exponent, standard deviation of measured multipath strength about the best-fit line, 1-second intercept point for the best-fit line, and average strength (in dB) of the LOS component above the best-fit line for the LOS measurement data.

Table 5-25. Path loss exponent, standard deviation of multipath strength about best-fit line, intercept of best- fit line, and LOS strength above best-fit line for LOS measurements. Location Path Loss Standard 1-second t LOS component Exponent n deviation about intercept point dB above best-

best-fit line s P B (dB) fit line (dB) (dB) LOS1 5.16 5.65 -357 10.9 LOS2 4.44 5.29 -313 8.63 LOS3 3.52 5.07 -255 12.5 LOS4 3.27 4.95 -242 9.95

Table 5-26 summarizes the results for all NLOS measurements and LOS measurements, individually and combined. The results show that LOS measurements exhibited a slightly larger path loss exponent and standard deviation compared to NLOS measurements. However, because the values are relatively close, it appears that a single path loss exponent and standard deviation can be used to characterize the site for both NLOS and LOS propagation, while simulations of LOS will include an additional signal component, namely the LOS components 10.5 dB higher than the best-fit line for the other multipath components.

185 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-26. Summary of multipath strength results for all measurements at the dense-scatterer site. Location Path Loss Exponent Standard deviation LOS component dB n about best-fit line above best-fit line

s P (dB) (dB) All NLOS 4.83 4.95 N/A All LOS 4.10 5.24 10.5 NLOS and LOS 4.54 5.06 N/A

5.3.6 Multipath Strength Correlation Coefficients Versus Delay

The measurements for NLOS6, which had the greatest number of measured power-delay profiles compared to other locations within the site, were processed to produce the correlation coefficients using the technique described in section 5.2.4 for 4, 8, and 16 propagation delay bins. Results are shown in Table 5-27 through Table 5-29. Although the results presented here seem to suggest decreasing correlation coefficients with increasing delay, measurement results in section 5.2.4 show that high correlation coefficients can exist in any delay bin, and there is not necessarily a consistent trend of monotonically increasing or decreasing values of correlation coefficients versus delay.

Differences in correlation coefficients among antenna pairs may also be affected by mutual coupling of antenna elements causing a dissimilar pattern of antenna elements across the array, in effect causing antenna pattern diversity. The measured correlation coefficients can be used to simulate vector channels for antenna arrays used in wideband systems.

186 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-27. NLOS Measurement Results (4 propagation delay bins). Delay Delay Correlation Coefficients Number of Bin Range (ns) Signal r12 r13 r14 r 23 r24 r 34 No. Components* 1 0-210 0.62942 0.62743 0.63907 0.63846 0.64184 0.64700 1657 2 210-421 0.47263 0.46657 0.52647 0.44548 0.45981 0.45714 2290 3 421-632 0.39867 0.36148 0.35690 0.36105 0.40892 0.29867 1136 4 632-843 0.14801 0.17851 0.12146 0.23415 0.18314 0.07175 152 Element Spacing l/2 l 3l/2 l/2 l l/2

Table 5-28. NLOS Measurement Results (8 propagation delay bins). Delay Delay Correlation Coefficients Number of Bin Range Components r12 r13 r14 r 23 r24 r 34 No. (ns) Signal* 1 0-105 0.73226 0.75130 0.71784 0.75499 0.76941 0.74555 492 2 105-210 0.52076 0.49964 0.55326 0.49363 0.48532 0.52334 1165 3 210-316 0.41198 0.36025 0.46810 0.40410 0.42581 0.41246 1142 4 316-421 0.32740 0.33451 0.33983 0.29788 0.29004 0.26510 1148 5 421-526 0.37857 0.34494 0.30520 0.41893 0.42646 0.32013 742 6 526-632 0.15214 0.17750 0.17262 0.02548 0.09292 0.00701 394 7 632-737 0.10679 0.15660 0.09025 0.20518 0.14112 0.05062 146 8 737-843 0.66539 0.12377 0.80588 -0.06541 0.65434 -0.09817 6 Element Spacing l/2 l 3l/2 l/2 l l/2

187 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-29. NLOS Measurement Results (16 propagation delay bins). Delay Delay Correlation Coefficients Number of Bin Range Components* r12 r13 r14 r 23 r24 r 34 No. (ns) 1 0-52 0.73780 0.80110 0.79264 0.75896 0.75246 0.83875 105 2 52-105 0.73068 0.74236 0.69963 0.75611 0.77685 0.72228 387 3 105-158 0.48077 0.43925 0.53715 0.42056 0.46994 0.47399 576 4 158-210 0.41665 0.40293 0.45802 0.46148 0.40721 0.48109 589 5 210-263 0.51223 0.39676 0.49171 0.43342 0.47014 0.43788 558 6 263-316 0.20517 0.21916 0.37548 0.25516 0.26969 0.29113 584 7 316-368 0.23466 0.28203 0.23221 0.22723 0.20330 0.17199 617 8 368-421 0.39035 0.30464 0.39947 0.32989 0.35294 0.30345 531 9 421-474 0.35500 0.34197 0.24475 0.43696 0.42898 0.32293 445 10 474-526 0.21663 0.12871 0.23244 0.16183 0.22856 0.09367 297 11 526-579 0.17773 0.24197 0.24641 0.01270 0.08605 0.05355 228 12 579-632 0.10884 0.10486 0.06676 0.05029 0.10112 -0.05999 166 13 632-684 0.04007 0.14786 0.12432 0.23377 0.08294 0.04031 108 14 684-737 0.24986 0.08046 -0.10462 -0.04656 0.16377 -0.01461 38 15 737-790 0.61112 0.55191 0.82011 0.20992 0.6381 0.73777 5 16 790-843 ** ** ** ** ** ** 1 Element Spacing l/2 l 3l/2 l/2 l l/2 * Signal components detected within 1544 power-delay profiles. ** Only one component in delay bin; correlation coefficient undefined.

5.4 Air-to-Ground Measurement Campaign

An air-to-ground measurement campaign was performed to characterize the wideband air-to- ground radio channel, to provide parameter input for the geometric air-to-ground channel model, and to provide measurement data for evaluation of the geometric air-to-ground channel model. Measurement results presented in this section apply to simulation and analysis of air-to-ground communications for applications such as UAVs and airborne network nodes.

188 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-30. Link budget calculations for each of the four elevation angles measured.

Measurement Pattern 1 Measurement Pattern 2 Locations Data Locations Data Input Param Output Param Units Value Input Param Output Param Units Value Range nm 1.8 Range nm 0.9 Altitude (MSL) ft 3,590 Altitude (MSL) ft 3,620 Ground Elev ft 2,150 Ground Elev ft 2,150 Altitude (AGL) ft 1,440 Altitude (AGL) ft 1,470 Range m 3,333.6 Range m 1,666.8 Altitude m 438.9 Altitude m 448.1 T-R m 3,362.4 T-R m 1,726.0 Elev. Angle deg 7.5 Elev. Angle deg 15.0 Path Loss Data Path Loss Data Freq Hz 2.05E+09 Freq Hz 2.05E+09 PL exp - 2 PL exp - 2 Ref dist m 1 Ref dist m 1 Ref PL dB 38.7 Ref PL dB 38.7 Path Loss dB 109.21 Path Loss dB 103.42 System Gains and Losses System Gains and Losses Tx Power dBm 27 Tx Power dBm 27 Rx Ant Gain dB 0 Rx Ant Gain dB 0 Tx Ant Pattern dB 2.04 Tx Ant Pattern dB 1.71 Total Losses dB 0 Total Losses dB 0 Rx Power dBm -80.2 Rx Power dBm -74.7 Measurement Pattern 3 Measurement Pattern 4 Locations Data Locations Data Input Param Output Param Units Value Input Param Output Param Units Value Range nm 0.9 Range nm 0.9 Altitude (MSL) ft 4,420 Altitude (MSL) ft 5,310 Ground Elev ft 2,150 Ground Elev ft 2,150 Altitude (AGL) ft 2,270 Altitude (AGL) ft 3,160 Range m 1,666.8 Range m 1,666.8 Altitude m 691.9 Altitude m 963.2 T-R m 1,804.7 T-R m 1,925.1 Elev. Angle deg 22.5 Elev. Angle deg 30.0 Path Loss Data Path Loss Data Freq Hz 2.05E+09 Freq Hz 2.05E+09 PL exp - 2 PL exp - 2 Ref dist m 1 Ref dist m 1 Ref PL dB 38.7 Ref PL dB 38.7 Path Loss dB 103.80 Path Loss dB 104.37 System Gains and Losses System Gains and Losses Tx Power dBm 27 Tx Power dBm 27 Rx Ant Gain dB 0 Rx Ant Gain dB 0 Tx Ant Pattern dB 1.16 Tx Ant Pattern dB 0.38 Total Losses dB 0 Total Losses dB 0 Rx Power dBm -75.6 Rx Power dBm -77.0

189 CHAPTER 5 – CHANNEL MEASUREMENTS

5.4.1 Measurement Overview

Measurements were performed for radio channels between the airspace over Blacksburg, Virginia and a ground location on the Virginia Tech campus. Four different elevation angles from the receiver were measured, where the elevation angle is defined to be the angle between the horizon and the aircraft as viewed from the receiver location.

Tx Antenna

Figure 5-53. Location of the transmitter antenna under aircraft fuselage and wing.

Figure 5-54. Ground location of the receiver array for the air-to-ground measurements.

A link budget was used to provide rough estimates of received power and to plan the possible elevation angles and flight paths. The link budgets for the four elevation angles are shown in Table 5-30. Constant altitude, circular flight paths around the receiver were chosen such that the received power of a line-of-sight signal component was equal to or greater than approximately – 80 dBm. A flight altitude above mean sea level (MSL) was chosen based on the altitude above ground level (AGL) and ground range required for the selected elevation angles.

190 CHAPTER 5 – CHANNEL MEASUREMENTS

Figure 5-53 illustrates the location of the transmitter antenna on the aircraft. A vertically polarized, monopole antenna was temporarily placed under the fuselage near the right wing for the measurements, where minimal obstructions and a large ground plane were present. Figure 5-54 illustrates the site of the receiver array among buildings on the Virginia Tech campus. Buildings up to four stories and automobiles surrounded the receiver location. A GPS waypoint was recorded at the receiver location, and the aircraft was flown at constant radii around the GPS waypoint during measurements.

5.4.2 Multipath RMS Delay Spread

RMS delay spread was calculated for all power-delay profiles. RMS delay spread results divided among channels and elevation angles are shown in Table 5-31. Figure 5-55, Figure 5-56, Figure 5-57, and Figure 5-58 show sample power-delay profiles measured for each elevation angle.

Table 5-31. RMS delay spread results for the air-to-ground measurement campaign. Elevation Channel RMS Delay Spread (ns) Angle (deg) Mean Std. Dev. Minimum Maximum 7.5 1 104 90.2 0 485 2 102 83.5 0 498 3 93.2 80.4 0 545 4 92.8 73.5 0 452 All 98.1 82.2 0 545 15 1 55.7 41.8 0 315 2 54.0 36.9 0 288 3 54.9 38.5 4.45 356 4 54.8 44.9 2.51 560 All 54.9 40.6 0 560 22.5 1 24.8 18.9 3.02 216 2 23.8 14.1 3.50 141 3 23.3 15.5 3.50 154 4 25.1 18.0 2.75 206 All 24.3 16.7 2.75 216 30 1 18.7 10.3 2.00 57.4 2 18.2 9.42 2.83 64.9 3 17.1 9.28 1.10 53.8 4 19.4 10.4 3.44 75.0 All 18.3 9.89 1.10 75.0

191 CHAPTER 5 – CHANNEL MEASUREMENTS

Power Delay Profile - Magnitude 5

0

-5

-10

-15

-20

-25

-30 Multipath Strength (dB) -35

-40

-45

-50 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Delay (us)

Figure 5-55. Sample power-delay profile for 7.5 degree elevation angle.

Power Delay Profile - Magnitude 5

0

-5

-10

-15

-20

-25

-30 Multipath Strength (dB) -35

-40

-45

-50 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Delay (us)

Figure 5-56. Sample power-delay profile for 15 degree elevation angle.

192 CHAPTER 5 – CHANNEL MEASUREMENTS

Power Delay Profile - Magnitude 5

0

-5

-10

-15

-20

-25

-30 Multipath Strength (dB) -35

-40

-45

-50 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Delay (us)

Figure 5-57. Sample power-delay profile for 22.5 degree elevation angle.

Power Delay Profile - Magnitude 5

0

-5

-10

-15

-20

-25

-30 Multipath Strength (dB) -35

-40

-45

-50 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Delay (us)

Figure 5-58. Sample power-delay profile for 30 degree elevation angle.

193 CHAPTER 5 – CHANNEL MEASUREMENTS

RMS Delay Spread Based On Measurements 1

0.9 Channel 1 Channel 2 0.8 Channel 3 Channel 4 0.7

0.6

0.5

0.4 7.5 deg 0.3 15 deg 0.2 22.5 deg Probability( RMS Delay Spread > Abscissa ) 0.1 30 deg 0 0 20 40 60 80 100 120 140 160 180 200 RMS Delay Spread (ns)

Figure 5-59. RMS delay spread CCDF for all measured elevation angles.

Figure 5-59 shows CCDF plots of RMS delay spread for elevation angles of 7.5, 15, 22.5, and 30 degrees on a single figure. The measurements show a trend of increasing RMS delay spread as elevation angle is decreased from 30 degrees to 7.5 degrees. This trend is corroborated by past air-to-ground measurement results presented in section 5.1.2. RMS delay spreads in excess of 500 ns were observed for the 7.5 and 15 degree elevation angles.

5.4.3 Multipath Excess Delay Spread

Excess delay spread was calculated for each elevation angle using all measured power-delay profiles. Table 5-32 shows mean and maximum excess delay spread values for 10 dB, 20 dB, 25 dB, and 30 dB levels. The excess delay spread results show that mean excess delay spread increases with decreasing elevation angle, a trend similar to that of RMS delay spread.

194 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-32. Excess delay spread values for air-to-ground measurements. Excess Delay Spread (ns) Level 10 dB 20 dB 25 dB 30 dB Mean Max Mean Max Mean Max Mean Max 7.5 deg 169 1380 431 1490 613 1550 703 1570 15 deg 104 1300 250 1480 407 1480 595 1590 22.5 deg 90.0 1031 127 1294 199 1294 352 1407 30 deg 89.0 256 108 471 157 1290 284 1340 Mean 113 992 229 1180 344 1400 484 1480

5.4.4 Distribution of Multipath Components

The distribution of multipath components over excess propagation delay was examined in a manner similar to that of section 5.3.4. The histograms in Figure 5-60 through Figure 5-63 show the average number of signal components per delay bin per profile for each channel and for all channels combined. One normalized histogram is plotted per elevation angle measured.

Figure 5-64 shows normalized histograms for each elevation angle and combined elevation angles on the same plot. The largest measured multipath excess delay was 1556 ns. The excess delay range was divided into 16 bins, resulting in bin widths of approximately 97 ns. Figure 5-65 and Table 5-33 show results for all elevation angles combined. It is interesting to note that the number of multipath components for a particular excess delay bin does not vary greatly as elevation angle is changed.

195 CHAPTER 5 – CHANNEL MEASUREMENTS

Average number of signal components per delay bin 3 All Channels Channel 1 2.5 Channel 2 Channel 3 Channel 4 2

1.5

1

Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-60. Average number of signal components using 16 delay bins for 7.5 degree elevation angle.

Average number of signal components per delay bin 3.5 All Channels 3 Channel 1 Channel 2 Channel 3 2.5 Channel 4

2

1.5

1

Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-61. Average number of signal components using 16 delay bins for 15 degree elevation angle.

196 CHAPTER 5 – CHANNEL MEASUREMENTS

Average number of signal components per delay bin 3.5 All Channels 3 Channel 1 Channel 2 Channel 3 2.5 Channel 4

2

1.5

1

Average number of components 0.5

0 0 500 1000 1500 Excess delay (ns)

Figure 5-62. Average number of signal components using 16 delay bins for 22.5 degree elevation angle.

Average number of signal components per delay bin 3.5 All Channels 3 Channel 1 Channel 2 Channel 3 2.5 Channel 4

2

1.5

1

Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-63. Average number of signal components using 16 delay bins for 30 degree elevation angle.

197 CHAPTER 5 – CHANNEL MEASUREMENTS

Average Number of Components

Excess delay (ns)

Figure 5-64. Average number of signal components using 16 delay bins for each elevation angle.

198 CHAPTER 5 – CHANNEL MEASUREMENTS

Air-to-Ground Measurements - Average number of signal components per delay bin 4 All Channels (1 through 4) 3.5

3

2.5

2

1.5

1 Average number of components 0.5

0 0 200 400 600 800 1000 1200 1400 1600 Excess delay (ns)

Figure 5-65. Average number of signal components using 16 delay bins for all air-to-ground measurements.

Table 5-33. Average number of signal components per delay bin per profile for air-to-ground measurements. Delay Range (ns) Average number of signal components per delay bin per profile 0 – 97 2.98 97 – 195 1.53 195 – 292 1.19 292 – 389 0.620 389 – 486 0.404 486 – 584 0.253 584 – 681 0.163 681 – 778 0.156 778 – 875 0.167 875 – 973 0.180 973 – 1070 0.107 1070 – 1167 0.0664 1167 –1264 0.0389 1264 – 1362 0.0228 1362 – 1459 0.00265 1459 – 1556 0.00139

199 CHAPTER 5 – CHANNEL MEASUREMENTS

Table 5-34. Average number of signal components per power-delay profile for each elevation angle measured during air-to-ground measurements. Measurement Type Average number of signal components per profile 7.5 7.54 15 8.61 22.5 7.79 30 7.74 All angles combined 7.88

Table 5-34 summarizes the results for each elevation angle. On average, each power delay profiles contained 7.88 measurable multipath components. Although measurement results in section 5.4.2 showed that RMS delay spread generally increases with decreasing elevation angle, these results show that the number of measured multipath components tends to remain constant with elevation angle. Since the number of multipath components in each delay bin also tend to remain constant as elevation angle changes, this suggests that the strengths of multipath components with long delays become larger as elevation angle decreases.

5.5 Summary

In this chapter, past measurement results and methods have been reviewed, and results and methods of new measurements have been reported. Measurement campaigns at Virginia Tech have produced characterizations of terrestrial and air-to-ground communication environments.

RMS delay spread and excess delay spread statistics were reported. The largest RMS delay spreads (over 1 m s) were observed for the rooftop measurement campaign. Mean RMS delay spread for the rooftop measurements was approximately 120 ns. The dense scatterer campaign showed mean RMS delay spreads of approximately 70 ns for NLOS channels and 37 ns for LOS channels. Mean excess delay spreads for the 20 dB level ranged from approximately 160 ns to 500 ns for the dense scatterer site. Mean RMS delay spreads for air-to-ground channels ranged from 18 ns to 98 ns, and RMS delay spread was shown to increase as elevation angle decreased from 30 degrees to 7.5 degrees. Mean excess delay spread for the 20 dB level for air-to-ground measurements ranged from 108 ns at a 30 degree elevation angle to 431 ns at a 7.5 degree

200 CHAPTER 5 – CHANNEL MEASUREMENTS elevation angle. The maximum excess delay at the 20 dB level was 1490 ns at a 7.5 degree elevation angle.

Distributions of multipath components across excess delay were reported for each campaign. The average number of measurable multipath components per power-delay profile for the rooftop measurements and the dense scatterer measurements was approximately 19, nearly equal for both sites, while RMS delay spread for the rooftop measurements was larger. Fewer multipath components were found in the air-to-ground power delay profiles, where approximately 8 existed on average. For air-to-ground channels, the number of components per power-delay profile was not found to be dependent upon elevation angle.

Correlation coefficients for fading of multipath components across an antenna array were computed for the rooftop measurements and the dense-scatterer measurements. LOS channels showed a high correlation in the first delay bins due to a dominant multipath component. Measurements showed that high correlation could also exist for bins of larger delay.

For the dense scatterer measurements, where measurement data for a number of locations within one environment was recorded, results on multipath strength versus propagation delay were produced. A path loss exponent was computed for each location by determining the best-fit line through measured multipath strengths on a power (dB) versus log-delay axis. The deviation of measured powers from the best-fit line was shown to be approximately Gaussian. The standard deviation of the measured distribution about the best-fit line was reported for each location. For LOS measurements, the mean relative strength of the LOS component compared to the best-fit line of delayed components was reported.

The results of this chapter are useful for analysis and simulation of radio channels. The results can be used as input to channel models and provide a basis for evaluation of channel models.

201 CHAPTER 5 – CHANNEL MEASUREMENTS

This page intentionally left blank.

202 Chapter 6

Wideband Vector Channel Simulation

This chapter describes a channel simulator that was developed based on channel model research and propagation measurements presented in this dissertation. This simulator was used to implement three of the geometric channel models discussed in Chapter 4. An understanding of the simulator is important for interpreting the channel model evaluation results described in Chapter 7. The objective of the channel simulator is to provide a means of producing channel impulse responses for wireless system simulation. The three channel models simulated are the geometrically based single-bounce elliptical (GBSBE) model, the elliptical sub-regions (ESR) model, and the geometric air-to-ground ellipsoidal (GAGE) model.

Presented first is an overview of the simulator architecture. All relevant input parameters are defined and described. Next, geometric relationships between transmitters, receivers, scatterers, and scattering regions are described and illustrated. The methods of computing multipath strength, delay, and direction of arrival are then described for each model. Rayleigh fading, log- normal strength variation, and Poisson distributions for scatterer counts are all used by the simulator to model as accurately as possible the channel behaviors observed and quantified

203 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION during measurements. The description of the simulator provided in this chapter will aid users of the simulation and provide guidance for development of new channel simulators.

6.1 Simulation Overview

The wideband vector channel simulator illustrated in Figure 6-1 simulates wideband vector channels. The simulator uses results of measured signal data as input to produce channel simulations based on geometric channel models. Channel impulse responses, which are represented as magnitude and delays of multipath components, are produced at the output.

ESR ESR Initial Produce Compute GBSBE Parameter GBSBE Geometry Geometry Input Calculations GAGE Plot GAGE Parameters

Computations Based on Physical Paths Compute Compute Apply Log- Apply Array Apply Path Add LOS Apply Log- Apply Array Apply Path Add LOS Normal Element Rayleigh Attenuation Component Normal Element Rayleigh Attenuation Component Variation Positions Fading & Delay Variation Positions Fading & Delay Responses Channel Impulse

Produce Intermediate Plots

Figure 6-1. Block diagram of wideband vector channel simulator.

Figure 6-1 shows all of the major functional components of the channel simulator. The simulator was programmed using MATLAB (see Appendix C for more information), and functional blocks of the source code are divided in a manner similar to the blocks shown in the diagram. Input parameters based on measurements and physical dimensions are used in the “Initial Parameter Calculations” block to determine preliminary simulation parameters, such as wavelength and

204 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION default correlation coefficient matrices, and to verify the validity of input parameters, such as comparing the number of Poisson parameters to the number of geometric sub-regions. In the “Compute Geometry” block, the simulator uses the model specified by the input to generate scatterers and compute distances and angles required for the subsequent blocks. Once the model geometry has been generated, the simulator can plot the locations of all entities and sub-regions in two or three dimensions.

A simulated channel impulse response is produced in stages in the block labeled “Computations Based on Physical Paths.” Each internal block uses the model geometry to produce or affect the strength of multipath components. Details of these processes are discussed in the following sections of this chapter. Several of the blocks can produce intermediate plots of results. This allows the simulation to be incrementally verified and facilitates tuning of parameters to produce accurate results.

Table 6-1 lists the input parameters of the simulator. As discussed in Chapter 4, geometric channel models use the physical configuration of transmitters, receivers, and scatterers to model radio channels. Physical configurations include transmitter-receiver separation, antenna array element positions, and distances to scatterers in the environment. While geometric parameters are the basis for the model, statistical distributions may be used to bind a model to a particular propagation environment. For example, statistical distribution functions may be used to determine locations and numbers of reflecting objects in the environment, and these distribution functions may be linked to measurements performed in a particular environment. Parameters of type “D” shown in the table are typically known or deterministic. Parameters of type “M” are derived from measurements. Parameters marked “A” typically must be assumed because of difficulty in measurement or because exact value for optimum simulation performance is unknown27.

27 For example, the number of sub-regions that produces the best simulation results is not well studied. A larger number of sub-regions may produce more accurate results but greatly increases the number of measurements and amount of processing required to characterize each sub-region.

205 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

Table 6-1. Input parameters used by the wideband vector channel model simulator. Input Parameter Parameter Description Type Model type D ESR, GBSBE, or GAGE. Frequency D Center frequency of operation in Hertz. Antenna element position D Antenna (x,y) coordinates in meters. Transmitter-receiver D Distance between transmitter and receiver in meters. separation Elevation angle D For GAGE model only. Elevation angle (in degrees) toward airborne station as seen from ground station (horizon is 0 degrees and vertical is 90 degrees). Log-distance path loss M Path loss exponent for propagation through ground exponent scatterers (n=2 is free space). Log-distance reference A Reference distance from transmitter within which free- distance space propagation is assumed. Reflection loss A Attenuation in dB of multipath signal experienced at each scatterer. LOS component strength M Offset (in dB) of line-of-sight component above level offset of multipath components compensated for delay. Number of sub-regions A Number of elliptically bounded sub-regions within which scatterers are distributed. Poisson parameters M Mean values of expected number of multipath components in each sub-region. Standard deviation of log- M Standard deviation (in dB) of log-normal random normal strength variation variable used to model variations of multipath strength. Maximum excess delay M Largest multipath delay measured or expected. Rayleigh fading M Correlation coefficients that define the correlation of correlation coefficient Rayleigh fading of multipath components applied to matrix each antenna element. Plot parameters D Flags that determine graphical output of the simulation. D = Parameter is deterministic or a selection chosen by the user. M = Parameter is a measured quantity or based on measurements. A = Parameter is typically assumed or based on assumptions used during measurements.

206 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

6.2 Simulation Geometries

The type of geometry used, namely ESR, GBSBE, or GAGE, is specified as an input to the simulation. Regardless of model type, the purpose of simulating the geometry is to produce coordinates of scatterers relative to the coordinates of the transmitters and receivers. For each scatterer location, a vector from the transmitter to the scatter and a vector from the scatterer to receiver are calculated. The magnitudes of both vectors are used to generate mean multipath strength and delay at the center of the receiver array. The latter vector is used to generate direction off arrival for the receiver array.

6.2.1 Simulating the ESR Model Geometry

For the ESR model, the transmitter and receiver are located on the x-axis (y=0) and x = ± f on a two-dimensional coordinate plane, as shown in Figure 6-2, where f is the focus distance from the center of the ellipses that define the sub-regions. Line-of-sight propagation time is calculated using the specified transmitter-receiver separation and is added to the specified maximum excess delay to obtain the maximum multipath delay (absolute delay between transmitter and receiver along the longest possible single-bounce path). The maximum excess delay is divided equally into the input number of sub-regions. For M sub-regions, there are M+1 bounding ellipses, where the innermost ellipse corresponds to a propagation delay equal to the line-of-sight propagation delay. This first ellipse has a minor axis length of zero, which forms a straight line between the transmitter and receiver and circumscribes zero area, and the outermost ellipse corresponds to the boundary for all scatterers that cause delays less than or equal to the maximum multipath delay. The ellipse major and minor axis parameters (a and b) for each are calculated from the delay of each boundary as described by the equations in section 4.3.2 and section 4.3.4.

207 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

Top View of Propagation Environment 25

20

15

10

5

0

-5 y-coordinate (m) -10

-15

-20

-25 -30 -20 -10 0 10 20 30 x-coordinate (m)

Figure 6-2. Geometry plot produced by the simulator for the ESR model showing a top view of transmitter (+) and receiver (o) locations, elliptical boundaries, scatterer locations, and propagation paths.

Top View of Propagation Environment 25

20

15

10

5

0

-5 y-coordinate (m) -10

-15

-20

-25 -30 -20 -10 0 10 20 30 x-coordinate (m)

Figure 6-3. Geometry plot produced by the simulator for the GBSBE model showing a top view of transmitter (+) and receiver (o) locations, elliptical boundary, scatterer locations, and propagation paths.

208 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

6.2.2 Simulating the GBSBE Model Geometry

The GBSBE geometry is similar to the ESR geometry except that only one region is defined as shown in Figure 6-3. The region is bounded by an outer ellipse corresponding to the maximum multipath delay; scatterers may fall uniformly throughout this region. The simulator uses the ESR software routines to generate the GBSBE geometry by specifying one region for the input. While the GBSBE model seems to be only a special case of the ESR model, the value in evaluating the GBSBE model comes from determining the degradation in performance, if any, of a lower complexity model.

6.2.3 Simulating the GAGE Model Geometry

The GAGE model represents three-dimensional air-to-ground channels rather than two- dimensional terrestrial channels, and while the geometry of the GAGE model is intuitively simple, the calculations of the model geometry are intrinsically more complex than those for the ESR and GBSBE models. As described in section 4.5 beginning on page 101, the model involves using three-dimensional ellipsoids to represent bounding surfaces of constant delay and two-dimensional ellipses to represent bounding lines for ground scatterers. In addition to transmitter-receiver separation and maximum multipath delay, the geometric calculations also require as input an elevation angle from the ground station to the airborne station, where the elevation angle from the ground station to the horizon is zero degrees, and the elevation angle from the ground station straight up is 90 degrees28.

Using methods similar to those of the ESR model, ellipsoidal surfaces that bound sub-regions of scatterers are calculated by dividing the ellipsoidal volume into ellipsoidal sub-volumes. Each one of the ellipsoidal bounding surfaces corresponds to a constant multipath delay. The parameters defining the bounding surfaces are used to compute the parameters of the corresponding ground-level bounding ellipses using the equations derived in section 4.5. Ground-level regions are thereby defined, within which ground-level scatterers are distributed for simulation of the air-to-ground channel.

28 Note that GAGE equations use a variable y, which is the complement of elevation angle, so that El = 90o – y.

209 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

Propagation Environment

1200

1000

800

600 z-coordinate (m)

400

200

0 500

-200 0 200 400 0 600 800 1000 1200 -500

y-coordinate (m)

x-coordinate (m)

Figure 6-4. Geometry plot produced by the simulator for the GAGE model showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 45 degrees.

210 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

Propagation Environment

1800

1600

1400

1200

1000

z-coordinate (m) 800

600

400

200

400

0 200

-400 0 -200 0 -200 200 -400 400

y-coordinate (m)

x-coordinate (m)

Figure 6-5. Geometry plot produced by the simulator for the GAGE model, showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 90 degrees.

211 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

Propagation Environment

600

z-coordinate (m) 0 400

500 200

0 1000 -200

1500 -400

-600 2000 y-coordinate (m)

x-coordinate (m)

Figure 6-6. Geometry plot produced by the simulator for the GAGE model, showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 0 degrees.

Unlike the ESR model, the receiver in the GAGE model is located at x=0 and y=0 on the x-y plane; it is also at z=0 in the three-dimensional coordinate system. As shown in Figure 6-4, the transmitter location falls on the y=0 plane at x and z coordinates determined by the transmitter- receiver separation and elevation angle provided as input. The ground-level elliptical sub- regions, whose parameters were derived from the ellipsoidal bounding surfaces, are depicted in Figure 6-4 on the x-z plane. All bounding ellipses share a common focus at the receiver, but the other focus of each bounding ellipse varies in position depending upon the delay represented by that ellipse29.

Figure 6-4 shows the geometry plot produced by the simulator for an elevation angle of 45 degrees. The limits of elevation angle and the corresponding geometry plots are shown in Figure

29 There is actually one case where ellipses share both foci, which happens when the elevation angle is set to zero degrees. As elevation angle decreases to very small values, the GAGE model converges to the GBSBE (or ESR) model.

212 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

6-5 and Figure 6-6. Figure 6-5 shows the case where the airborne station is directly overhead the ground station at an elevation angle of 90 degrees. In this case, the ground-level boundaries become circular. In Figure 6-6, the elevation angle is zero degrees (i.e., the airborne station is on the ground). The simulation using the geometry in Figure 6-6 produces the same results as the simulation for the GBSBE model (or ESR, depending whether sub-regions are defined) given the same input parameters.

6.3 Multipath Component Distribution, Strength, and Delay

Delay for each propagation path is computed using the propagation distance of each path and the speed of propagation in free space (3x108 m/s). Attenuations for each path are determined using the log-distance path loss model for the specified path loss exponent and reference distance given as input. The details are as follows.

6.3.1 Distribution of Multipath Components in Delay

Within each propagation delay range that defines a scattering region (or sub-region), the distribution of multipath components versus delay is a function of the locations of the scatterers that fall in each region. The number of scatterers generated in each region is based on measurements performed in the type of environment being modeled. The mean value of the number of multipath components measured in a particular region is used as the parameter of a Poisson distribution. A Poisson random number generator is used to produce the number of scatterers that are uniformly distributed throughout each region that has been characterized by measurements. For example, if sixteen regions have been defined for an ESR model, then sixteen measured mean values of multipath component count will be required by the channel simulation.

Uniform distribution of scatterers in each elliptical region is performed by computing a uniform distribution of points within a rectangle that circumscribes the ellipse and eliminating points that fall outside of the elliptical region. Two independent random variables are used to generate the x and y positions of each scatterer. Then, the x-versus-y equation of the ellipse is used to check the position of the scatterer relative to the ellipse. For sub-regions consisting of an inner and outer ellipse, points outside the outer ellipse points inside the inner ellipse eliminated from the

213 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION generated set. Figure 6-7 illustrates a dense distribution of scatterers in the seventh (non-zero area) elliptical region for the GAGE model. Several checks like this were performed to verify correct distribution of scatterers for all models simulated.

Propagation Environment

800

600

400

z-coordinate (m) 200

0 500 0 500 0 1000 -500 1500 y-coordinate (m) x-coordinate (m)

Figure 6-7. Dense uniform distribution of scatterers in the seventh scattering region for the GAGE model.

6.3.2 Multipath Delay

Absolute propagation delay for each simulated multipath component is calculated in two stages. In the first stage, the delay along the two legs of propagation from the transmitter to the center of the receiver array by way of each scatterer is calculated for each scatterer30. The center of the receiver array is defined by the encircled ‘R’ as shown in Figure 6-8(b) for the GBSBE and ESR

models, where the origin of the array element axis xe-ye is located at the focus of the elliptical boundary. Figure 6-9(b) shows the location of the center of the receiver array for the GAGE

model, where the origin of the array element axis xe-ye is located at the origin of the x-y axis. In the second stage of multipath delay calculation, the extra delay imposed by the offset of the array

30 Free-space propagation is assumed, and the delay in seconds is simply the distance in meters divided by 3x108 m/s.

214 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION element from the center of the array is determined. The extra distance is calculated using the vector from the receiver array center to the array element by computing the component of the vector parallel to the propagation path.

It is sometimes necessary to use a measure of phase along with absolute propagation delay. The simulation provides phase for each simulated multipath, which can be calculated using

æ ct abs êct abs úö f = 2p ç - ê ú÷ radians ( 6.1 ) è l ë l ûø

where t abs is the absolute propagation delay and l is the wavelength.

Incident multipath component y ye b S

xe ye R x e x a Transmitter Receiver Array Antennaelement array

Additional delay due to array element position

(a) (b)

Figure 6-8. Absolute propagation delay for the GBSBE and ESR models is calculated using (a) the distance from the transmitter to the center of the receiver array by way of the scatterer and (b) the distance between parallel lines through the receiver array center and the array element drawn orthogonally to the propagation path.

215 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

Additional delay due to array element position y S

ye

Incident multipath ye component

xe x xe T R Ground Airborne

Receiver Top View Transmitter Antenna array (View down from positive z-axis) element

(a) (b)

Figure 6-9. Absolute propagation delay for the GAGE model is calculated using (a) the distance from the transmitter to the center of the receiver array by way of the scatterer and (b) the distance between parallel lines through the receiver array center and the array element drawn orthogonally to the propagation path.

6.3.3 Strength Modeling for ESR and GBSBE

Multipath component strength is simulated based on the distances between the transmitter, scatterers, and receiver and is influenced by reflection loss of the scatterers. A log-distance path loss exponent defines the characteristic of strength versus path distance for each multipath component. Path loss exponent for simulating an environment can be determined from measurements or by comparing the environment to well studied environments for which the path loss exponent is known. Reflection loss is the strength of a multipath component just after reflection relative to the strength of the component just prior to reflection expressed in dB.

Figure 6-10 illustrates the relative strength of multipath components versus delay influenced only by log-distance path loss and reflection loss for a non-line-of-sight channel. Results are shown on both dB-versus-delay and dB-versus-log-delay31 axes. The dB axis shows values of negative path loss to depict relative multipath component power. The dB-versus-delay plot shows a smooth decrease of multipath strength with delay. In the dB versus-log-delay plot, there is an obvious linear trend of multipath component strength, which supports the strength and path loss exponent equations discussed in section 5.3.5. As discussed in section 5.3.5, the slope of the line shown on the plot is a function of the path loss exponent.

31 The log-delay axis values represent absolute propagation delay, not relative delay.

216 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

As in all applications of the log-distance path loss model, the reference distance for a reference path loss must be assumed. Free space propagation (n=2) is assumed between the transmitter and the reference path loss distance; at this distance a breakpoint occurs, and the path loss trend changes to the path loss exponent specified for the model. Reference distances approximately equal to the mean distance between the transmitter and the closest scatterers surrounding the transmitter are appropriate. Reference distances should be larger than the far-field distance, which is a function of physical antenna extent and wavelength.

Reflection loss affects all reflected multipath components equally since all reflected multipath components experience a single bounce by a scatterer assumed to have the same reflection loss exhibited by all other scatterers. As such, changing the reflection coefficient has the effect of adding or subtracting a single dB value from all components shown on the plot, simply translating all components up or down on the plot.

Relative Multipath Strength Versus Delay -130

-140

-150

-160

-170

(Negative) Path Loss (dB) -180 200 400 600 800 1000 1200 1400 1600 1800 Absolute Propagation Delay (ns) -130

-140

-150

-160

Magnitude (dB) -170

-180 -6.7 -6.6 -6.5 -6.4 -6.3 -6.2 -6.1 -6 -5.9 -5.8 -5.7 log (Absolute Propagation Delay [sec]) 10

Figure 6-10. Typical strength-versus-delay plot (ESR model) for a channel impulse response affected only by log-distance path loss and reflection loss (non-line-of-sight channel).

217 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

6.3.4 Strength Modeling for GAGE

The propagation environment for air-to-ground channels causes multipath attenuation to occur differently compared to terrestrial channels because of distance differences in free-space propagation legs. Figure 6-11 illustrates the air-to-ground propagation environment with two scatterers. The first multipath component follows a path from the transmitter to Scatterer 1 to the ground receiver. The second multipath component follows a path that reflects off of Scatterer 2 to the receiver. Each reflected propagation path experiences the same reflection loss at the scatterers for this explanation. Both Scatterer 1 and Scatterer 2 lie on the ground-level constant-delay ellipse32, which means that both multipath components have the same propagation delay. While the line-of-sight component (if it is not obstructed) experiences a single leg of free- space propagation, each reflected multipath component experiences an air leg and a ground leg. Air legs experience free-space propagation, but ground legs can be modeled by the log-distance path loss model because of the presence of ground-level obstructions.

For ESR and GBSBE terrestrial models, the influence of log-distance path loss and uniform reflection loss causes two multipath components with the same delay to experience the same attenuation because the same distance through n ¹ 2 obstructed regions is traversed by both multipath components. In the air-to-ground environment, however, the distances through the n ¹ 2 obstructed regions are different depending upon the azimuthal radial from the receiver on which the scatterer lies. Because of the difference in distances of these legs and the n = 2 air legs, multipath components with the same delay can experience different magnitudes of attenuation even though log-distance path loss and reflection loss are the only attenuation factors applied.

A sample channel impulse response produced by the GAGE model simulation is shown in Figure 6-12. Multipath strength is plotted on dB-versus-delay and dB-versus-log-delay axes. Unlike the ESR and GBSBE simulations, multipath component strengths on the dB-versus-log-delay plot do not fall on a straight line because of the differences in ground-leg propagation distances. This fact provides insight into the air-to-ground channel in that strength of multipath components

32 In the side view of the propagation environment, the scatterers do not appear on the edge boundary of the ellipsoid because they lie on the surface at positions in front of or behind the x-z plane.

218 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION for particular delays are a function of direction of arrival, which directly relates to the ground- level propagation distance.

Airborne z Transmitter

Ellipsoid Boundary axis) -

Multipath 1 Air Leg (n=2) Side View Scatterer Multipath 2 Air Leg (n=2) 2 Scatterer

(View along y LOS Propagation1 Path (n=2) x Ground Scattering Region Ground Level Receiver

y axis) - ¹2) Multipath 2 Multipath 2 Scatterer Air Leg (n=2) 1 Ground Leg (n 2) ¹ x Ground Airborne

Top View Receiver Transmitter Multipath 1 Multipath 1 Ground Leg (n Air Leg (n=2) Ground-Level Scatterer

(View down from positive z Constant-Delay Ellipse 2

Figure 6-11. Top and side view of propagation environment for air-to-ground radio channels.

219 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

Relative Multipath Strength Versus Delay -115

-120

-125

-130

(Negative) Path Loss (dB) -135 6400 6600 6800 7000 7200 7400 7600 7800 8000 Absolute Propagation Delay (ns) -115

-120

-125

-130 Magnitude (dB)

-135 -5.2 -5.19 -5.18 -5.17 -5.16 -5.15 -5.14 -5.13 -5.12 -5.11 -5.1 log (Absolute Propagation Delay [sec]) 10

Figure 6-12. Example strength-versus-delay plot (GAGE model) for a channel impulse response affected only by log-distance path loss and reflection loss.

6.3.5 Line of Sight Components

Line-of-sight (LOS) path signal components are treated differently than reflected components for strength modeling for ESR, GBSBE, and GAGE models. After the model geometry has been used to produce reflected component strengths and delays, the LOS component is added to the channel impulse response. The delay of the LOS component at the receiver array center is determined from the straight-line distance between the transmitter and receiver. Variations in delay due to array element positions are then managed as described in section 6.3.2. The strength of the LOS component for the ESR and GBSBE models can be treated as partially obstructed so that n ¹ 2 propagation occurs.

Figure 6-13 illustrates a simulated channel impulse response using the ESR model where the LOS component has been added. The strength of the LOS component relative to the reflected components can be controlled using the LOS component strength offset input parameter, which can be determined from measurements. The LOS component is not attenuated by reflection loss

220 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION and therefore is not affected by the reflection loss input parameter. As shown in Figure 6-13 in the dB-versus-log-delay plot, the strength of the LOS component rises above the trend of the reflected components based on the input reflection loss and LOS offset parameters.

Relative Multipath Strength Versus Delay -100

-120

-140

-160

(Negative) Path Loss (dB) -180 0 200 400 600 800 1000 1200 1400 1600 1800 Absolute Propagation Delay (ns) -100

-120

-140

-160

Magnitude (dB) -180

-200 -7 -6.5 -6 -5.5 log (Absolute Propagation Delay [sec]) 10

Figure 6-13. Simulated channel impulse response for the ESR model after the LOS component is added.

6.3.6 Log-Normal Multipath Strength Variation

Measurements indicated a log-normal distribution of multipath component strength about the best-fit line through the strength values on a dB-versus-log-delay plot. A Gaussian random variable was included in the simulator to account for this log-normal variation. The standard deviation (in dB) of the strength variation is an input parameter to the simulator. The strength variation is applied to the reflected components and optionally to the LOS component. Log- normal variations are applied to reflected components to account for strength variations observed in actual channels due to shadowing, variable reflection coefficients, and combination of

221 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION multipath components with the resolution of the measurement system33. Log-normal variations are applied to LOS components to account for shadowing and combination of multipath components within the resolution of the measurement system34.

Figure 6-14 illustrates a channel impulse response simulated with the ESR model after the log- normal strength variation has been applied. The characteristics of multipath strengths appear to more closely resemble those of measured power-delay profiles compared to simulated results produced up until this point in the process (e.g., compared to Figure 6-13).

Relative Multipath Strength Versus Delay -100

-120

-140

-160

-180

(Negative) Path Loss (dB) -200 0 200 400 600 800 1000 1200 1400 1600 1800 Absolute Propagation Delay (ns) -100

-120

-140

-160

Magnitude (dB) -180

-200 -7 -6.5 -6 -5.5 log (Absolute Propagation Delay [sec]) 10

Figure 6-14. Simulated channel impulse response for the ESR model after the log-normal strength variation has been applied.

33 This contribution to strength variation due to measurement system resolution is appropriate for comparing simulated channel impulse responses with measured power-delay profiles. 34 While true LOS components do not experience shadowing, this simulator makes provisions for components that follow LOS paths but are attenuated by obstructions and are not attenuated by reflection loss.

222 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

6.3.7 Rayleigh Fading

A provision for correlated Rayleigh fading among antenna array elements is included in the simulation. When multipath components are assumed to be diffuse or multiple specular components shorter than the multipath resolution of the receiver, those multipath components will fade across the array. The simulator generates correlated Rayleigh random variables, one for each antenna element, that affect multipath strength received by each element.

Correlated Rayleigh values are produced by first generating independent Gaussian random values to serve as in-phase and quadrature components, which are combined to form complex Gaussian values. The independent complex Gaussian values are made into correlated complex Gaussian values using a Cholesky matrix. The correlation coefficient matrix for the complex Gaussian values is calculated from the desired Rayleigh correlation coefficient matrix. As described in [Goz02], let the correlation coefficient matrix for Gaussian random variables be given by

é 1 r12 L r1N ù ê ú ~ r 1 L r C = ê 21 2N ú ( 6.2 ) ê M M O M ú ê ú ër N1 r N 2 L 1 û

Let the desired correlation coefficient matrix for the Rayleigh random variables be defined by

~ ~ é 1 r12 L r1N ù ê r~ 1 L r~ ú C = ê 21 2N ú ( 6.3 ) ê M M O M ú ê ~ ~ ú ër N1 r N 2 L 1 û

The relationship between the Rayleigh correlation coefficients r ij and the Gaussian correlation ~ coefficients r ij is given by

223 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

æ 2 r~ ö ~ ç ij ÷ p (1+ rij )Ei ç ÷ - 1+ r~ 2 ç ij ÷ ( 6.4 ) r = è ø ij p 2 - 2

The function Ei (h) is the complete elliptical integral of the second kind with modulus h , which does not have a closed form solution. Lookup tables have been produced using numerical methods to solve the expression. Table 6-2 lists correlation coefficients for Gaussian random variables and corresponding correlation coefficients for Rayleigh random variables based on the equation ( 6.4 ) [Goz02].

Table 6-2. Relationship between correlation coefficients of Gaussian random variables and correlation coefficients of Rayleigh random variables computed from the envelope of the Gaussian random variables. Rayleigh Gaussian Rayleigh Gaussian Rayleigh Gaussian Rayleigh Gaussian Correlation Correlation Correlation Correlation Correlation Correlation Correlation Correlation Coefficient Coefficient Coefficient Coefficient Coefficient Coefficient Coefficient Coefficient ~ ~ ~ ~ r ij r ij r ij r ij r ij r ij r ij r ij 0.00 0.0000 0.25 0.0559 0.50 0.2227 0.75 0.5410 0.05 0.0047 0.30 0.0737 0.55 0.2752 0.80 0.6073 0.10 0.0056 0.35 0.0965 0.60 0.3327 0.85 0.6974 0.15 0.0243 0.40 0.1494 0.65 0.4133 0.90 0.7913 0.20 0.0337 0.45 0.1836 0.70 0.4562 0.95 0.9005

Using values in Table 6-2 and through interpolation, the channel simulator calculates a correlation coefficient matrix for the Gaussian random variables based on the desired Rayleigh random variable correlation coefficient matrix. Then, independent complex Gaussian random values are generated for each antenna element. These independent Gaussian random values are transformed into correlated Gaussian random values using a Cholesky decomposition of the Gaussian correlation coefficient matrix. Let W be an N-by-l matrix with zero-mean, complex Gaussian values stored in the rows of W, where l is the length of the rows of Gaussian values and

224 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION the rows are independent. A matrix X is desired that contains rows of zero-mean, complex Gaussian values, where the correlation among rows is specified by correlation coefficient matrix ~ C . A lower triangular coloring matrix L is calculated using a Cholesky decomposition35 such that ~ LLH = C ( 6.5 )

Then, let

X = LW ( 6.6 )

It can be shown that the matrix multiplication of L by W produces matrix X that contains N rows ~ of l complex Gaussian values, wherein the correlation of rows is determined by matrix C , using the expression ~ E{XX H }= E{LWW H LH }= LLH = C ( 6.7 )

Calculating the envelope of the rows of X results in N vectors of Rayleigh-distributed random values having correlation coefficients defined in C .

An example of Rayleigh faded multipath components is illustrated in Figure 6-15. Channel impulse responses for four antenna array elements are superimposed on the plot. Large differences in delay among multipath components are caused by different propagation paths. Very small differences in delay are caused by excess delay due to array element position.

35 When using the MATLAB function chol(.), the resulting matrix must be transposed before it is used by these equations because chol(.) produces an upper triangular matrix.

225 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

Relative Multipath Strength Versus Delay -110

-120

-130

-140

-150

-160

-170

-180 (Negative) Path Loss (dB)

-190

-200

-210 0 200 400 600 800 1000 1200 1400 1600 1800 Absolute Propagation Delay (ns)

Figure 6-15. Channel impulse response of four array element superimposed on one plot after correlated Rayleigh fading has been applied.

6.4 Direction of Arrival

The ESR, GBSBE, and GAGE models directly produce direction of arrival (DOA) information since the simulated positions of scatterers are known. The channel model simulator makes the assumption that the size of the array is small compared to the distances traversed by multipath components. Using this assumption, the DOA for a particular multipath component is the same for each antenna element of the array.

6.4.1 Direction of Arrival for ESR and GBSBE

The ESR and GBSBE models define direction of arrival as shown in Figure 6-16. The receiver array is located at the right focus of the ellipse. The array element axis origin (xe-ye) is located at the center of the receiver array. Direction of arrival is defined as the angle between the x-axis and the vector connecting the scatterer to the center of the receiver array. DOA ranges from -p to p radians (-180 to 180 degrees). The simulator defines a positive DOA to be a rotation from

226 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION the negative direction of the x-axis clockwise; the scatterer shown in Figure 6-16 produces a multipath component with a positive DOA.

y b S

ye DOA x e x a Transmitter Receiver Array

Figure 6-16. Definition of direction of arrival for the ESR and GBSBE models.

y S

y e DOA xe x T Ground Airborne Receiver Top View Transmitter (View down from positive z-axis)

Figure 6-17. Definition of direction of arrival for the GAGE model.

227 CHAPTER 6 – WIDEBAND VECTOR CHANNEL SIMULATION

6.4.2 Direction of Arrival for GAGE

The GAGE model defines direction of arrival as shown in Figure 6-17. The receiver antenna array is located at the axis origin. Direction of arrival is defined to be angle between the projection of the line-of-sight path onto the x-y plane (which falls on the x-axis) and the vector connecting the scatterer to the receiver array center. A positive DOA is defined to be a rotation from the positive x-axis counterclockwise, as illustrated in Figure 6-17.

6.5 Summary

This chapter has presented a detailed description of the simulator used to implement the geometrically based single-bounce elliptical (GBSBE) model, the elliptical sub-regions (ESR) model, and the geometric air-to-ground ellipsoidal (GAGE) model. The simulator produces output based on physical dimensions and parameters derived from measurements. Channels are simulated based on locations of scatterers in the environment and relative positions of the transmitter and receiver. Statistical distributions (Gaussian, Rayleigh, and Poisson) are used to model strength variations and counts of multipath components in the propagation environment. At the output, the simulator produces channel impulse responses, which include multipath strength, delay, phase, and direction of arrival at each element of an antenna array. This simulator was used as a vehicle to evaluate geometric channel models as discussed in Chapter 7.

228 Chapter 7

Channel Model Evaluation

Geometric channel models are often used for simulation because of their intuitive link to physical characteristics of propagation environments. This chapter provides an evaluation of three geometric channel models with respect to their ability to produce channel impulse responses that accurately represent characteristics of measured radio channels. This evaluation provides validation not only for the channel models themselves but also for wireless system simulations whose results are influenced by the realism of the channel models employed.

The evaluation approach used here is to compare results derived from channel impulse responses produced by a channel model with results derived from measured power-delay profiles. These results derived from measured and simulated channels may be as simple as RMS delay spread or as complex as effective gain achieved through the use of a two-dimensional rake receiver. By establishing criteria that are of importance to a wide range of old and new wireless system technologies, the evaluation can have the most relevance to the wireless field.

The specific criteria used for this evaluation include multipath signal strength characteristics, RMS delay spread, excess delay spread, multipath fading statistics, antenna diversity gain, and

229 CHAPTER 7 – CHANNEL MODEL EVALUATION

two-dimensional rake receiver gain. Comparisons between results derived from modeled and measured channels are performed for three channel models, namely the elliptical sub-regions (ESR) model, the geometrically based single-bounce elliptical (GBSBE) model, and the geometric air-to-ground (GAGE) model, which are theoretically defined in Chapter 4.

System Simulation System Simulation

Transmitter Transmitter

Channel Channel Measurements Model Channel

Receiver Receiver

Comparison Statistical Statistical Results Results

Model Evaluation

Figure 7-1. A block diagram of the process for evaluating channel models.

The method for channel model evaluation is shown schematically in Figure 7-1. For each criterion, two identical signal processes were executed to represent each branch illustrated in Figure 7-1. In one process, the channel was based solely on channel measurements; in the second process, the channel was based on the output from a channel model. The channel model itself may use information from the channel measurements as input, which allows a best-case comparison of modeled channels with their associated measured channels. The output of each process is statistically summarized (e.g., mean values, standard deviations, cumulative distribution functions) and then compared.

230 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.1 Elliptical Sub-Regions Channel Model

The elliptical sub-regions (ESR) model was a good candidate for evaluation because of its ability to accept multiple sets of input parameters for multiple geometric regions rather than assuming a single set of parameters applied uniformly across a single geometric region. The results are especially of interest in relation to the geometrically based single-bounce elliptical model, whose evaluation is presented in section 7.2.

The ESR model was evaluated using measurements performed for the dense-scatterer measurement campaign discussed in section 5.3. This measurement site characterized line-of- sight (LOS) and non-line-of-sight (NLOS) channels. As a consequence, the ESR model is evaluated using measured and modeled signal data for both LOS and NLOS sites. LOS and NLOS simulations were performed separately and used different input channel parameters as required by measurement results.

7.1.1 Simulation Parameters

Table 7-1 lists the input parameters for the ESR model used to simulate the NLOS measurement site. The number of regions (16) was chosen based on the delay ranges characterized during measurements, ranges which achieve a balance between model resolution and amount of measurement data required. Element locations were chosen to match the array that was used for dense-scatterer measurements. Parameters of frequency, path loss exponent, standard deviation of strength variation, maximum excess delay, and transmitter-receiver separation were chosen equal to those used for or derived from measurements. Parameters of log-distance path loss reference distance and reflection loss are assumed values36.

Table 7-2 lists the input parameters for the LOS simulations of the dense-scatterer site. Several values are largely similar to those for NLOS locations, but exact values based on LOS measurements that were different than NLOS measurement values were used to provide a more meaningful evaluation.

36 Reflection loss affects the absolute strength of received multipath components rather than their relative values. Since the models are evaluated using relative strength values, the selection of reflection loss is not critical for NLOS channels.

231 CHAPTER 7 – CHANNEL MODEL EVALUATION

Table 7-1. Major simulation parameters for elliptical sub-regions model for NLOS channels. Parameter Value Number of sub-regions 16 Poisson parameters Equal to measured values for combined NLOS locations (see Table 5-21 on page 167) Frequency 2050 MHz Path loss exponent 4.83 Log-distance path loss reference distance 1 m Standard deviation of log-normal strength 4.95 dB variation Reflection loss 10 dB Maximum excess delay 1588 ns Transmitter-receiver separation Equal to values for NLOS locations (see Table 5-14 on page 150) Element locations (xe, ye) coordinates: (0, 3l / 4 ); (0, 1l / 4 ); (0, –1l / 4 ); (0, –3l / 4 ) in meters

Table 7-2. Major simulation parameters for elliptical sub-regions model for LOS channels. Parameter Value Number of sub-regions 16 Poisson parameters Equal to measured values for combined NLOS locations (see Table 5-22 on page 168) Frequency 2050 MHz Path loss exponent 4.10 Log-distance path loss reference distance (for 1 m single-bounce multipath components) Standard deviation of log-normal strength 5.24 dB variation Reflection loss 10 dB LOS component dB above best-fit line 10.5 dB (includes reflection loss in simulator) Maximum excess delay 1557 ns Transmitter-receiver separation Equal to values for LOS locations (see Table 5-14 on page 150) Element locations (xe, ye) coordinates: (0, 3l / 4 ); (0, 1l / 4 ); (0, –1l / 4 ); (0, –3l / 4 ) in meters

Figure 7-2 shows the modeled propagation environment appropriate for the parameters given in Table 7-1 and Table 7-2. Elliptical boundaries correspond to excess multipath delay divided into equal delay intervals. The transmitter is located at the plus symbol, and the receiver is located at the circle. Randomly generated scatterer positions, whose count in each region depends upon a

232 CHAPTER 7 – CHANNEL MODEL EVALUATION

specified Poisson parameter, are shown as dots. Lines connecting the transmitter and receiver by way of each scatterer are single-bounce propagation paths. From this geometry (and other input parameters), the strength, delay, and direction of arrival of multipath components in channel impulse response are computed.

Top View of Propagation Environment 250

200

150

100

50

0

-50 y-coordinate (m) -100

-150

-200

-250 -300 -200 -100 0 100 200 300 x-coordinate (m)

Figure 7-2. Example of geometric channel simulation (elliptical sub-regions model) showing transmitter location (plus symbol at focus), receiver location (circle at other focus), scatterers (dots), propagation paths (yellow lines), and elliptical sub-region boundaries.

7.1.2 Multipath Signal Strength

Relative strength and delay of multipath components in channel impulse responses affect performance of radio systems. For narrowband systems, multipath strengths and delays in the channel are associated with the fading depth of signal envelopes and relate to the requirement for an equalizer to mitigate inter-symbol interference (ISI). For wideband direct-sequence spread- spectrum (DS-SS) systems, multipath strengths and delays relate to rake receiver requirements (e.g., number of fingers, searcher window size, gains achieved). For these reasons, multipath

233 CHAPTER 7 – CHANNEL MODEL EVALUATION

strength scatter plots and strength distribution plots were produced by the simulator for comparison to measured results.

Figure 7-3 through Figure 7-8 depict strength information output by simulations of the ESR model for the NLOS locations (NLOS1-NLOS6) at the dense-scatterer site. One pair of plots is given for each location. The plot labeled (a) in each figure is a scatter plot of multipath strength versus log-delay. The plot labeled (b) in each figure shows a normalized histogram of multipath component strength along with a theoretical Gaussian probability density function for comparison.

The simulated NLOS strength results37 can be compared to the measurement results provided in section 5.3.5 starting on page 169. The histograms of multipath strength for simulated channels is very similar to those for measured channels, as expected since the Gaussian strength variation trend was designed into the channel simulator. Strength-versus-log-time scatter plots differ slightly between simulated and measured channels. Scatter plots for simulated channels show approximately equal distribution on either side of and along the best-fit line, while measured channels contain ranges of delay where multipath strength points moderately deviate from the best-fit line in clusters. Differences early in the profile where measurements fall below the best- fit line are likely due to obstructions shadowing multipath with short delays. Sporadic deviations in later delays are likely due to differences in reflection coefficients and path loss exponents, which the simulator treats as constants over the entire environment. In general, the strength characteristics of channel impulse responses produced by the ESR model appear to be satisfactory.

37 Simulations and measurements were processed to provide relative multipath strength data for comparison.

234 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-3. NLOS 1 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-4. NLOS 2 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

235 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-5. NLOS 3 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-6. NLOS 4 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

236 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-7. NLOS 5 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-8. NLOS 6 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

237 CHAPTER 7 – CHANNEL MODEL EVALUATION

The simulations of the ESR model used for Figure 7-3 through Figure 7-8 include Gaussian strength variation but not Rayleigh fading of multipath components. In order to compare multipath strength distributions with and without Rayleigh fading, the plots in Figure 7-9 and Figure 7-10 were produced. Figure 7-9 is the output of the ESR simulation using 1000 simulated channel impulse responses for NLOS6 with Gaussian strength variation but not Rayleigh fading. Figure 7-10 was produced by the ESR simulation with both Gaussian strength variation and Rayleigh fading, where the Gaussian standard deviation for Figure 7-10 was adjusted such that the standard deviation of the strength variation for the combined effect of Gaussian and Rayleigh distributions equals that when only Gaussian variations were applied. The comparison between the plots show that when all multipath components are truly Rayleigh faded, the distribution skews away from the Gaussian PDF. This suggests that the multipath strength characteristics of the measured channels, which are better represented by the Gaussian PDF, can be modeled more accurately using only Gaussian variation of strength. This is evidence that multipath components in the measured channels were not all affected by Rayleigh fading.

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-9. NLOS 6 simulated multipath strength (ESR) for 1000 impulse responses (without Rayleigh fading): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

238 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-10. NLOS 6 simulated multipath strength (ESR) for 1000 impulse responses (Rayleigh fading, no log-normal deviation): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. Standard deviation about best-fit line of 5.4 dB results

Figure 7-11 through Figure 7-14 show ESR simulation results for the LOS locations at the dense- scatterer site. These plots can be compared to the measurement results presented in section 5.3.5 starting on page 169. Except for later delays, where small Poisson parameters resulted in sparse multipath components, scatter plots for simulations appear to have a regular spreading of multipath components across delay. Measurements of LOS locations, however, showed short delay ranges containing strong clusters of multipath components. This suggests that a few multipath components at particular delays dominated measurements at each LOS location. The methods used by the ESR model do not directly provide a way to allow persistent multipath components that remain dominant in all generated channel impulse responses. While the model may work well for data combined for all measurement locations, it falls somewhat short of accurately modeling strength for individual LOS locations because of its inability to include concentrations of dominant multipath components.

239 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-11. LOS 1 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.1 Simulated 0.09 Gaussian

0.08

0.07

0.06

0.05 PDF

0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-12. LOS 2 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

240 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.1 Simulated 0.09 Gaussian

0.08

0.07

0.06

0.05 PDF

0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-13. LOS 3 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.1 Simulated 0.09 Gaussian

0.08

0.07

0.06

0.05 PDF

0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-14. LOS 4 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

241 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.1.3 RMS Delay Spread

RMS delay spread was calculated for each channel impulse response generated by the ESR simulator. A summary of RMS delay spread, divided among NLOS locations, is shown in Table 7-3. The table also includes results of measured channels for comparison of mean, standard deviation, minimum, and maximum RMS delay spread.

Table 7-3. RMS delay spread results for simulations (ESR) and measurements of NLOS dense scatterer locations. Location RMS Delay Spread (ns) Mean Std. Dev. Minimum Maximum Sim Meas Sim Meas Sim Meas Sim Meas NLOS1 87.4 67.5 28.4 10.1 16.9 40.2 169 108 NLOS2 84.8 60.9 26.6 10.0 26.4 0.00 176 91.0 NLOS3 79.1 70.2 26.1 12.1 25.5 35.9 198 152 NLOS4 82.5 78.6 25.8 10.7 28.4 51.6 162 112 NLOS5 72.8 70.7 25.6 7.70 24.1 49.3 170 95.3 NLOS6 64.4 69.4 24.3 13.3 19.8 31.3 142 368

Results show that the simulator generally produces channel impulse responses with mean RMS delay spreads larger that those for measured channels. Standard deviations of RMS delay spread were also larger for simulated channels. This overestimation of mean RMS delay spread is likely due to measured channels containing strong multipath components early in their power-delay profiles. Strong multipath components early in the profiles reduce RMS delay spread because weaker, long-delay components become less significant.

Complementary cumulative distribution functions (CCDF) were produced for simulated NLOS locations for comparison to CCDFs of measurement data shown in section 5.3.2 beginning on page 151. These CCDFs show again that RMS delay spread is overestimated by the ESR model. In order to force the ESR model to simulate RMS delay spread more accurately for NLOS channels, the maximum excess delay could be reduced or the path loss exponent could be

242 CHAPTER 7 – CHANNEL MODEL EVALUATION increased. While this will affect other characteristics of the simulated channel impulse responses, such a compensation is appropriate if RMS delay spread is the most important characteristic of the responses required by certain wireless system simulations.

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-15. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS1 (b) NLOS2.

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2

Probability( RMS Delay Spread > Abscissa ) 0.1 Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-16. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS3 (b) NLOS4.

243 CHAPTER 7 – CHANNEL MODEL EVALUATION

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-17. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS5 (b) NLOS6.

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2

Probability( RMS Delay Spread > Abscissa ) 0.1 Probability( RMS Delay Spread > Abscissa ) 0.1

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-18. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS6 simulated using log-normal variation about best-fit power (dB) versus log-delay line, and (b) NLOS6 simulated using log-normal variation and Rayleigh fading for multipath components.

Results using solely a log-normal distribution of multipath strength variation and results using both Gaussian and Rayleigh distributions for multipath strength were produced and compared. Figure 7-18 shows CCDF plots of RMS delay spread for NLOS6 based on 1000 simulated channel impulse responses. Plot (a) in the figure summarizes RMS delay spread for simulations

244 CHAPTER 7 – CHANNEL MODEL EVALUATION

using only log-normal variation of multipath strength. Plot (b) in the figure uses log-normal variation and Rayleigh fading, where the standard deviation of the Gaussian variation was adjusted so that the combination effects of the Gaussian and Rayleigh distributions produced an overall standard deviation equal to that used for plot (a) in the figure. These simulations resulted in mean RMS delay spreads of (a) 62.8 ns and (b) 61.7 ns, respectively. This insignificant difference in mean RMS delay spreads suggests that Rayleigh fading may be used in the ESR simulation without significantly affecting RMS spread of the output responses.

Table 7-4 shows RMS delay spread for each LOS channel impulse response simulated using the ESR model, divided among NLOS locations. The table includes results of measured channels for comparison of mean, standard deviation, minimum, and maximum RMS delay spread. Figure 7-19 and Figure 7-20 depict CCDFs for RMS delay spread for each LOS location. The results show that the simulation can overestimate or underestimate the RMS delay spread compared to measurements. The simulations show an increase in RMS delay spread with transmitter-receiver separation (see for T-R separation values for LOS locations in Table 5-14 on page 150). Measurements, however, show RMS delay spread remaining relatively constant over all locations.

Table 7-4. RMS delay spread results for simulations (ESR) and measurements of LOS dense scatterer locations. Location RMS Delay Spread (ns) Mean Std. Dev. Minimum Maximum Sim Meas Sim Meas Sim Meas Sim Meas LOS1 50.1 34.4 12.3 4.81 27.1 21.4 103 51.2 LOS2 39.0 38.8 10.3 8.31 15.3 0.00 77.6 73.3 LOS3 28.8 39.0 6.87 12.1 13.7 20.1 51.7 91.8 LOS4 18.7 34.2 50.3 8.7 7.39 16.9 34.9 69.9

245 CHAPTER 7 – CHANNEL MODEL EVALUATION

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-19. RMS delay spread CCDF for simulated (ESR) channels (a) LOS1 (b) LOS2.

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-20. RMS delay spread CCDF for simulated (ESR) channels (a) LOS3 (b) LOS4.

7.1.4 Excess Delay Spread

Excess delay spread results for simulated and measured channels for the NLOS dense-scatterer locations are shown in Table 7-5. Means of excess delay spread results at the 10 dB level for measurements exceed those for simulation. This is explained by the tendency of the measured power delay profiles to have strong components at early delays. For 20 dB levels and higher, the

246 CHAPTER 7 – CHANNEL MODEL EVALUATION simulated results approach the values of the measured results, where weaker measured and simulated multipath components at longer delays tend to have the same strength.

Table 7-6 lists excess delay spread results for simulated and measured LOS channels. As with the simulated RMS delay spread results, excess delay spread based on simulated channel impulse responses tends to increase with increasing transmitter-receiver separation. Measured excess delay spread means do not follow this trend for the dense-scatterer site.

Table 7-5. Excess delay spread values for simulated (ESR) and measured NLOS channel impulse responses. Excess Delay Spread (ns) 10 dB Level 20 dB Level 25 dB Level 30 dB Level Location Mean Max Mean Max Mean Max Mean Max Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas NLOS1 155 200 537 480 389 390 743 1300 516 549 1009 1300 635 682 1029 1500 NLOS2 143 204 466 447 372 328 875 697 510 440 889 811 621 601 1199 1510 NLOS3 125 272 479 580 351 435 775 775 487 581 1228 1250 606 693 1228 1450 NLOS4 141 252 460 572 378 499 868 776 505 615 981 888 630 712 1250 1380 NLOS5 104 243 407 493 311 380 840 747 434 503 864 909 556 637 971 1210 NLOS6 96 207 379 478 269 367 711 758 379 471 830 1365 508 620 1165 1450

Table 7-6. Excess delay spread values for simulated (ESR) and measured LOS channel impulse responses. Excess Delay Spread (ns) 10 dB Level 20 dB Level 25 dB Level 30 dB Level Location Mean Max Mean Max Mean Max Mean Max

Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas LOS1 29.1 115 209 335 194 196 458 533 316 230 591 725 424 313 1003 751 LOS2 19.0 131 173 501 138 233 374 790 237 300 566 790 364 408 659 791 LOS3 11.3 123 131 509 95.5 222 338 651 165 315 358 835 264 432 568 868 LOS4 5.53 89.1 60.7 421 55.3 162 196 586 107 263 275 786 177 390 384 861

247 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.1.5 Multipath Fading

Impulse response data from the dense-scatterer measurements and ESR model simulations was used to generate fading envelopes for comparison. Signal envelopes were formed by performing a vector sum of all signal components in each channel impulse response and taking the magnitude of the result. Envelope magnitude data from all antenna elements was combined to increase the number of samples available.

Cumulative distribution functions (CDF) of signal envelope strength for simulated and measured fading are shown in Figure 7-21 and Figure 7-22. Signal levels were normalize so that the CDFs show envelope strength relative to the median for each signal. A theoretical CDF for Rayleigh fading, which was also normalized to its median value, is also shown on each plot.

Results shown in Figure 7-21 indicate that CDFs for measurements at all NLOS locations fall very close to the theoretical Rayleigh CDF. Simulated channels also show a Rayleigh trend. Note that Rayleigh fading of the signal envelope discussed here is not the same as Rayleigh fading of individual multipath components. Multipath components at a receiver site can exhibit no fading, while the signal envelope formed by the vector sum of all multipath components may be very Rayleigh in nature. Rayleigh fading of multipath components requires multipath having the same delay or close delays within the resolution of the receiver to be combined at the receiver. Signal envelopes, however, are a combination of all multipath components in the channel impulse response.

LOS results in Figure 7-22 indicate a Rician fading characteristic (with a non-zero K value) for simulated channels and measured channels. Strong line-of-sight components in the measured and simulated channels cause the probability of deep fades to be lower compared to Rayleigh fading. This suggests that the strength of the line-of-sight component relative to the strengths of the multipath components is modeled accurately for the purposes of multipath fading.

248 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Received Signal Strength for Simulated NLOS Locations CDF of Received Signal Strength for Measured NLOS Locations 1 1

0.9 0.9

0.8 0.8

0.7 0.7 NLOS1 NLOS1 0.6 0.6 NLOS2 NLOS2 NLOS3 NLOS3 0.5 NLOS4 0.5 NLOS4 NLOS5 NLOS5 0.4 NLOS6 0.4 NLOS6 Rayleigh Rayleigh 0.3 0.3

Probability ( Strength < Abscissa ) 0.2 Probability ( Strength < Abscissa ) 0.2

0.1 0.1

0 0 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Signal Strength Relative to Median (dB) Signal Strength Relative to Median (dB) (a) (b)

Figure 7-21. Signal strength CDF for each NLOS location derived from (a) channel impulse response simulations (ESR) and (b) measured channels.

CDF of Received Signal Strength for Simulated LOS Locations CDF of Received Signal Strength for Measured LOS Locations 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 LOS1 0.6 LOS1 LOS2 LOS2 LOS3 0.5 LOS3 0.5 LOS4 LOS4 Rayleigh Rayleigh 0.4 0.4

0.3 0.3

Probability ( Strength < Abscissa ) 0.2 Probability ( Strength < Abscissa ) 0.2

0.1 0.1

0 0 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Signal Strength Relative to Median (dB) Signal Strength Relative to Median (dB) (a) (b)

Figure 7-22. Signal strength CDF for each LOS location derived from (a) channel impulse response simulations (ESR) and (b) measured channels.

249 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.1.6 Antenna Diversity

Gains achieved through antenna diversity applied to measured and simulated channels were computed for comparison. Maximal ratio combining (MRC) was selected because it enables the best fading mitigation (statistically) compared to other types of linear diversity combiners [Ree02]. Since the highest amount of diversity gain is achieved for narrowband signals, continuous-wave signals are assumed for this comparison. An antenna element separation of l / 2 was used. Figure 7-23 through Figure 7-28 show CDFs of signal envelope strengths for NLOS dense-scatterer site simulations and measurements. Each plot shows two CDFs of relative signal envelope power, one CDF corresponding to a receiver using single-element and one CDF corresponding to the output of MRC diversity combining.

Table 7-7 lists approximate diversity gains for simulated and measured NLOS locations for the 1% and 10% CDF levels. These results show that simulated and measured diversity gain at the 10% level are approximately equal within one dB. At the 1% level, diversity gain for measured channels is slightly larger (about 2.3 dB on average) than the diversity gain for simulated channels. It appears that this is due to measured channels experiencing deeper fades a lower percentage of the time.

Figure 7-29 through Figure 7-32 are CDF plots of simulations and measurements for LOS locations at the dense-scatterer site. CDFs of relative envelope power for a single-element and for MRC-diversity output are shown on each plot. Table 7-8 lists diversity gain for the 10% and 1% CDF levels for LOS simulations and measurements. While at three of the LOS locations diversity gain at the 10% level differs by 1 dB or less between measured and simulated results, diversity gain differences of up to 6 dB at the 1% CDF level were observed. This suggests that simulated channels may have gone into deeper fades or simulated channels exhibited lower envelope correlation coefficients among elements.

250 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element Single Element MRC Diversity MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-23. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element Single Element MRC Diversity MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-24. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

251 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element Single Element MRC Diversity MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-25. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element Single Element MRC Diversity MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-26. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

252 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element Single Element MRC Diversity MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-27. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS5 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element Single Element MRC Diversity MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-28. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS6 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

253 CHAPTER 7 – CHANNEL MODEL EVALUATION

Table 7-7. Approximate diversity gain for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels. Diversity Gain (dB) Location 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured NLOS1 3 2 6 4 NLOS2 2 4 4 8 NLOS3 2 3 3 7 NLOS4 3 3 4 9 NLOS5 3 4 4 7 NLOS6 2 3 5 5

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element MRC Diversity

Single Element MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-29. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

254 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element MRC Diversity

Single Element MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-30. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

Single Element MRC Diversity

Single Element MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-31. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

255 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10 Single Element MRC Diversity

Single Element MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-32. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

Table 7-8. Approximate diversity gain for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels. Diversity Gain (dB) Location 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured LOS1 1.5 0.5 8 2 LOS2 1.5 2 5 3 LOS3 1.5 0.5 5 2 LOS4 1 1 5.5 5

7.1.7 Two-Dimensional Rake Receiver

A two-dimensional rake receiver is a space-time signal processing architecture that joins a traditional rake receiver with smart antenna capabilities. A two-dimensional rake combines resolvable multipath components in the temporal domain as well as combining or beamforming on multipath components in the spatial domain. Processing used for evaluation here temporally and spatially combines multipath components from four antenna array elements using four rake

256 CHAPTER 7 – CHANNEL MODEL EVALUATION fingers per antenna element. The four strongest multipath components are used for temporal rake combining, and co-phased rake output signals are summed to produce the composite output signal.

Figure 7-33 through Figure 7-38 show CDFs of the received signal envelope with and without the use of a two-dimensional rake receiver for NLOS locations. Table 7-9 provides approximate gains achieved through the use of the two-dimensional rake for simulated and measured channels. Gains for 10% and 1% CDF levels are shown. Mitigation of fading was generally better for measured channels compared to simulated channels. Simulated channels showed gains up to 10 dB at the 1% CDF level, while measured channel gains of up to 20 dB were observed.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 100 100

Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

10-2 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-33. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

257 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 100 100 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

10-2 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-34. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 100 10 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 10-2 10

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-35. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

258 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 100 100 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

10-2 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-36. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 100 10 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 10-2 10

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-37. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS5 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

259 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 10 100 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 Single Element (Channel 1) 10 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

10-2 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-38. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS6 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

Table 7-9. Approximate fading levels differences between 2-D rake output and single channel output for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels. Fading Level Relative to Mean Signal Strength – 2-D Rake Output Minus Single Channel Output Location (dB) 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured NLOS1 4 5 10 14 NLOS2 6 7.5 10 20 NLOS3 3.5 5 5 16 NLOS4 5.5 8 9 16 NLOS5 5.5 7 7 15 NLOS6 4 8.5 8 16

260 CHAPTER 7 – CHANNEL MODEL EVALUATION

Figure 7-39 through Figure 7-42 were created from LOS location simulations and measurements, showing CDFs of relative signal envelope strengths with and without the application of a two- dimensional rake. Table 7-10 shows the approximate gains achieved using the two-dimensional rake for both simulated and measured channels. Gains for 10% and 1% CDF levels show slightly larger gains for simulated channels compared to measured channels. Gains for simulated channels up to 10 dB at the 1% CDF level where achieved, while measured channel reached gains of 6 dB at the 1% level. Unlike simulations of the NLOS locations, LOS simulations of the dense-scatterer site tend to overestimate achievable gains using a two-dimensional rake receiver.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 10 100 Single Element (Channel 1) 2-D Rake (4 fingers per chan) Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 10 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-39. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

261 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output 0 CDF of Single Element Signal Strength & 2-D Rake Output 10 100 Single Element (Channel 1) 2-D Rake (4 fingers per chan) Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-40. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 10 100

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 10 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-41. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

262 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output 0 CDF of Single Element Signal Strength & 2-D Rake Output 10 100

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-42. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

Table 7-10. Approximate fading levels differences between 2-D rake output and single channel output for LOS locations computed from simulated (ESR) channel impulse responses and measured channels. Fading Level Relative to Mean Signal Strength – 2-D Rake Output Minus Single Channel Output Location (dB) 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured LOS1 3.5 2 8 6 LOS2 2.5 2 8 5 LOS3 3 1.5 7.5 4 LOS4 1.5 2 10 5

263 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.1.8 ESR Comparison Summary

Results of the evaluation of the ESR channel model through comparison of simulated ESR channel impulse responses and actual channel measurements are summarized by the following points: · In general, the ESR model provides a reasonable representation of the channel but should be tuned to achieve the desired channel characteristics. For example, for the simulation of wireless systems employing diversity or two dimensional rake receivers in LOS channels, the strength of LOS component strength could be adjusted to meet a desired Rician distribution K-factor.

· The ESR model as implemented produces largely accurate Gaussian distributions of multipath strength about a dB-versus-log-delay straight-line trend for NLOS channels. Gaussian distributions of strength produced by the model can be made to match the measured multipath strength distributions by using the standard deviation from measurements as an input to the channel model simulator. Visual differences between the dB-versus-log-time scatter plots are apparent, such as deeper fades for a few multipath components, indicating that these multipath components may be Rayleigh faded. The channel model simulator can be set to use Rayleigh fading for all multipath components in the channel, but this causes a skewing of the strength distribution away from Gaussian.

· The ESR model does not accurately represent clustering of multipath at particular delays as observed in measured NLOS and LOS power-delay profiles. Rather, as it was simulated for this research, the ESR model produces smooth distributions of multipath components across propagation delay in the channel impulse response. Adjustments could be made to the model input to account for clustering, such as significantly increasing the Poisson parameter for a scattering sub-region corresponding to the delay bin in which the cluster occurs. Strength adjustment factors could also be used to increase the strength of clusters above the strength trend of other multipath components in the channel impulse response.

264 CHAPTER 7 – CHANNEL MODEL EVALUATION

· NLOS channel impulse responses produced by the ESR model simulation exhibited higher RMS delay spread than the measurements the model was intended to represent. The larger simulated RMS delay spreads are likely due to comparatively larger multipath components at small propagation delays in measured profiles. In general, strong clusters early in the profile reduce RMS delay spread, and strong clusters late in the profile increase RMS delay spread. A provision for stronger (or even weaker) clusters that deviate from the strength trend of other multipath components could resolve this discrepancy. Simulated LOS channels show increasing RMS delay spread with distance, but measured LOS channels do not show a similar trend. While larger RMS delay spread is expected with larger distance, additional multipath components for measured LOS channels late in delay may have been considerably weaker than dominant early delays, causing a loss of this trend due to dynamic range limitations of the measurement receiver.

· ESR NLOS excess delay spread results for the 10 dB level tend to be overestimates compared to measured results. For larger levels (20 dB, 25 dB, and 30 dB), simulation results seem to better represent measurements. This is expected since relative strengths of simulated multipath components in later delays, where weaker multipath components exist, are more accurately modeled compared to those of early delays.

· The ESR model produces vector channel impulse responses that result in reasonable MRC antenna diversity characteristics for NLOS channels. For NLOS channels, measurements resulted in slightly lower achievable diversity gain compared to simulation. Simulations of LOS channels produced an optimistic estimate of achievable diversity gain.

· Mitigation of fading in NLOS channels using a two-dimensional rake receiver was generally better for measured vector channels compared to simulated channels. Gains for simulated channels were up to 10 dB at the 1% CDF level, while gains for measured channels up to 20 dB were computed. Simulations of LOS channels produced an optimistic estimate of achievable gains using spatial-temporal combining of multipath components.

265 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.2 Geometrically Based Single-Bounce Elliptical Channel Model

The geometrically based single-bounce (GBSBE) channel model is similar to the elliptical sub- regions model except that it uses a single geometric region in which to distribute scatterers. Therefore, through comparing the evaluation of the GBSBE model with the evaluation of the ESR model, the value of using the additional regions and the associated increase in complexity of the ESR model can be judged.

Like the ESR model, the GBSBE model was evaluated using measurements taken at the dense- scatterer measurement site discussed in section 5.3. Line-of-sight (LOS) and non-line-of-sight (NLOS) measurements are used in the evaluation. LOS and NLOS simulations were performed separately and used different input channel parameters corresponding to LOS and NLOS measurement results.

7.2.1 Simulation Parameters

Table 7-11 details the GBSBE input parameters used to simulate the NLOS measurement site. Element locations were chosen to match the array that was used for dense-scatterer measurements and the simulations of the ESR model. Frequency, path loss exponent, standard deviation of strength variation, maximum excess delay, and transmitter-receiver separation are equal to those parameters used for or computed from measurements. Log-distance path loss reference distance and reflection loss are still assumed values38, but these values were chosen to be the same as those used for the ESR model simulations.

Table 7-12 lists the input parameters used for the GBSBE LOS simulations of the dense-scatterer site. Some values are different than those for NLOS GBSBE parameters because of measurement result differences between LOS and NLOS locations at the site.

38 Again, these parameters affect the absolute strength of received multipath components rather than their relative values. Since GBSBE and ESR models are using the same values here, absolute strength of components produced by these models could actually be compared, but relative strengths are of interest here so that evaluations of both models with respect to measurements can be compared using the same criteria.

266 CHAPTER 7 – CHANNEL MODEL EVALUATION

Table 7-11. Major simulation parameters for GBSBE model for NLOS channels. Parameter Value Number of regions 1 (equivalent to sub-regions model with one region) Poisson parameter (average number of 21.8 (from Table 5-23 on page 169) scatterers) Frequency 2050 MHz Path loss exponent 4.83 (from Table 5-26 on page 186) Log-distance path loss reference distance 1 m Standard deviation of log-normal strength 4.95 dB variation Reflection loss 10 dB Maximum excess delay 1588 ns Transmitter-receiver separation Equal to values for NLOS locations (see Table 5-14 on page 150) Element locations (xe, ye) coordinates: (0, 3l / 4 ); (0, 1l / 4 ); (0, –1l / 4 ); (0, –3l / 4 ) in meters

Table 7-12. Major simulation parameters for GBSBE model for LOS channels. Parameter Value Number of regions 1 (equivalent to sub-regions model with one region) Poisson parameters 15.3 (from Table 5-23 on page 169) Frequency 2050 MHz Path loss exponent 4.10 (from Table 5-26 on page 186) Log-distance path loss reference distance 1 m Standard deviation of log-normal strength 5.24 dB variation Reflection loss 10 dB LOS component dB above best-fit line 10.5 dB (includes reflection loss in simulation) Maximum excess delay 1557 ns Transmitter-receiver separation Equal to values for LOS locations (see Table 5-14 on page 150) Element locations (xe, ye) coordinates: (0, 3l / 4 ); (0, 1l / 4 ); (0, –1l / 4 ); (0, –3l / 4 ) in meters

The propagation environment simulated for the GBSBE model is shown in Figure 7-43. A single elliptical boundary that represents the largest single-bounce multipath delay is shown. The plus symbol and circle on the plot indicate the transmitter and receiver locations, respectively. The dots on the plot indicate locations of randomly generated scatterer positions, whose count within the entire elliptical region depends upon the input Poisson parameter. Single-bounce

267 CHAPTER 7 – CHANNEL MODEL EVALUATION

propagation paths are shown as lines that connect the transmitter, each scatterer, and the receiver. This geometry was used to produce channel impulse responses for comparison to measured channels at the modeled site.

Top View of Propagation Environment 250

200

150

100

50

0

-50 y-coordinate (m) -100

-150

-200

-250 -300 -200 -100 0 100 200 300 x-coordinate (m)

Figure 7-43. Example of geometric channel simulation (GBSBE model) showing transmitter location (plus symbol at focus), receiver location (circle at other focus), scatterers (dots), propagation paths (yellow lines), and elliptical boundary for uniformly distributed scatterers.

7.2.2 Multipath Signal Strength

Figure 7-44 through Figure 7-49 illustrate the characteristics of multipath strength produced by simulations of the GBSBE model for the NLOS locations (NLOS1-NLOS6). A pair of strength plots was produced for each of the locations NLOS1 through NLOS6. The (a) plot in each figure is a scatter plot of multipath strength versus log-delay, and the (b) plot in each figure illustrates a normalized histogram of multipath component relative strength and an overlaid Gaussian probability density function.

268 CHAPTER 7 – CHANNEL MODEL EVALUATION

Measurement results in section 5.3.5 starting on page 169 can be used for comparison to the multipath strength plots in this section. Multipath strength histograms for simulated channels and measured channels are similar, as expected because of the Gaussian strength variation of the simulator that is based on measurements. Strength-versus-log-delay scatter plots for simulated channels are different than those for measured channels in two respects. First, like the results of the ESR model, scatter plots for simulated channels show approximately equal distribution on either side of the best-fit line; measured channels, however, contain clusters of multipath whose strength deviates from the best-fit line. Obstructions causing shadowing of multipath with short delays is likely the cause of multipath falling below the best-fit line for early delays as shown by measurements. Differences in reflection coefficients and path loss exponents experienced during measurements are likely the cause of deviations for later delays. The second difference between measured and simulated scatter plots is the density of multipath occurrences versus propagation delay. On the dB-versus-log-time plot, simulations show a clear trend of increasing density as delay increases, unlike the trend of measurements and the ESR model. This difference is due to the uniform distribution of scatterers throughout the elliptical region. Because the ESR model specifies placement of scatterers more densely in sub-regions corresponding to shorter delays, multipath components appear more evenly distributed on a log-delay plot.

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-44. NLOS1 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

269 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-45. NLOS2 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-46. NLOS3 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

270 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-47. NLOS4 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-48. NLOS5 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

271 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-49. NLOS6 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

Figure 7-50 through Figure 7-53 illustrate GBSBE channel model simulation results for the LOS locations at the dense-scatterer site. Measurement results presented in section 5.3.5 starting on page 169 can be compared to these plots of results. In addition to a steady increase in multipath component density as delay increases on the log-delay plot, simulated LOS channel impulse responses do not contain the dense clusters of components shown in plots of LOS measurement results. Like the shortfall of the ESR model, the GBSBE does not accurately model the few multipath components at particular delays that dominated responses measured at each LOS location. The GBSBE model does not provide a way to allow persistent, dominant multipath components for a series of simulations. It appears that the model may perform satisfactorily for data combined for several LOS measurement locations, but it does not accurately model multipath strength for individual LOS locations because of its inability to include clusters of dominant multipath components.

272 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-50. LOS1 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.1 Simulated 0.09 Gaussian

0.08

0.07

0.06

0.05 PDF

0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-51. LOS2 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

273 CHAPTER 7 – CHANNEL MODEL EVALUATION

PDF of differences between simulated multipath strength and best-fit line 0.09 Simulated 0.08 Gaussian

0.07

0.06

0.05

PDF 0.04

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-52. LOS3 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

PDF of differences between simulated multipath strength and best-fit line 0.08 Simulated Gaussian 0.07

0.06

0.05

0.04 PDF

0.03

0.02

0.01

0 -30 -20 -10 0 10 20 30 Multipath strength difference (dB) (a) (b)

Figure 7-53. LOS4 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

274 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.2.3 RMS Delay Spread

RMS delay spread was calculated for channel impulse responses produced by the GBSBE channel model simulator. RMS delay spread statistics for simulated and measured channels for each NLOS location at the dense-scatterer site are shown in Table 7-13.

Table 7-13. RMS delay spread results for simulations (GBSBE) and measurements of NLOS dense scatterer locations. Location RMS Delay Spread (ns) Mean Std. Dev. Minimum Maximum Sim Meas Sim Meas Sim Meas Sim Meas NLOS1 172 67.5 72.4 10.1 20.5 40.2 352 108 NLOS2 167 60.9 76.5 10.0 25.4 0.00 356 91.0 NLOS3 167 70.2 76.9 12.1 33.2 35.9 385 152 NLOS4 168 78.6 80.1 10.7 17.1 51.6 391 112 NLOS5 179 70.7 76.9 7.70 26.0 49.3 430 95.3 NLOS6 150 69.4 76.3 13.3 12.2 31.3 409 368

Table 7-13 shows that the GBSBE model simulator produces channel impulse responses with large RMS delay spreads and large standard deviation of RMS delay spreads compared to those for measured channel responses. Two explanations support the high RMS delay spread of simulations. First, the existence of strong multipath components early in the measured power- delay profiles cause late multipath, which normally increases RMS delay spread, to affect RMS delay spread less significantly. Second, the uniform distribution of scatterers over the entire elliptical region in the simulation causes a relatively large number of multipath components to exist late in delay, where few multipath components normally exist as seen during measurements. This has the effect of increasing RMS delay spread for GBSBE simulations.

Complementary cumulative distribution functions (CCDF) of RMS delay spread for simulated NLOS locations are shown in Figure 7-54 through Figure 7-56. These results can be compared to the RMS delay spread results shown in section 5.3.2 beginning on page 151. The CCDFs support that RMS delay spread is overestimated by the GBSBE model to a greater degree than

275 CHAPTER 7 – CHANNEL MODEL EVALUATION the ESR model. This suggests that either the number of scatterers needs to be reduced or the path loss exponent needs to be increased in order to simulate channels with a specified RMS delay spread using the GBSBE model. Also, a restriction could be placed on maximum multipath delay to shorten RMS delay spread, but weak, long-delay multipath components would fail to be modeled accurately.

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-54. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS1 (b) NLOS2.

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-55. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS3 (b) NLOS4.

276 CHAPTER 7 – CHANNEL MODEL EVALUATION

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-56. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS5 (b) NLOS6.

Simulated channel impulse responses were also simulated using the GBSBE model for locations LOS1 through LOS4. Table 7-14 statistically summarizes the results. CCDFs of RMS delay spread for each location are shown in Figure 7-57 and Figure 7-58. Like the ESR model, the results show that simulations can overestimate or underestimate the RMS delay spread compared to measurements. A trend of increasing RMS delay spread with transmitter-receiver separation is again noted, as opposed to measurements that show RMS delay spread remaining relatively constant over all locations.

Table 7-14. RMS delay spread results for simulations (GBSBE) and measurements of LOS dense scatterer locations. Location RMS Delay Spread (ns) Mean Std. Dev. Minimum Maximum Sim Meas Sim Meas Sim Meas Sim Meas LOS1 42.3 34.4 11.5 4.81 20.4 21.4 84.6 51.2 LOS2 27.3 38.8 8.84 8.31 12.2 0.00 58.9 73.3 LOS3 17.4 39.0 6.64 12.1 6.46 20.1 72.1 91.8 LOS4 9.31 34.2 3.70 8.7 3.15 16.9 29.8 69.9

277 CHAPTER 7 – CHANNEL MODEL EVALUATION

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-57. RMS delay spread CCDF for simulated (GBSBE) channels (a) LOS1 (b) LOS2.

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Simulated Channels 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 Probability( RMS Delay Spread > Abscissa ) Probability( RMS Delay Spread > Abscissa ) 0.1 0.1

0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-58. RMS delay spread CCDF for simulated (GBSBE) channels (a) LOS3 (b) LOS4.

7.2.4 Excess Delay Spread

Results of excess delay spread using the GBSBE model for simulated channels and for measured channels are shown in Table 7-15 for NLOS locations. Means of excess delay spread at the 10 dB level for simulations are close to those for measurement data. For 20 dB levels and higher, the simulated excess delay spread results exceed those for measured channels. This is likely due to the use of uniform distribution of scatterers over the entire elliptical region, causing the

278 CHAPTER 7 – CHANNEL MODEL EVALUATION

probability of scatterers that produce longer delays to be higher than that for measurements where the count of multipath components at long delays is lower. The existence of even one large delay multipath component within 20 dB to 30 dB of the strong components causes excess delay spread at these levels to be large.

Excess delay spread results for simulated and measured LOS channels are shown in Table 7-16. As with the simulated RMS delay spread results, increasing excess delay spread based on simulated channel impulse responses has a strong correlation with increasing transmitter-receiver separation. Means of measured excess delay spread do not strictly adhere to this trend.

Table 7-15. Excess delay spread values for simulated (GBSBE) and measured NLOS channel impulse responses. Excess Delay Spread (ns) 10 dB Level 20 dB Level 25 dB Level 30 dB Level Location Mean Max Mean Max Mean Max Mean Max Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas NLOS1 222 200 1081 480 696 390 1432 1300 884 549 1432 1300 1103 682 1520 1500 NLOS2 222 204 1092 447 627 328 1468 697 872 440 1468 811 1047 601 1492 1510 NLOS3 243 272 1142 580 640 435 1402 775 869 581 1418 1250 1052 693 1496 1450 NLOS4 225 252 1135 572 648 499 1416 776 854 615 1512 888 1064 712 1537 1380 NLOS5 231 243 1418 493 626 380 1418 747 856 503 1432 909 1060 637 1531 1210 NLOS6 202 207 1107 478 571 367 1352 758 784 471 1430 1365 979 620 1441 1450

Table 7-16. Excess delay spread values for simulated (GBSBE) and measured LOS channel impulse responses. Excess Delay Spread (ns) 10 dB Level 20 dB Level 25 dB Level 30 dB Level Location Mean Max Mean Max Mean Max Mean Max Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas LOS1 3.75 115 206 335 55.8 196 356 533 152 230 836 725 353 313 1458 751 LOS2 2.95 131 166 501 22.8 233 414 790 76.4 300 497 790 186 408 855 791 LOS3 0.623 123 61.3 509 11.7 222 438 651 40.3 315 490 835 100 432 566 868 LOS4 0.027 89.1 5.40 421 6.45 162 150 586 16.9 263 201 786 33.4 390 331 861

279 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.2.5 Multipath Fading

Fading envelopes generated from GBSBE simulations of impulse responses were compared to fading envelopes generated from measured power-delay profiles. As with the ESR model evaluation, signal envelopes were formed by performing a vector sum of all signal components in each channel impulse response and taking the magnitude of the result. Envelope information from all antenna elements was used.

Figure 7-59 and Figure 7-60 show cumulative distribution functions (CDF) of signal envelope strength for fading resulting from simulated and measured channels. Signal levels were normalized to the median of signal strength for the CDF. A theoretical, median-normalized CDF for Rayleigh fading is also shown on each plot. Figure 7-59 shows that CDFs for measurements at all NLOS locations fall very close to the theoretical Rayleigh CDF, as demonstrated previously. For simulated channels, however, the CDF deviates from the Rayleigh characteristic such that deeper fades are more probable. For LOS channels, Figure 7-60 shows that fading calculated from measured responses exhibits a Rician characteristic. Simulation results also show a Rician characteristic but with a larger K-factor. The difference in the LOS CDFs suggests that the GBSBE model produces multipath components with a weaker combined power relative to the LOS component power in comparison to measured channels.

CDF of Received Signal Strength for Simulated NLOS Locations CDF of Received Signal Strength for Measured NLOS Locations 1 1

0.9 0.9

0.8 0.8

0.7 0.7 NLOS1 0.6 0.6 NLOS2 NLOS3 0.5 0.5 NLOS4 NLOS1 NLOS5 0.4 NLOS2 0.4 NLOS6 NLOS3 Rayleigh 0.3 NLOS4 0.3 NLOS5 NLOS6 Probability ( Strength < Abscissa ) 0.2 Probability ( Strength < Abscissa ) 0.2 Rayleigh 0.1 0.1

0 0 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Signal Strength Relative to Median (dB) Signal Strength Relative to Median (dB) (a) (b)

Figure 7-59. Signal strength CDF for each NLOS location derived from (a) channel impulse response simulations (GBSBE) and (b) measured channels.

280 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Received Signal Strength for Simulated LOS Locations CDF of Received Signal Strength for Measured LOS Locations 1 1

0.9 LOS1 0.9 LOS2 LOS3 0.8 0.8 LOS4 Rayleigh 0.7 0.7

0.6 0.6 LOS1 LOS2 LOS3 0.5 0.5 LOS4 Rayleigh 0.4 0.4

0.3 0.3

Probability ( Strength < Abscissa ) 0.2 Probability ( Strength < Abscissa ) 0.2

0.1 0.1

0 0 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Signal Strength Relative to Median (dB) Signal Strength Relative to Median (dB) (a) (b)

Figure 7-60. Signal strength CDF for each LOS location derived from (a) channel impulse response simulations (GBSBE) and (b) measured channels.

7.2.6 Antenna Diversity

Maximal ratio combining (MRC) with an antenna element separation of l / 2 was used to compare diversity gains achieved for simulated and measured channels. Figure 7-61 through Figure 7-66 show signal strength envelope CDFs for simulations and measurements of NLOS locations. A CDF of strength for a receiver using single antenna element and a CDF for a receiver using MRC diversity combining are shown on each plot.

Approximate diversity gains for simulated and measured NLOS locations for the 1% and 10% CDF levels are shown in Table 7-17. These results show that measured channel diversity gains at the 10% level are 0.5 dB to 3 dB higher than diversity gains for simulated channels. At the 1% level, differences in diversity gain range from 1.5 dB to 4 dB.

Figure 7-67 through Figure 7-70 show single-element and MRC diversity CDF plots for LOS locations. Approximate diversity gain for the 10% and 1% CDF levels for LOS simulations and measurements are tabulated in Table 7-18. Diversity gains at 10% and 1% levels for measured and simulated channels are similar but relatively small. Differences between diversity gains for measured and simulated channels are 2 dB or less.

281 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

-1 -1 10 Single Element 10 Single Element MRC Diversity MRC Diversity

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-61. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

-1 -1 Single Element 10 Single Element 10 MRC Diversity MRC Diversity

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-62. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

282 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

-1 -1 10 Single Element 10 Single Element MRC Diversity MRC Diversity

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-63. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

-1 -1 Single Element 10 Single Element 10 MRC Diversity MRC Diversity

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-64. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

283 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

-1 -1 10 Single Element 10 Single Element MRC Diversity MRC Diversity

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-65. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS5 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10

-1 -1 10 Single Element 10 Single Element MRC Diversity MRC Diversity

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-66. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS6 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

284 CHAPTER 7 – CHANNEL MODEL EVALUATION

Table 7-17. Approximate diversity gain for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels. Diversity Gain (dB) Location 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured NLOS1 1.5 2 6.5 4 NLOS2 1 4 6 8 NLOS3 1.5 3 3 7 NLOS4 1.5 3 6.5 9 NLOS5 1.5 4 5 7 NLOS6 1.5 3 5 5

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10 Single Element MRC Diversity

Single Element MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-67. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

285 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10 Single Element MRC Diversity

Single Element MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-68. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10 Single Element MRC Diversity

Single Element MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-69. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

286 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 0 10 10 Single Element MRC Diversity

Single Element MRC Diversity -1 -1 10 10

-2 -2 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-70. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

Table 7-18. Approximate diversity gain for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels. Diversity Gain (dB) Location 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured LOS1 1 0.5 1.5 2 LOS2 0.5 2 1.5 3 LOS3 0.25 0.5 0.5 2 LOS4 <0.25 1 <0.25 2

287 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.2.7 Two-Dimensional Rake Receiver

The two-dimensional rake receiver processing used for simulated and measured channels temporally and spatially combines multipath components from four antenna array elements using four rake fingers per element. One-dimensional rake receivers temporally combine the four strongest multipath components, and co-phased rake output signals are combined to produce the two-dimensional rake output signal.

CDFs of the received signal envelope with and without the use of a two-dimensional rake receiver for NLOS locations are shown in Figure 7-71 through Figure 7-76. Approximate gains achieved using the two-dimensional rake for simulated and measured channels are shown in Table 7-19. Similar to ESR model results, mitigation of fading using the two-dimensional rake was generally better for measured channels compared to simulated channels. Gains for simulated channels up to 12 dB were achieved at the 1% CDF level, while gains for measured channels up to 20 dB were observed.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 0 10 10 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-71. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

288 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 0 10 10 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-72. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 0 10 10 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-73. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

289 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 0 10 10 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-74. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 0 10 10 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-75. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS5 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

290 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 0 10 10 Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-35 -30 -25 -20 -15 -10 -5 0 5 10 15 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-76. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS6 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

Table 7-19. Approximate fading levels differences between 2-D rake output and single channel output for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels. Fading Level Relative to Mean Signal Strength – 2-D Rake Output Minus Single Channel Output Location (dB) 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured NLOS1 4 5 12 14 NLOS2 3 7.5 6 20 NLOS3 4 5 8.5 16 NLOS4 4.5 8 12 16 NLOS5 3 7 12 15 NLOS6 6 8.5 10 16

291 CHAPTER 7 – CHANNEL MODEL EVALUATION

For LOS locations at the dense-scatterer site, Figure 7-77 through Figure 7-80 show CDFs of relative signal envelope strengths with and without the application of a two-dimensional rake. Approximate gains achieved using the two-dimensional rake for both simulated and measured channels are shown in Table 7-20. Gains for 10% and 1% CDF levels show larger gains for measured channels compared to simulated channels. In fact, gains for the simulated channels are virtually nonexistent. Gains for measured channels up to 6 dB at the 1% CDF level where achieved. When gains are relatively small, such as in this case for the 10% CDF level, evaluation of model performance based on achievable gains becomes less meaningful based on the resulting small differences between measured and simulated gains.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 10 100

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 10 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-77. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

292 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output 0 CDF of Single Element Signal Strength & 2-D Rake Output 10 100

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-78. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 10 100

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 10 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-79. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

293 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output 0 CDF of Single Element Signal Strength & 2-D Rake Output 10 100

Single Element (Channel 1) 2-D Rake (4 fingers per chan) Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-80. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

Table 7-20. Approximate fading levels differences between 2-D rake output and single channel output for LOS locations computed from simulated (GBSBE) channel impulse responses and measured channels. Fading Level Relative to Mean Signal Strength – 2-D Rake Output Minus Single Channel Output Location (dB) 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured LOS1 0.25 2 <0.25 6 LOS2 <0.25 2 <0.25 5 LOS3 <0.25 1.5 <0.25 4 LOS4 <0.25 2 <0.25 5

294 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.2.8 GBSBE Comparison Summary

In comparing measured channel characteristics with results produced by simulations of the GBSBE model, the following observations were made:

· In general, the GBSBE model appears to produce realistic simulations of NLOS and LOS radio channels. To accurately represent specific characteristics of radio channels, the model needs to be tuned using the input parameters. The model appears to be less accurate compared to the ESR model.

· The GBSBE model produces Gaussian distributions of multipath strength (about a dB- versus-log-delay straight line) that generally match those of NLOS measurements. This is expected since the Gaussian trend was designed into the model using measurements. Discrete clustering of multipath components in NLOS and LOS measured channels is not handled by the GBSBE model. Unlike the ESR model, the GBSBE model does not provide a way of increasing multipath count in a particular range of delay by increasing the Poisson parameter for the corresponding scattering region. For NLOS channels, occasional deviations of strength above the straight-line trend for early delay ranges are not handled by the GBSBE model.

· Mean RMS delay spread for NLOS channels was higher for simulated channels compared to measured channels. This is likely related to two causes. First, measured NLOS channels showed relatively strong multipath early in delay, which was not accurately managed by the GBSBE model. Second, the GBSBE model does not have the ability to account for fewer scatterers that cause multipath for long delays compared to the count of scatterers that cause multipath with short delays. For LOS channels, simulated result showed a correlation of increasing mean RMS delay spread with increasing distance, while measurements did not show this trend.

· For NLOS channels, mean excess delay spreads at the 10 dB level for simulated and measured channels were similar. For 20 dB, 25 dB, and 30 dB levels, excess delay spread means for simulated channels exceeded those for measured channels. For LOS

295 CHAPTER 7 – CHANNEL MODEL EVALUATION

channels, simulated results showed a strong trend between mean excess delay spread and transmitter-receiver separation. Measured results did not necessarily follow this trend.

· Fading for simulated channels is shown to be similar to measured channels with respect to cumulative distribution functions. Fading was Rayleigh for NLOS channels and Rician for LOS channels. Rician K-factors were slightly larger for simulated channels.

· The GBSBE model appears to produce channel impulse responses appropriate for reasonably simulating MRC antenna diversity. For 1% CDF levels, diversity gains of measured NLOS channels were shown to exceed those for simulated channels, but gain differences were 4 dB or less. For measured and simulated LOS channels, gains were similar but small, making the comparison difficult to definitively judge.

· Performance of a two-dimensional rake receiver was shown to be better for measured channels. Gain differences at the 1% CDF level ranged from 2 dB to 14 dB between NLOS simulations and measurements. At the 10% level, gain differences of 4 dB or less were observed.

Despite some shortcomings of the GBSBE model, the model is useful for generating channel impulse responses where characterizations of input parameters for the ESR model are not available. Differences between simulated and measured channel characteristics, such as RMS delay spread, can be reduced by adjusting GBSBE input parameters to achieve results that better match desired characteristics (if known). The tuned model can then be used for system simulations.

7.3 Geometric Air-to-Ground Ellipsoidal Channel Model

The geometric air-to-ground channel model was first developed for this dissertation, and therefore this is its first test of ability to represent the actual air-to-ground channel. The air-to- ground measurements presented in Chapter 5 serve to provide the measurement parameter input for the GAGE model and act as the source of measurement characteristic comparison. Air-to- ground measurements were performed for four elevation angles, and results from several

296 CHAPTER 7 – CHANNEL MODEL EVALUATION hundred power-delay profiles were used for evaluation of each elevation angle. Simulation results for all measured elevation angles are presented here, allowing a comparison of results for a variety of conditions.

7.3.1 Simulation Parameters

Details of the GAGE input parameters used to simulate the air-to-ground channel are shown in Table 7-21. Antenna element locations, frequency, transmitter-receiver separation, and elevation angles mimic those used for measurements. Since propagation distance through ground regions depends upon azimuthal angle, log-distance path loss parameters could not be calculated from measured data. However, the measured air-to-ground measurements were performed largely for line-of-sight channels, and terrestrial measurements have been performed to characterize the ground region near where the ground station was located; therefore, results from the LOS locations at the dense-scatterer site were used to define the GAGE input parameters of path loss exponent and standard deviation of strength variation. Maximum excess delay was set to the largest excess delay logged during air-to-ground measurements. As in the evaluation of the ESR and GBSBE models, log-distance path loss reference distance remains an assumed value, which was chosen equal to that used for ESR and GBSBE model simulations. Reflection loss was selected as a function of elevation angle as described in section 7.3.2.

Because of the non-uniform distribution of measured multipath component count versus delay (see section 5.4.4), a sub-regions approach was taken with the GAGE model. Equal intervals of multipath excess delay were used. The delays correspond to concentric ellipsoids in three dimensional space that form elliptical intersections with the ground plane; these elliptical intersections share one common focus at the ground-based receiver location. The simulated air- to-ground propagation environment for the GAGE model is shown in Figure 7-81. The ground- level elliptical boundaries depicted represent equal intervals of excess multipath delay. The transmitter and receiver are located at the elevated plus symbol and ground-level circle, respectively. Ground-level dots correspond to randomly generated scatterer positions, the counts of which depend upon specified Poisson parameters. Lines connecting the transmitter, scatterer, and receiver are the single-bounce propagation paths.

297 CHAPTER 7 – CHANNEL MODEL EVALUATION

Table 7-21. Major simulation parameters for geometric air-to-ground ellipsoidal channel model. Parameter Value Number of sub-regions 16 Poisson parameters Equal to values measured during air-to-ground measurements (see Table 5-33 on page 199) Frequency 2050 MHz Path loss exponent 4.10 Standard deviation of strength variation 5.24 dB Reflection loss Varies based on elevation angle (see section 7.3.2) Maximum excess delay 1556 ns Transmitter-receiver separation Equal to values used for measurements (see Table 5-30 on page 189)

Propagation Environment

600

400

200 z-coordinate (m) 0 500 0

500 0 1000 1500 -500 y-coordinate (m) x-coordinate (m)

Figure 7-81. Example of geometric air-to-ground channel model simulation showing transmitter location (plus symbol at elevated ellipsoid focus), receiver location (circle at ellipsoid and ground ellipse shared focus), scatterers (dots), propagation paths (green lines), and sub-region boundaries of constant propagation delay.

298 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.3.2 RMS Delay Spread

Measured RMS delay spread results showed a strong correlation with elevation angle, a trend which was anticipated for simulated channels. However, initial RMS delay spread results did not show the expected elevation angle dependency. Figure 7-82 shows CCDFs of RMS delay spread for a constant reflection coefficient of 10 dB. The plot labeled (a) shows simulation results, and the plot labeled (b) shows results derived from measurements of the channel. The measured results illustrate the dependency of RMS delay spread distribution on elevation angle. However, the results based on simulated channel impulse responses clearly fail to follow a similar trend.

As a result of the RMS delay spread distribution discrepancy, it was hypothesized that the elevation angle dependency was a result of reflection loss being a function of elevation angle. Although varying the number of multipath components as a function of elevation angle could also be used to increase or reduce RMS delay spread as needed to match measurements, air-to- ground measurement results described in section 5.4.4 showed that the number of multipath components in each of 16 delay bins did not vary significantly with changes in elevation angle. Therefore, a variable reflection loss was used and the hypothesis tested.

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Measurements 1 1 Elevation angle 7.5 deg Channel 1 0.9 Elevation angle 15 deg 0.9 Channel 2 Elevation angle 22.5 deg Channel 3 0.8 Elevation angle 30 deg 0.8 Channel 4

0.7 0.7

0.6 0.6

0.5 0.5 7.5 deg 0.4 0.4 15 deg 0.3 0.3

0.2 0.2 22.5 deg Probability( RMS Delay Spread > Abscissa ) 0.1 Probability( RMS Delay Spread > Abscissa ) 0.1 30 deg 0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-82. CDF of RMS delay spread for four elevation angles for (a) simulated (GAGE) channel impulse responses and (b) measured channels. A constant reflection loss was used.

299 CHAPTER 7 – CHANNEL MODEL EVALUATION

RMS delay spread results using a variable reflection loss are shown in Figure 7-83. Plot (a) is an RMS delay spread CCDF based on simulated channels, and plot (b) is an RMS delay spread CCDF base on measured channels. Reflection loss values used to produce these CCDFs of RMS delay spread results are shown in Table 7-22. The CCDF plots show that a variable refection loss can be used to produce accurate modeling of RMS delay spread distributions. Mean and standard deviation of RMS delay spread results for simulated and modeled channels are shown in Table 7-23. The table shows good agreement between simulated and measured values for all elevation angles. For the remaining GAGE channel model discussions, simulations use the reflection losses set forth in Table 7-22.

Table 7-22. Reflection losses as a function of elevation angle used to produce the most accurate RMS delay spread results for the GAGE model. Elevation Angle Reflection Loss 7.5 14 15 21 22.5 30 30 33

RMS Delay Spread Based On Simulated Channels RMS Delay Spread Based On Measurements 1 1 Elevation angle 7.5 deg Channel 1 0.9 Elevation angle 15 deg 0.9 Channel 2 Elevation angle 22.5 deg Channel 3 0.8 Elevation angle 30 deg 0.8 Channel 4

0.7 0.7

0.6 0.6

0.5 0.5 7.5 deg 0.4 0.4 15 deg 0.3 0.3

0.2 0.2 22.5 deg Probability( RMS Delay Spread > Abscissa ) 0.1 Probability( RMS Delay Spread > Abscissa ) 0.1 30 deg 0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 RMS Delay Spread (ns) RMS Delay Spread (ns) (a) (b)

Figure 7-83. CCDF of RMS delay spread for four elevation angles for (a) simulated (GAGE) channel impulse responses and (b) measured channels. Reflection loss was defined to be a function of elevation angle.

300 CHAPTER 7 – CHANNEL MODEL EVALUATION

Table 7-23. RMS delay spread results for air-to-ground simulations using the GAGE model versus measurements. Elevation RMS Delay Spread (ns) Angle (deg) Mean Standard Deviation Simulated Measured Simulated Measured 7.5 104 98.1 65.8 82.2 15 55.5 54.9 36.4 40.6 22.5 23.0 24.3 12.6 16.7 30 18.7 18.3 10.7 9.89

7.3.3 Multipath Signal Strength

As discussed earlier, path loss for the GAGE model is fundamentally different than path loss for the ESR and GBSBE models because the distance traversed by multipath components through the scattering region is dependent upon direction of arrival. Notwithstanding that fact, scatter plots of multipath strength versus log-delay were produced for comparison of the GAGE model to measurements. Figure 7-84 through Figure 7-87 illustrate scatter plots based on simulated and measured channels. In comparing these figures, it can be noted that the measured plots show sporadic delay intervals where strong multipath components exist. These clusters of strong multipath are likely due to dominant scatterers in the environment that reflected energy effectively. The GAGE model has no provision for directly modeling these clusters; however, Poisson parameters for each sub-region could be adjusted to produce clusters of multipath components.

301 CHAPTER 7 – CHANNEL MODEL EVALUATION

(a) (b)

Figure 7-84. Scatter plot of multipath strength versus log of propagation delay for the 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles.

(a) (b)

Figure 7-85. Scatter plot of multipath strength versus log of propagation delay for the 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles.

302 CHAPTER 7 – CHANNEL MODEL EVALUATION

(a) (b)

Figure 7-86. Scatter plot of multipath strength versus log of propagation delay for the 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles.

(a) (b)

Figure 7-87. Scatter plot of multipath strength versus log of propagation delay for the 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles.

303 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.3.4 Excess Delay Spread

Excess delay spread results for simulated and measured air-to-ground channels are shown in Table 7-24. For all excess delay spread levels, nearly all means of excess delay spread for measurements exceed those for simulation. Both simulations and measurements show a decrease in mean excess delay spread as elevation angle increases. Discrepancies between simulated and measured mean excess delay spread become smaller in terms of percentages as excess delay spread level increases. Differences such as these can be caused by errors in selection multipath strength distribution parameters, errors in selection of log-distance path loss exponents for the ground propagation leg, or the variability of model parameters with propagation distance or azimuthal angle39.

Table 7-24. Excess delay spread values for simulated and measured air-to-ground channel impulse responses. Excess Delay Spread (ns) Elevation 10 dB Level 20 dB Level Angle Mean Max Mean Max Sim Meas Sim Meas Sim Meas Sim Meas 7.5 94.8 169 1185 1380 460 431 1358 1490 15 3.40 104 673 1300 206 250 1335 1480 22.5 0 90.0 0 1031 11.9 127 588 1294 30 0 89.0 0 256 3.57 108 574 471

Excess Delay Spread (ns) Elevation 25 dB Level 30 dB Level Angle Mean Max Mean Max Sim Meas Sim Meas Sim Meas Sim Meas 7.5 589 613 1509 1550 656 703 1509 1570 15 400 407 1359 1480 567 595 1361 1590 22.5 96.0 199 1197 1294 290 352 1318 1407 30 47.7 157 992 1290 196 284 1257 1340

39 The model assumes constant input parameters as the aircraft circles the receiver location. In practice, however, the environmental characteristics may not be uniform in azimuthal angle around the receiver.

304 CHAPTER 7 – CHANNEL MODEL EVALUATION

7.3.5 Multipath Fading

Fading envelopes for the air-to-ground channel were computed by vector sum of multipath components in measured power-delay profiles and simulated channel impulse responses. CDFs of signal envelopes, normalized to median values, are shown in Figure 7-88. For comparison of measured data, simulated data, and theory, CDFs for Rayleigh fading are also shown in the plots. Figure 7-89 indicates that air-to-ground CDFs for simulations and measurements exhibit Rician characteristics. Simulated channels show a slightly larger Rician K-factor.

CDF of Received Signal Strength for Simulated Air-to-Ground Channels CDF of Received Signal Strength for Measured Air-to-Ground Channels 1 1

Elevation angle 7.5 deg 0.9 0.9 Elevation angle 7.5 deg Elevation angle 15 deg Elevation angle 22.5 deg 0.8 Elevation angle 15 deg 0.8 Elevation angle 22.5 deg Elevation angle 30 deg Rayleigh 0.7 Elevation angle 30 deg 0.7 Rayleigh 0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3 Probability ( Strength < Abscissa ) 0.2 Probability ( Strength < Abscissa ) 0.2

0.1 0.1

0 0 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Signal Strength Relative to Median (dB) Signal Strength Relative to Median (dB) (a) (b)

Figure 7-88. Signal strength CDF for each air-to-ground elevation angle derived from (a) channel impulse response simulations and (b) measured channels.

7.3.6 Antenna Diversity

Maximal ratio combining (MRC) was applied to the simulated and measured air-to-ground channels using an antenna element separation of l / 2 . Figure 7-89 through Figure 7-92 show CDFs of relative signal envelope power. One CDF in each plot corresponds to a receiver using single antenna element, and the other CDF on each plot corresponds to the output of MRC diversity combining.

Shown in Table 2-1 are approximate diversity gains for simulated and measured air-to-ground channels for the 1% and 10% CDF levels. These results show that only modest diversity gains of

305 CHAPTER 7 – CHANNEL MODEL EVALUATION

2.5 dB or less are achievable for measured channels. Diversity gains for simulated channels are close to those for measured channels, where differences for the 10% level are less than 0.5 dB and differences for the 1% level are less than 1.5 dB.

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 10 100

Single Element MRC Diversity Single Element MRC Diversity -1 10 10-1

-2 10 10-2 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-89. CDF of received signal strength using maximal ratio combining and using a single antenna for 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output 0 CDF of Single Element Signal Strength & Diversity Combiner Output 10 100 Single Element MRC Diversity

Single Element MRC Diversity -1 10 10-1

-2 10 10-2 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-90. CDF of received signal strength using maximal ratio combining and using a single antenna for 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

306 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & Diversity Combiner Output CDF of Single Element Signal Strength & Diversity Combiner Output 0 10 100 Single Element MRC Diversity

Single Element MRC Diversity

-1 10 10-1

-2 10 10-2 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-91. CDF of received signal strength using maximal ratio combining and using a single antenna for 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & Diversity Combiner Output 0 CDF of Single Element Signal Strength & Diversity Combiner Output 10 100 Single Element MRC Diversity

Single Element MRC Diversity

-1 10 10-1

-2 10 10-2 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-3 -3 10 10 -25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-92. CDF of received signal strength using maximal ratio combining and using a single antenna for 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

307 CHAPTER 7 – CHANNEL MODEL EVALUATION

Table 7-25. Approximate diversity gain for simulated and measured air-to-ground channel impulse responses. Diversity Gain (dB) Elevation 10% CDF Level 1% CDF Level Angle Simulated Measured Simulated Measured 7.5 0.75 0.75 4 2.5 15 0.5 0.75 1 2 22.5 <0.25 0.25 0.25 1 30 <0.25 <0.25 0.25 0.25

7.3.7 Two-Dimensional Rake Receiver

Two-dimensional rake receiver processing was used to produce the CDFs shown in Figure 7-33 through Figure 7-38. Using four fingers, the receiver processing coherently combined multipath components in space and delay. The CDFs show relative received signal envelope power with and without the use of a two-dimensional rake receiver for simulated and measured air-to-ground channels. Approximate gains at 10% and 1% CDF levels achieved through the use of the two- dimensional rake are shown in Table 7-26. Simulated and measured gains at the 1% CDF level were similar and showed decreasing gain with increasing elevation angle. Up to 8 dB of gain at the 1% CDF level was achieved for simulated channels at and up to 7 dB for measured channels was achieved. Gains at the 10 % CDF level were small.

308 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output 0 CDF of Single Element Signal Strength & 2-D Rake Output 10 100 Single Element (Channel 1) Single Element (Channel 1) 2-D Rake (4 fingers per chan) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-93. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 10 100 Single Element (Channel 1) Single Element (Channel 1) 2-D Rake (4 fingers per chan) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 10 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-94. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

309 CHAPTER 7 – CHANNEL MODEL EVALUATION

CDF of Single Element Signal Strength & 2-D Rake Output 0 CDF of Single Element Signal Strength & 2-D Rake Output 10 100 Single Element (Channel 1) Single Element (Channel 1) 2-D Rake (4 fingers per chan) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 -2 10 10

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-95. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

CDF of Single Element Signal Strength & 2-D Rake Output CDF of Single Element Signal Strength & 2-D Rake Output 0 10 100

Single Element (Channel 1) Single Element (Channel 1) 2-D Rake (4 fingers per chan) 2-D Rake (4 fingers per chan)

-1 -1 10 10 Probability ( Strength < Abscissa ) Probability ( Strength < Abscissa )

-2 10 10-2

-25 -20 -15 -10 -5 0 5 10 15 -25 -20 -15 -10 -5 0 5 10 15 Strength Relative to Mean (dB) Strength Relative to Mean (dB) (a) (b)

Figure 7-96. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

310 CHAPTER 7 – CHANNEL MODEL EVALUATION

Table 7-26. Approximate fading levels differences between 2-D rake output and single channel output for air-to-ground channels computed from simulated channel impulse responses and measured channels. Fading Level Relative to Mean Signal Strength – 2-D Rake Output Minus Single Channel Output Elevation (dB) Angle 10% CDF Level 1% CDF Level Simulated Measured Simulated Measured 7.5 3.5 0.5 8 7 15 1.5 0.5 2.5 3 22.5 <0.5 0.5 1 2 30 0.5 0.5 0.5 1.5

7.3.8 GAGE Comparison Summary

Comparison of the GAGE model with the air-to-ground measurements resulted in the following observations:

· In general, the GAGE model performs satisfactorily with respect to comparisons of RMS delay spread characteristics, fading characteristics, MRC diversity gains, and two- dimensional rake receiver gains.

· RMS delay spread characteristics of simulated channels accurately follow characteristics of measured channels when reflection loss is tuned. CDFs of RMS delay spread show agreement when the model is tuned based on mean RMS delay spread. RMS delay spread characteristics of measured and simulated channels show the same trend with changes in elevation angle.

· Differences in excess delay spread results between measured and modeled channels vary depending on elevation angle and excess delay spread level. For the 10 dB level, simulated channels based on the GAGE model tend underestimate excess delay spread.

311 CHAPTER 7 – CHANNEL MODEL EVALUATION

At larger levels, excess delay spread results tend to match for lower elevation angles but deviate for higher elevation angles.

· Using the GAGE model, simulated and measured vector channel impulse responses appear to compare well with respect to MRC antenna diversity characteristics. Although gains are small, and thereby difficult to judge accurately, differences in diversity gains were 1.5 dB or less.

· Results using a two-dimensional rake receiver showed a favorable comparison between measured and modeled channels. Gain differences of only 1 dB or less were noted for the 1% CDF level; gain differences for the 10% CDF level were 3 dB or less. For the 7.5 degree elevation angle, measurements and simulations both resulted in large gain (7 dB and 8 dB respectively). Gains at the 1% CDF for other elevation angles were modest, on the order of 1 dB to 3 dB for measured and simulated channels.

7.4 Summary

Three geometric channel models have been compared to measurements of channels from which model input parameters were derived. Ideally, the characteristics of measured and modeled channels would exactly match. However, because model results rely on theoretical statistical distributions that summarize behavior of the channel, at least slight errors in modeling are expected.

The ESR and GBSBE models shared the deficiency of not being able to produce strong clusters of multipath components that were apparent in measured power-delay profiles. Scatter plots of multipath strength for the GBSBE model indicated that multipath components were sparsely scattered for early delays compared to measurements. The ESR model performed better in this regard by providing a means to distribute multipath scatterers more densely in regions that induce multipath with early delays.

312 CHAPTER 7 – CHANNEL MODEL EVALUATION

The ESR model performed better than the GBSBE model for producing simulated channel impulse responses with RMS delay spreads that matched measured channels. For NLOS channels, percentage differences between mean RMS delay spreads of ESR-simulated channels and those of measured channels ranged from approximately 3% to 33%, while percentage differences for GBSBE-simulated channels ranged from approximately 73% to 86%. The ESR model also generally performed better with respect to LOS mean RMS delay spread results. For the GAGE model, provisions for variable reflection losses based on elevation angle resulted in only single-digit percent differences between measured and simulated mean RMS delay spread results.

Simulations of multipath fading showed that the ESR model performs better than the GBSBE model for its ability to produce channels with fading characteristics that match those of measured channels. Relative signal strength CDFs showed that measured NLOS fading was Rayleigh distributed, and channels produced by the ESR model were closer to Rayleigh than channels produced by the GBSBE model. CDFs of envelope fading for LOS channels showed that measured channels exhibited Rician fading characteristics, as did the channels produced by the ESR and GBSBE models. However, the CDFs of the ESR model better match the CDFs of the measurements with regard to the Rician K-factor. For the GAGE model, CDFs of fading for simulated channels aligned very well with CDFs of fading for measured channels. Measured and simulated air-to-ground channels exhibited Rician fading with similar K-factors.

The ESR and GBSBE models produced similar results with respect to antenna diversity gain for NLOS channels. For LOS channels, the ESR model produced gains that were on average approximately 3 dB higher than measured results at the 1% CDF level, and the GBSBE model produced gains that were on average approximately 2 dB lower than measured results at the 1% CDF level. While exact values and differences of diversity gains vary, measured channels with large diversity gains were generally associated with modeled channels with large diversity gains. Likewise, simulations of channels with modest measured gains generally produced simulated responses with modest gains.

313 CHAPTER 7 – CHANNEL MODEL EVALUATION

The ESR and GBSBE models both underestimated the gain achievable using a two-dimensional rake receiver. At the 1% CDF level, the mean difference between gains achieved for measured responses and gains achieved for simulated responses using the ESR model was 8 dB. For the GBSBE model, the mean difference was 6 dB. For the GAGE model, simulated two- dimensional rake results generally matched those based on measurements.

The models generally demonstrated a good ability to produce channel impulse responses with reasonable values for RMS delay spread, excess delay spread, fading envelopes, diversity gain, and gain using a two dimensional rake receiver. Although some simulated output values deviated from measured results, those values were still within ranges that are sensible for the environments modeled. The key to accurately modeling a target environment is to tune the input parameters of the model such that the simulated channel impulse responses exhibit the important characteristics of the target environment. Once tuned, a model can be used to generate an arbitrarily large amount of channels for testing communication system designs through simulations. With this in mind, the true value of these geometric models is the ability to use a relatively small amount of measurement data to generate an enormous amount of channel data.

314

Chapter 8

Conclusion

This research has addressed areas of radio channel measurement and modeling, smart antennas, and software radio. A union of these areas helped produce a new measurement system and new research results applicable to design and analysis of systems using antenna arrays.

8.1 Summary of Research

A survey of published literature on antenna array theory provided direction for this research. Smart antenna arrays are a proven method for increasing capacity, improving performance, and enhancing quality of service for wireless communication systems. Designing successful smart antenna systems requires channel measurements and models for testing and validation of algorithms.

Development of the wideband measurement receiver successfully demonstrated the benefits and feasibility of an object-oriented, software radio architecture. Demand for the system over approximately five years illustrated the value of a flexible software radio receiver architecture. Over the same period of time, ease of capabilities expansion and maintainability highlighted the advantages of encapsulation and abstraction inherent in an object-oriented design. Provisions for

315 CHAPTER 8 – CONCLUSION

future applications built into the system at design time and an interface to standardized simulation software allowed implementation of sponsored research and classroom applications that had not been envisioned for the system during its development.

Channel models of various types were researched and a new technique for three-dimensional geometric channel modeling was developed using ellipsoids. The ellipsoidal geometry was applied to the problem of modeling air-to-ground channels. Equations appropriate for addressing air-to-ground channel modeling were derived and used for analysis and simulation of multipath time-of-arrival and direction-of-arrival characteristics for a ground-based receiver. Experience gained through this work formed a basis for measurement planning, vector channel simulation, and channel model evaluation.

Measurements produced results for characterization and input parameters for channel models. Terrestrial measurements were designed to meet the needs of channel model evaluation. Air-to- ground measurements characterized a channel not often studied in addition to producing data for channel model testing. Measured power-delay profiles were processed to characterize time dispersion in radio channels using RMS delay spread and excess delay spread, and maximum multipath delays were computed for input to geometric channel models. Quantitative measurement results on multipath strength trends, multipath counts versus delay, path loss exponents, and signal envelope fading will assist researchers dealing with the types of channels studied here.

A channel simulator was developed to implement and evaluate three geometric channel models. The simulator demonstrated steps beyond what was clearly defined for the models in publications. These steps were required for accurate simulation of characteristics observed in actual radio channels, such as strength variations due to stochastic properties of the environment and fading of multipath components across an antenna array. The simulator can be used for future research in propagation and communication system simulation, and it can be expanded to include other channel models or improvements on currently supported models.

316 CHAPTER 8 – CONCLUSION

Three geometric channel models (ESR, GBSBE, and GAGE) were evaluated based on their ability to produce channel impulse responses with characteristics that matched characteristics of measured power-delay profiles. The models demonstrated a reasonable ability to represent measured channels with respect to RMS delay spread, excess delay spread, fading envelopes, diversity gain, and gain using a two dimensional rake receiver. Most deviations away from measured characteristics were relatively minor in that the resulting characteristics were within limits for reasonable the types of channels measured, and similar discrepancies could be expected when comparing the measurements presented here with measurements at other sites in similar propagation environments. Tuning of model input parameters is a recommended method of achieving specific characteristics of target environments. The advantage of channel models is the ability to use summarizing statistics based on relatively few measurements to generate a far larger number channel impulse responses for simulation.

8.2 Original Contributions

This research has produced the following contributions:

· A fully functional, software-defined radio receiver was designed and constructed; this system continued to be used by multiple researchers for other research projects. · An application of object-oriented, multi-threaded software design techniques to software radio architecture was demonstrated. · A geometric air-to-ground ellipsoidal channel model was developed and tested; analytical and simulated results yield insight into the air-to-ground radio channel. · Evaluations of existing geometric channel models were performed and documented in detail. · Measurement techniques were developed to characterize and model multipath strength variations, correlation of multipath component strengths, and multi-leg propagation for air-to-ground channels. · A multi-topic compilation of literature on modern software development techniques, smart antennas, software radios, channel modeling, and channel measurements.

317 CHAPTER 8 – CONCLUSION

This research is directly responsible for new radio channel measurements, experimental results, and demonstration capabilities:

· Terrestrial channel measurements, air-to-ground channel measurements, and multiple antenna array experiments were performed to serve multiple research projects (sponsored by Allen Telecom, Altera, DARPA, Grayson Wireless, LGIC, Office of Naval Research, Texas Instruments, and NASA/Virginia Space Grant Consortium). · Wideband measurements were performed along highways in Blacksburg, Virginia and Richmond, Virginia to characterize channels and measure multipath isolation between antennas used for single-frequency repeaters (sponsored by Allen Telecom, MIKOM). · Low-to-ground wideband channel measurements were made over line-of-sight and forested paths at 300 MHz and 1.9 GHz (sponsored by ITT Aerospace/Communications Division). · In-building wideband channels were measured for wireless LAN (802.11) propagation and interference research (sponsored by CNS/Virginia Tech). · Performance of transmit diversity was measured and demonstrated in indoor channels (sponsored by Texas Instruments). · The software-defined receiver was used to test adaptive antenna array algorithms developed by graduate students for a software radio course (Virginia Tech). · Power-delay profiles for indoor and outdoor channels were processed for research and development of hidden Markov models (sponsored by LGIC). · Measurements in NLOS and LOS environments were processed to support space- time processing research and hidden Markov modeling for the NAVCIITI program (sponsored by Office of Naval Research). · Improvements of MPEG video signal transmissions using antenna diversity were demonstrated with the software-defined receiver; the receiver communicated with a MPEG test bed over a TCP/IP network to form a distributed simulation platform (sponsored by DARPA).

318 CHAPTER 8 – CONCLUSION

· Measurement receiver and test bed demonstrations were performed for representatives of Congress and federal government to showcase wireless research at Virginia Tech. · Received signal measurements and channel measurements were performed for development of the VT-STAR MIMO test bed system (sponsored by MPRG Industrial Affiliates). · Numerous demonstrations of the measurement receiver and test bed were performed for visitors to Virginia Tech, including industrial sponsors, academic colleagues, symposium attendees, government representatives, and private donors.

8.3 Future Work

This research has revealed opportunities for future work on the following topics:

Measurements and measurement systems · The techniques and methodologies of the current wideband measurement system should be used to develop a more portable system with the same or greater capabilities; portions of software and hardware of the current system could be directly inherited for this purpose. · Software for determining direction of arrival of multipath components with high resolution should be written for the measurement system. · MIMO channel algorithms should be implemented on the measurement system receiver. · The FPGA spread-spectrum transmitter developed for this research should be further developed into a multi-channel transmitter for MIMO channel characterization. · Measurements in several locations in multiple environments should be performed to compare channel models to a wider range of measurement results. · Direction of arrival statistics should be measured in multipath channels and compared with results of channel models.

319 CHAPTER 8 – CONCLUSION

Channel modeling · Evaluations of statistical- and measurement-based models should be performed and compared to the capabilities and accuracy of geometric channel models. · A analysis of the sensitivity of geometric channel model output to change of model input parameters should be performed. · The geometric air-to-ground channel model should be compared against high-altitude and long-range airborne measurements to determine applicability.

Smart Antennas · New and existing antenna array configurations and algorithms should be tested simultaneously with channel measurements to establish relationships between array performance and channel characteristics. · Performance of various beamforming algorithms applied to measured and simulated channels should be compared. · Existing smart antenna simulation code should be slightly modified so that they become software radio modules and can be evaluated in actual channels using the measurement receiver.

8.4 Closing

In summary, this research has produced several developments in radio channel measurements and channel modeling related to smart antennas. The results should serve engineers and researchers who continue work in propagation and wireless communication system design. As long as wireless communications continues to develop, radio channels will need to be measured, characterized, and modeled for applications to come.

320

Epilogue

The metaphorical lead character of this dissertation, as of this writing, remains alive and well. I feel a sense of pride in seeing that the measurement system’s usefulness has delayed its inevitable cannibalization, a fate that seems to befall all hardware creations as a sacrifice to build better and faster systems constructed from scratch and starved for components. Such resourcefulness along with perseverance drive our field, a discipline in which an enormous effort on the part of the individual marks the next blaze along a faint trail for the next explorer. Of great significance are the accomplishments of pioneers. Of greater significance is the inspiration of minds who follow.

During one of my excursions from academia, an island whose surrounding waters can isolate and protect yet periodically madden, I discovered Giovanni de Lutero’s (Dosso Dossi) Learned Man of Antiquity, an Italian painting circa 1520 that symbolized for me the power of math and science. The remarkably muscular man in this striking image wore the expression of a scholar, whose brawn seemed to be built not by lifting the stone tablet he firmly held in his extended arm, but by pursuit of the unreadable but recognizable mathematical expressions carved into the tablet. The scholar stared beyond the painting’s border, toward a brightness that was divine in spite of this scientific threat to a world of religious explanations. This work depicted a secular transition of thought with the approval of God, and it was a prophetic painting of societal direction for the next five-hundred years.

321 EPILOGUE

My life’s theme of science and math delivered me to engineering, and my father ignited my interest in telecommunications as I recall from my earliest memories of listening to dinner-table conversations after his workdays at the phone company. Wireless was (and is) the magic show of telecommunications, drawing into its sideshow tent many kids and adults and adult-kids, and I’ve spent decades trying to figure out how to perform as many tricks as possible. What I’ve had to come to accept is that each magician in wireless has his or her own niche, and not one thoroughly understands all of the illusions.

Wireless will follow a path to destinations we cannot yet conceive. While I’ve heard pundits speak of approaching saturation in the wireless field, I can say that after climbing to this doctoral peak, I see plenty of open space and a future that extends beyond any visible horizon. Maybe it takes a climb to a summit, not necessarily doctoral, and an unobstructed view only possible at the top, to look toward the fringe of mist and know that beyond what is immediately visible there is overwhelming potential along the adventurous trails ahead.

322

Appendix A

Measurement Receiver MATLAB Signal Interface

A.1 MATLAB Interface Overview

The measurement receiver includes software to interface with the MATLAB engine. The interface has been fully tested with MATLAB version 5.3.1. The MATLAB interface allows m- files written for MATLAB to execute using actual signal data from the measurement receiver. By connecting an m-file to the measurement receiver through the interface, a MATLAB simulation defined by the m-file becomes an actual radio processing module as part of the measurement receiver, operating on signal snapshots from all four channels in real time.

The interface works by inserting variables in the MATLAB workspace and filling these variables with signal data and other data. Once the variables are populated, the measurement receiver software instructs MATLAB to call the user’s m-file. The framework allows for results to be plotted on a single figure (subplots are allowed). The m-file is called once each time a snapshot of the four channels is available; if the m-file completes in a time period longer than the

323 APPENDIX A – MEASUREMENT RECEIVER MATLAB SIGNAL INTERFACE

between-snapshot period, then the m-file will not be called until MATLAB has completed processing the m-file. For best results, all m-files that are called by the m-file named in the interface should be placed in the same folder (disk directory).

Data Source Measurement MATLAB ENGINE Receiver MATLAB • Execution of m-file Received Data Main Interface Variables • Plotting of data or Application Software Logged Data Object Called with each snapshot User M-File

Figure A-1. Data flow through measurement receiver to MATLAB workspace.

A.2 Workspace Variables

The measurement receiver software automatically opens the MATLAB engine when the MATLAB interface is started. When the interface is instructed to execute by the user, the measurement receiver software passes data to the MATLAB workspace in several variables. The variables passed into the workspace are described in Table A-1. The table shows the variable name, the type of variables and numbers expected, and a description of the contents.

The variables Ch1Signal, Ch2Signal, Ch3Signal, Ch4Signal are vectors that contain the sampled signal data. The length of the vectors is variable and depends upon the configuration of the measurement receiver; typically 15,000 samples are sufficient for applications such as multipath profile characterization algorithms. Each element of the vectors represents a sample taken by the A/D converter. The vectors are synchronized, meaning that the sample represented in the first element of Ch1Signal was sampled at the same instant as the first elements of Ch2Signal, Ch3Signal, and Ch4Signal. In other words, Ch1Signal[n] is sampled at the same time as Ch2Signal[n], Ch3Signal[n], and Ch4Signal[n].

324 APPENDIX A – MEASUREMENT RECEIVER MATLAB SIGNAL INTERFACE

The samples represented by Ch1Signal, Ch2Signal, Ch3Signal, Ch4Signal are actually sampled IF. Typically, a center IF frequency of 150 MHz is used, but there is no restriction on using other bands within the 200 KHz to 400 MHz IF bandwidth. As an example, if a 2050 MHz sinusoid is received by channel one and a 1900 MHz local oscillator frequency is used, then Ch1Signal will contain a sinusoid with a frequency of 150 MHz. In addition, consecutive samples in Ch1Signal will be separated in time by 1/SampleRate, and the magnitude of each sample is in units of volts referenced to the channel one antenna port.

SweepNum represents the snapshot number assigned to the snapshot by the measurement receiver. This number gives a counter to use as a reference when processing multiple snapshots with m-files and the MATLAB interface. The TimeStamp variable is a constant-length string that indicates the time and date at which snapshot was acquired by the measurement receiver; all signal vectors for the associated snapshot are acquired simultaneously at the time given in TimeStamp.

A.3 Real-Time Plotting

The MATLAB interface automatically opens a MATLAB figure for each instance of the interface. This means that the m-file called by the interface can plot on the single figure opened by the interface. Because the interface needs to handle figures for multiple instances of the interface, the figure(.) command in MATLAB generally should not be used in the m-file. However, subplots are permitted using the subplot(.) command in the m-file.

Plotting is typically performed at the end of the m-file to display the results. If no condition statements exist around the plot command, the plot will be generated each time the m-file is called and, therefore, each time the measurement receiver passes signal data to the MATLAB workspace. To create a plot, use the plot(.) command in the m-file. The associated title(.), xlabel(.), ylabel(.), and axis(.) commands may be used.

325 APPENDIX A – MEASUREMENT RECEIVER MATLAB SIGNAL INTERFACE

Table A-1. Description of variables passed into MATLAB workspace by measurement receiver. Variable Name Type Description Ch1Signal 1xn matrix (vector) of Signal data from channel one of the double-precision values. measurement receiver. Units are volts referenced to the antenna port (50 ohms real impedance). Length of vector (n) is determined by the snapshot length in samples taken by the measurement receiver. Ch2Signal 1xn matrix (vector) of Signal data from channel two of the double-precision values. measurement receiver. Units are volts referenced to the antenna port (50 ohms real impedance). Length of vector (n) is determined by the snapshot length in samples taken by the measurement receiver. Ch3Signal 1xn matrix (vector) of Signal data from channel three of the double-precision values. measurement receiver. Units are volts referenced to the antenna port (50 ohms real impedance). Length of vector (n) is determined by the snapshot length in samples taken by the measurement receiver. Ch4Signal 1xn matrix (vector) of Signal data from channel four of the double-precision values. measurement receiver. Units are volts referenced to the antenna port (50 ohms real impedance). Length of vector (n) is determined by the snapshot length in samples taken by the measurement receiver. SampleRate Scalar, double-precision Sample rate (samples/sec) used by the value measurement receiver to sample signals at each channel. SweepNum Scalar, integer Snapshot number used as an index to keep track of snapshots. Snapshots from each channel with the same SweepNum value were sampled simultaneously. TimeStamp String, constant-length Time stamp corresponding to the time a particular snapshot of channels was acquired. Example: Thu Jun 28 15:20:29.592 2001

A.4 Example M-File

An m-file listing that shows how to use the signal data and how to produce real-time plots is shown in Figure A-2. This m-file uses the Ch2Signal variable that is inserted into the MATLAB workspace by the measurement receiver software. The fast Fourier transform (FFT) of

326 APPENDIX A – MEASUREMENT RECEIVER MATLAB SIGNAL INTERFACE

Ch2Signal is computed and stored in the ChSpec variable. The frequency vector FreqMHz whose elements correspond to the elements of ChSpec is computed using the SampleRate variable, which is also inserted into the MATLAB workspace by the measurement receiver. A calibration factor is subtracted from the ChSpec vector; this calibration factor is determined experimentally using a receiver input signal of known power.

% This file serves as an example of using m-files with VIPER. % An FFT is performed using the signal from channel 2, and the % FFT is plotted. W. Newhall 2001

% Receiver software puts Ch2Signal, SampleRate, etc., in the workspace.

% Set local oscillator offset for correct frequency axis LocalOscillator = 1900; % LO freq in MHz

% Take the FFT of the Channel 2 Signal ChSpec = abs( fft( Ch2Signal ) ); ChSpecDb = 20*log10( ChSpec ); NumFFTPts = length( ChSpec );

% Calculate frequency vector FreqStep = SampleRate / (NumFFTPts-1); Freq = 0:FreqStep:SampleRate; FreqMHz = Freq/1e6 + LocalOscillator;

% Points to plot and calibration offset Pts = 1:(NumFFTPts/2); ChSpecDb = ChSpecDb - 67.5; % Calibration factor for FFT plot

% Plot the spectrum plot( FreqMHz(Pts), ChSpecDb(Pts) ); grid on; title( 'FFT of Ch2Signal' ); xlabel( 'Frequency (MHz)' ); ylabel( 'dBm' );

Figure A-2. Sample m-file listing showing how to use the signal data and produce real-time plots.

The m-file is executed in the measurement receiver software by launching the MATLAB interface from the menu bar. The MATLAB interface application is shown in Figure A-3. The path to the m-file and the m-file name are entered into the application edit boxes. The m-file can be executed once or continuously per selection chosen on the application window.

327 APPENDIX A – MEASUREMENT RECEIVER MATLAB SIGNAL INTERFACE

Figure A-3. MATLAB interface application launched from the measurement receiver software.

Figure A-4 shows the result of one snapshot when running the example m-file listed in Figure A-2. The received signal was a BPSK-modulated PN sequence centered at 2050 MHz. The RF filter band limiting can be seen at 2000 MHz and 2100 MHz. The lowbass IF filter cutoff is evident at 2300 MHz where the noise falls sharply.

Figure A-4. Spectrum plot produced by m-file listed in Figure A-2.

328 APPENDIX A – MEASUREMENT RECEIVER MATLAB SIGNAL INTERFACE

A.5 Steps for Developing m-files for the Measurement Receiver

The following steps suggest a concise method for developing m-files for the measurement receiver.

1. Understanding data format: The measurement receiver produces measurements of voltage-versus-time of an intermediate-frequency (IF) signal. MATLAB can be used to process this data.

2. Explore measurement receiver data: Obtain sample data in *.mat format. Load data into MATLAB using load command in MATLAB. Each *.mat file is one snapshot of data from the measurement receiver . Explore this data to be sure it is understood. This is exactly the type of data that will be placed in the MATLAB workspace when m-file is called by the measurement receiver in real time.

3. Design algorithms using sample data: Design algorithms in MATLAB m-files so that they accept sampled IF signals. At the beginning of the m-file, use the load command to load a snapshot of sample data (stored in the *.mat file). Later, the load command will be removed once the m-file has been demonstrated to work successfully on the sample data. If the m-file doesn’t work using the sample data, it will not work when called in real-time by the measurement receiver. Successful operation on the sample data is a must.

4. Use phase and amplitude calibration if necessary: Each channel of signal data may have phase and amplitude offsets relative to the other channels. Using the *.mat file that contains signals acquired through a signal splitter, determine phase and amplitude calibration constants. These constants should be applied to signals by algorithms that need to know the phase and amplitude offsets of the RF front end channels.

5. Playback data: Use the playback feature of the measurement receiver software to test your m-file on logged data. The *.vdf files contain binary measurement receiver data.

· Run ViperExe off of the CD (or copy all files to your hard drive).

329 APPENDIX A – MEASUREMENT RECEIVER MATLAB SIGNAL INTERFACE

· Use FILE->START PLAYBACK and then select the file you want to play back.

· Then, APPLICATIONS->VIPER MATLAB, then enter the path and your m-file name

in the edit boxes and select EXECUTE. NOTE: MATLAB does not work with spaces in folder names, so do not use spaces (if necessary, change the actual folder path where your m-files are stored). Also do not use ".m" at end of m-file name when entering the m-file name in the measurement receiver software.

· FILE->STOP PLAYBACK can be used to stop the playback of data.

6. Execute m-file using real-time data: When the m-file works on playback data, then it can be executed on the receiver in real time. With the measurement receiver set up

correctly, select CONTROL -> CONFIGURE RECEIVER and select the options appropriate for

the experiment. SELECT CONTROL -> START RECEIVER to start the acquisition of

snapshots. Use the APPLICATIONS->VIPER MATLAB feature as described in the previous step.

7. Changing m-file while running measurement receiver: When changing the m-file while playing back files with VIPER (e.g., to experiment with different constants or algorithms within the m-file), stop the VIPER MATLAB application (but not necessarily playback of the file) with the STOP button, save the m-file, type “clear all ” in the MATLAB workspace. Then, hit EXECUTE in the VIPER MATLAB application to restart the execution with the new m-file. This is necessary because MATLAB may cache values and code when “clear all” is not used.

330

Appendix B

VT-STAR Development

B.1 Overview

VT-STAR (Virginia Tech Space-Time Advanced Receiver) was developed as a test bed for space-time processing. VT-STAR consists of a transmitter and receiver, each with two-element antenna arrays, for implementing two-by-two MIMO (multiple-input, multiple-output) channel algorithms. The VT-STAR system was built concurrently with research presented in this dissertation and influenced ideas for array processing. Further descriptions of VT-STAR and its applications are described in [Goz01]. Results of experiments performed with VT-STAR are presented in [Goz02b].

B.2 VT-STAR Transmitter

The VT-STAR transmitter uses a TMS320C67 DSP board and four THS 5x61 digital-to-analog conversion (DAC) boards to generate in-phase (I) and quadrature (Q) baseband signals. Generation of baseband rather than intermediate frequency (IF) signals was used so that bandwidth capabilities of the transmitter could be maximized. The RF section of the transmitter

331 APPENDIX B – VT-STAR DEVELOPMENT

accepts as input the baseband signals produced by the DAC boards and modulates RF signals transmitted through the radio channels using two transmitter antennas.

Each branch of the transmitter RF section uses two stages of frequency up-conversion to produce modulated signals centered at 2050 MHz (see Figure B-1 and Figure B-2). The two RF branches use local oscillators locked to a common reference. The first up-conversion stage in each branch accepts in-phase and quadrature inputs from the DAC boards and creates a modulated intermediate frequency (IF) signal at 68 MHz. A single 68 MHz local oscillator drives the I/Q modulator in each branch using a signal splitter. The second frequency up-conversion stage translates the 68 MHz IF signal up to 2050 MHz using a second local oscillator at 1982 MHz, and the 2050 MHz modulated signal is filtered and amplified. Two vertically-polarized, co- planar, quarter-wavelength monopole antennas transmit the signal through the radio channel.

THS56x1 ZEM-4300 DAC Board BPF I/Q Mod X f = 2050 MHz 2050 MHz ZFMIQ-70ML o THS56x1 1982 MHz DAC Board Splitter 10 MHz Splitter Atten ZESC-2-11 Ref ZESC-2-11 THS56x1 68 MHz Signal Gen

TMS320C67 DSP DAC Board 1982 MHz I/Q Mod ZFMIQ-70ML X BPF THS56x1 2050 MHz fo = 2050 MHz DAC Board ZEM-4300

Figure B-1. Transmitter section of VT-STAR.

332 APPENDIX B – VT-STAR DEVELOPMENT

Figure B-2. Photograph of VT-STAR transmitter section.

B.3 VT-STAR Receiver

The VT-STAR receiver uses an RF section followed by a THS 1206 four-channel digital-to- analog converter board and a TMS320C67 DSP board to process received signals. The receiver RF section has two antennas to receive the signals, and the received spectrum is down-converted to I and Q baseband signals. Baseband rather than IF signals are sampled to maximize the bandwidth capabilities of the receiver.

Each branch of the receiver RF section uses two stages of frequency down-conversion to produce baseband I and Q outputs suitable for sampling by the analog-to-digital converters (see Figure B-3 and Figure B-4). Two vertically-polarized, co-planar, quarter-wavelength monopole antennas are used to receive signals. The received signals are filtered and amplified prior to the first frequency down-conversion stage. A single 1982 MHz local oscillator translates the 2050 MHz received signal to a 68 MHz IF. The IF signal is amplified and filtered prior to being down-converted to baseband I/Q by the demodulators. A second local oscillator in the receiver produces a 68 MHz sinusoid that is split to drive the I/Q demodulators.

333 APPENDIX B – VT-STAR DEVELOPMENT

SLP1.9 ZHL- ZEM- ZFL- ZFL- 2050 MHz 1724HLN 4300 1000GH 1000H LPF BPF I/Q Demod BPF X 68 MHz ZFMIQ-70D 2050 MHz 1982 MHz AGC LPF 68 MHz Splitter 10 MHz Splitter ZESC-2-11 Ref ZESC-2-11 1982 MHz AGC LPF 2050 MHz THS1206 ADC BPF I/Q Demod TMS320C67 DSP BPF X 68 MHz ZFMIQ-70D 2050 MHz LPF ZHL- ZEM- ZFL- ZFL- 1724HLN 4300 1000GH 1000H SLP1.9 Figure B-3. Receiver section of the VT-STAR.

Figure B-4. Photograph of VT-STAR receiver RF section.

The VT-STAR operating frequency of 2050 MHz was chosen because of propagation similarities compared to the U.S. PCS band, worldwide 3G radio bands, and the U.S. 2.4 GHz unlicensed band. Performance improvements demonstrated in the 2050 MHz band by VT-STAR would be realizable by worldwide wireless communication systems operating in nearby bands. Two stages of frequency conversion were chosen to allow amplification to be divided among the stages, mitigating receiver instability due to high gain at a single band within each chain. Monopole antennas were selected because of their simple design, demonstrating that performance gains can be realized using antennas that are practical for handheld wireless devices. Antenna spacing can be varied on the VT-STAR to test the performance of the system versus antenna spacing for

334 APPENDIX B – VT-STAR DEVELOPMENT different radio environments. The receiver RF chains were designed to accept automatic gain control (AGC) signals so that the DSP can control the gain of the RF front end. Imbalances between the I and Q channels of the chains are characterized and compensated with scaling factors in DSP.

Table B-1. Specifications for VT-STAR transmitter and receiver. RF Parameter Value Center Frequency 2050 MHz Maximum Signal Bandwidth 750 KHz Receiver Noise Floor (Antenna Port) -110 dBm Maximum Receiver Input Power -60 dBm Transmitter Input Baseband I/Q, 35 mV RMS Receiver Output Baseband I/Q, 140 mV RMS Transmit Power (Maximum/Nominal) 28 dBm / 0 dBm Transmitter/Receiver Input/Output Impedance 50 ohm

335 APPENDIX B – VT-STAR DEVELOPMENT

This page intentionally left blank.

336

Appendix C

Channel Model Simulator Parameters

The parameters for the channel model simulator presented in Chapter 6 are documented in this appendix. Variables are shown exactly as the are used in MATLAB. The purpose is to aid future users and developers of the simulator.

C.1 Top Level Structures

When the simulator is run, the simulation channel parameters, vector channel results, and plot parameters are the only variables seen with the MALAB ‘whos’ function. All simulator input and output are stored in these structures.

» whos Name Size Bytes Class ChanParams 1x1 2384 struct array PLOT_PARAMS 1x1 660 struct array (global) VecChan 1x1 5320 struct array

Grand total is 444 elements using 8364 bytes

337 APPENDIX C – CHANNEL MODEL SIMULATION PARAMETERS

»

C.2 Channel Parameters Structure

The channel parameters structure contains the input used by the simulator. Scalars, vectors, and cell arrays are stored in fields of this structure. For the ESR model and GBSBE models, the channel parameters structure contains the following fields:

» ChanParams

ChanParams =

Frequency: 2.05e+009 Lambda: 0.14634 ArrayElementPosition: {1x4 cell} PathLossExponent: 4.83 RefDist: 1 ReflectionLoss: 10 LosOffset: [] NumRegions: 16 PoissonParams: [1x16 double] GaussianStdDev: 4.95 UseRayleighFading: 1 MaxExcessDly: 1.588e-006 TRSeparation: 41.1 ModelType: 'GESR'

»

For the GAGE model, the channel parameters structure changes slightly. The differences are shown in the following channel parameter fields:

» ChanParams

ChanParams =

338 APPENDIX C – CHANNEL MODEL SIMULATION PARAMETERS

Frequency: 2.05e+009 Lambda: 0.14634 ArrayElementPosition: {1x4 cell} PathLossExponent: 4.1 RefDist: 1 ReflectionLoss: 10 LosOffset: 0.5 NumRegions: 16 PoissonParams: [1x16 double] GaussianStdDev: 5.24 UseRayleighFading: 0 MaxExcessDly: 1.556e-006 TRSeparation: 1925.1 ElevationAngleDeg: 22.5 ModelType: 'GAGE'

»

C.3 Intermediate Plots

Intermediate plots are displayed or inhibited using the plot parameters structure. To produce a plot, set the associated plot parameter field equal to one. To inhibit a plot, omit the field or set the field to zero:

» PLOT_PARAMS

PLOT_PARAMS =

PlotGeometry: 1 PlotGeoImpulseResponse: 0 PlotLosImpulseResponse: 0 PlotLogNormImpulseResponse: 1 PlotRayleighImpulseResponse: 1

»

339 APPENDIX C – CHANNEL MODEL SIMULATION PARAMETERS

C.4 Vector Channel Structure

The vector channel structure contains the output and intermediate results of the simulator. The information in the structure is divided into impulse response results and geometry results.

» VecChan

VecChan =

ImpulseResponse: [1x1 struct] Geometry: [1x1 struct]

»

The geometry field of the vector channel structure contains intermediate results related to model geometry. Scatter coordinates, scatter counts, transmitter coordinates, receiver coordinates, and ellipse axis lengths are stored in the fields.

» VecChan.Geometry

ans =

ScatLoc: [22x2 double] NumScat: [2 7 4 3 2 1 1 1 1 0 0 0 0 0 0 0] NumComp: [2 7 4 3 2 1 1 1 1 0 0 0 0 0 0 0] TxLoc: [-20.55 0] RxLoc: [20.55 0] MajorAxis: [1x17 double] MinorAxis: [1x17 double]

»

The impulse response field of the vector channel structure contains the strengths, delays, and directions of arrival (DOA) of multipath components. Strength, delay, and DOA at the center of the receiver array is stored. Strength and delay for each antenna element is also stored.

340 APPENDIX C – CHANNEL MODEL SIMULATION PARAMETERS

» VecChan.ImpulseResponse

ans =

TauRxCenter: [22x1 double] AlphaRxCenter: [22x1 double] DOARxCenter: [22x1 double] Tau: {1x4 cell} Alpha: {1x4 cell}

»

C.5 Multiple Simulation Runs

Numerous simulations can be executed automatically with the code developed for this dissertation. This was performed by defining a channel parameter cell array and a vector channel result cell array. As seen when the simulations are executed, these cell arrays can be two- dimensional. One dimension of the cell array corresponds to different measurement sites. The other dimension corresponds to a simulation run for that site.

341 APPENDIX C – CHANNEL MODEL SIMULATION PARAMETERS

This page intentionally left blank.

342

References

[Bad00] Bada A.M., Maddiotto M., “Design and Realisation of Digital Radio Transceiver Using Software Radio Architecture,” IEEE 51st Vehicular Technology Conference (VTC2000), vol. 3, pp. 1727-1731, 2000. [Ber02] Bertoni H.L., Torrico S.A., “Propagation Prediction for Urban Systems,” Handbook of Antennas in Wireless Communications, Edited by Godara L.C., pp. 3-1 to 3-33, CRC Press, 2002. [Bod97] Bodnar Z., Herczku Z., Frigyes I., “Wideband Measurements of Radio Propagation Channels in Land Mobile and Satellite Mobile Communication Systems,” IEEE 6th International Conference on Universal Personal Communication (1997), vol. 1, pp. 20-24, 1997. [Bre02] Bretz E.A., “Clear Skies Ahead,” IEEE Spectrum, pp. 78-81, vol. 39, no. 1, January 2002. [Bur00] Buracchini E., “The Software Radio Concept,” IEEE Communications Magazine, pp. 138-143, September 2000. [Cav00] Cavers J., Mobile Channel Characteristics, Kluwer Academic Publishers, 2000.

343 REFERENCES

[Chu87] Chuang J.C., “The Effects of Time Delay Spread on Portable Radio Communications Channels with Digital Modulation,” IEEE Journal on Selected Areas of Communications, vol. SAC-5, no. 5, June 1987. [Chr00] Chryssomallis M., “Smart Antennas,” IEEE Antennas and Propagation Magazine, vol. 42, no. 3, pp. 129-136, June 2000. [Cla68] Clarke R., “A Statistical Theory of Mobile Radio Reception,” Bell Systems Technical Journal, vol. 47, 1968. [Coh98] Cohen A., Woodring M., Win32 Multithreaded Programming, O’Reilly & Associates, Inc., 1998. [Cou90] Couch L.W., Digital and Analog Communication Systems 3ed., Macmillan Publishing Company, 1990. [Cou97] Couch L.W., Digital and Analog Communication Systems 5ed., Macmillan Publishing Company, 1997. [Cox72] Cox D.C., “Delay Doppler Characteristics of Multipath Propagation at 910 MHz in Suburban Mobile Radio Environment,” IEEE Transactions on Antennas and Propagation, vol. AP-20, no. 5, September 1972. [Dav99] Davis K.V., “JTRS – An Open, Distributed-Object Computing Software Radio Architecture,” Proceedings of the 18th Digital Avionics Systems Conference, pp. 9.A.6-1 to 9.A.6-8, vol. 2, October 1999. [Die00] Dietrich C.B., "Adaptive Arrays and Diversity Antenna Configurations for Handheld Wireless Communication Terminals," Ph.D. Dissertation, Virginia Tech, Blacksburg, VA, 2000. [Die01] Dietrich C.B., Dietze K., Nealy J.R., Stutzman W.L., "Spatial, Polarization, and Pattern Diversity for Wireless Handheld Terminals," IEEE Transactions on Antennas and Propagation, vol. 49, no. 9, pp. 1271-1281, September 2001. [Dix01] Dixon J.L., Wilkes J.E., “A ‘Low-Cost’ Software Radio Test Bed,” IEEE 53rd Vehicular Technology Conference (VTC2001), vol. 3, pp. 1874-1878, 2001. [DoC14] United States Department of Commerce, Bureau of Navigation, Radio Service, Radio Communications Laws of the United States and the International Radiotelegraph Convention Regulations Governing Radio Operators and the Use of Radio Apparatus on Ships and on Land, Washington Government Printing Office, July 27, 1914.

344 REFERENCES

[DoC96] United States Department of Commerce, United States Frequency Allocations, National Telecommunications and Information Administration, Office of Spectrum Management, March 1996. [Dye98] Dyer G., Gilbert T.G., Henriksen S., Sayadian E., “Mobile Propagation Measurements using CW and Sliding Correlator Techniques,” Antennas and Propagation International Symposium, vol. 4, pp. 1896-1899, June 1998. [Ent90] Entsminger G., The Tao of Objects, M&T Publishing, Inc., 1990. [Erb98] Erben H., Sabatakakis K., “Advanced Software Radio Architecture for 3rd Generation Mobile Systems,” IEEE 48th Vehicular Technology Conference (VTC98), vol. 2, pp. 825-829, 1998. [Ert99] Ertel R.B., Antenna Array Systems: Propagation and Performance, Ph.D. Dissertation, Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia, July 1999. [Goz01] Gozali R., Mostafa R., Palat R.C., Marikar S., Robert P.M., Newhall W.G., Beaudette C., Tsiakkouris S.A., Anderson C., Neel, J., Woerner B.D., Reed, J.H., “Virginia Tech Space-Time Advanced Radio (VT-STAR),” Radio and Wireless Conference (RAWCON 2001), pp. 227–231, 2001. [Goz02] Gozali R., Space-Time Codes for High Data Rate Wireless Communications, Ph.D. Dissertation, Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia, 2002. [Goz02b] Gozali R., Mostafa R., Palat R.C., Robert P.M., Newhall W.G., Woerner B.D. and Reed J.H., “MIMO Channel Capacity Measurements Using the VT-STAR Architecture,” IEEE Vehicular Technology Conference VTC 2002-Fall, Vancouver, British Columbia, Canada, September 24-28, 2002. [Gra94] Graham I., Object-Oriented Methods 2ed., Addison-Wesley Publishing Company, 1994. [Hat80] Hata M., “Empirical Formula for Propagation Loss in Land Mobile Radio Services,” IEEE Transactions on Vehicular Technology, vol. 29, pp. 317-325. [IS2000] TIA/EIA, IS-2000.1-A, Introduction to cdma2000 Standards for Spread Spectrum Systems, March 2000.

345 REFERENCES

[IS95A] TIA/EIA, IS-95-A, Mobile Station – Base Station Compatibility Standard for Dual- Mode Wideband Spread Spectrum Cellular Systems. [Jah96] Jahn A., Bischl H., Heib G., “Channel Characterisation for Spread Spectrum Satellite Communications,” IEEE 4th International Symposium on Spread Spectrum Techniques and Applications, vol. 3, pp. 1221-1226, 1996. [Jah94] Jahn A., Lutz E., “DLR Channel Measurement Programme for Low Earth Orbit Satellite Systems,” IEEE 3rd Annual International Conference on Universal Personal Communications, pp. 423-439, 1994. [JSTD8] TIA/EIA, J-STD-008, Personal Station – Base Station Compatibility Requirements for 1.8-2.0 GHz Code Division Multiple Access (CDMA) Personal Communication System. [Jan02] Janaswamy R., “Spatial Diversity for Wireless Communications,” Handbook of Antennas in Wireless Communications, Edited by Godara L.C., pp. 19-1 to 19-24, CRC Press, 2002. [Jer92] Jeruchim M.C., Balaban P., Shanmugan K.S., Simulation of Communication Systems, Plenum Press, 1992. [Jon00] Jondral F., Wiesler A., Machauer R., “A Software Defined Radio Structure for 2nd and 3rd Generation Mobile Communications Standards,” IEEE 6th Int. Symp. On Spread-Spectrum Tech. & Applic., NJIT, September 6-8, 2000. [Kav00] Kavak A., Torlak M., Vogel W.J., Xu G., “Vector Channels For Smart Antenna – Measurements, Statistical Modeling, and Directional Properties in Outdoor Environments,” IEEE Transactions on Microwave Theory and Techniques, vol. 48, no. 6, June 2000. [Kit95] Kitchener D., Dalley J.E.J., Smith M.S., “Antenna Diversity in Outdoor Microcells,” 9th International Conference on Antennas and Propagation, vol. 2, pp. 1-4, 1995. [Kho95] Khoshafian S., Razmik A., Object Orientation 2ed., John Wiley & Sons, Inc., 1995. [Kri96] Krief P., Prototyping with Objects, Prentice Hall, 1996. [Kri02] Krishnamoorthy S., “PRISM – Measurement System for the ISM Band,” MPRG Propagator, to be published Spring 2002.

346 REFERENCES

[Lar99] Larsson M., Spatio-Temporal Channel Measurements at 1800 MHz for Adaptive Antennas,” IEEE 49th Vehicular Technology Conference (VTC99), vol. 1, pp. 376- 380, 1997. [Lee82] Lee W.C.Y., Mobile Communications Engineering, McGraw Hill, 1982. [Lee00] Lee G., Chang Y., Yuan S., “A Software Framework for Software Radio,” Proc. International Conference on Communication Technology (WCC-ICCT 2000), vol. 2, pp. 1102-1105, 2000. [Lut20] de Lutero G. (a.k.a. Dosso Dossi), Learned Man of Antiquity, ca. 1520-1522, Chrysler Museum of Art, Norfolk, Virginia. [Lib95] Liberti J.C., Analysis of CDMA Cellular Radio Systems Employing Adaptive Antennas, Ph.D. Dissertation, Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia, September 1995. [Lu97] Lu M., Titus L., Litva J., “A Physical Spatio-Temporal Model of Multipath Propagation Channels,” IEEE 47th Vehicular Technology Conference (VTC97), vol. 2, pp. 810-814, 1997. [Mas00] Masui H., Ishii M., Sakawa K., Shimizu H., “Microwave Spatio-Temporal Channel Characteristics Measured at Base Station in Urban Environment,” IEEE 52nd Vehicular Technology Conference (VTC2000), vol. 2, pp. 829-832, 2000. [Mit93] Motola J., “Software Radios: Survey, Critical Evaluation, and Future Directions,” IEEE Aerospace and Electronics Systems Magazine, vol. 8, issue 4, pp. 25-36, April 1993. [Mit95] Mitola J., “The Software Radio Architecture,” IEEE Communications Magazine, pp. 26-38, May 1995. [Mit99] Mitola J., “Software Radio Architecture,” IEEE Journal on Selected Areas in Communications, vol. 17, no.4, pp. 514-538, April 1999. [Moe99] Moessner K., Seiamak V., Tafazolli R., “A Minimum Air Interface for Software Radio Based on Distributed Object Technology,” 1999 IEEE International Conference on Personal Wireless Communications, pp. 369-373, February 1999. [New97] Newhall W.G., Wideband Propagation Results, Simulation Models, and Processing Techniques for a Sliding Correlator Measurement System, Masters Thesis, Bradley

347 REFERENCES

Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia, December 1997. [Ng02] Ng B.P., Er M.H., “Basic Array Theory and Pattern Synthesis Techniques,” Handbook of Antennas in Wireless Communications, Edited by Godara L.C., pp. 16-1 to 16-42, CRC Press, 2002. [Oda00] Oda Y., Tsunekawa K., Hata M., “Geometrically Based Direction Channel Model for Urban Mobile Communication Systems,” 2000 IEEE-APS Conference on Antennas and Propagation for Wireless Communications, pp. 87-90, 2000. [Par89] Parsons J.D., Gardiner J.G., Mobile Communication Systems, Blackie and Son, Ltd., 1989. [Par92] Parsons J.D., The Mobile Radio Propagation Channel, John Wiley & Sons, Inc., 1992. [Pet97] Petrus P., Novel Adaptive Array Algorithms and Their Impact on Cellular System Capacity, Ph.D. Dissertation, Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia, March 1997. [Ree02] Reed J.H., Software Radio: A Modern Approach to Radio Engineering, Prentice Hall, 2002. [Sta94] Stapleton S.P., Carbo X., McKeen T., “Spatial Channel Simulator for Phased Arrays,” IEEE Vehicular Technology Conference (VTC94), pp. 1789-1792, 1994. [Smi91] Smith H., Gardiner J.G., “Wideband Characterisation of the High Elevation Orbit Satellite-Mobile Channel at L-Band,” IEEE 41st Vehicular Technology Conference (VTC91), pp. 23-28, 1991 [Str91] Stroustrup B., The C++ Programming Language 2ed., Addison-Wesley Publishing Company, 1991. [Sul94] Sullo G.C., Object Engineering – Designing Large-Scale Object-Oriented Systems, John Wiley & Sons, Inc., 1994. [Vib02] Viberg M., Svantesson T., “Direction-of-Arrival Estimation in Mobile Communications,” Handbook of Antennas in Wireless Communications, Edited by Godara L.C., pp. 20-1 to 20-50, CRC Press, 2002. [Wes00] West G., General Class: Upgrade to the High-Frequency Worldwide Ham License, Master Publishing, Inc., 2000.

348 REFERENCES

[Wil01] Wilson P.F., Papazian P.B., Cotton M.G., Lo Y., Bundy S.C., “Simultaneous Wide- Band Four-Antenna Wireless Channel-Sounding Measurements at 1920 MHz in a Suburban Environment,” IEEE Transactions on Vehicular Technology, vol. 50, no. 1, January 2001. [Wol00] Wolmarans E.M., Truter A.J., “Software Radio: Implementation Aspects,” EUROCOMM 2000, pp. 38-42, May 2000.

349 REFERENCES

This page intentionally left blank.

350

Author Biographical Notes

William Newhall grew up in Bridgewater, New Jersey and moved to Blacksburg, Virginia to study at Virginia Polytechnic Institute and State University (Virginia Tech). He received his B.S. summa cum laude and in-honors from the Bradley Department of Electrical Engineering in 1994. In 1997 and 2003, respectively, Dr. Newhall received his M.S. and Ph.D. degrees in Electrical Engineering from Virginia Tech. Dr. Newhall’s graduate work concentrated on wireless communications at the Mobile and Portable Radio Research Group (MPRG). Dr. Newhall was the recipient of the General Motors Scholarship, the NASA/Virginia Space Grant Consortium Graduate Fellowship, the Davenport Fellowship, the Golden Key Scholarship, the Radio Club of America scholarship, and several awards based on research and academic merit. Concurrent with his enrollment Virginia Tech, Dr. Newhall served several engineering roles through employment at Grayson Wireless, Delco Electronics, and Virginia Tech and as an independent engineering consultant. He has authored numerous publications in areas of wireless communications. Dr. Newhall is an instrument-rated private pilot and general aviation enthusiast.

351