Characterization and Modeling of Wireless Channel Transitions
A thesis presented to
the faculty of the Russ College of Engineering and Technology of Ohio University
In partial fulfillment
of the requirements for the degree
Master of Science
Susheel Kumar Bokdia Rajendar
March 2009
© 2009 Susheel Kumar Bokdia Rajendar. All Rights Reserved. 2
This thesis titled
Characterization and Modeling of Wireless Channel Transitions
by
SUSHEEL KUMAR BOKDIA RAJENDAR
has been approved for
the School of Electrical Engineering and Computer Science
and the Russ College of Engineering and Technology by
David W. Matolak
Associate Professor of Electrical Engineering and Computer Science
Dennis Irwin
Dean, Russ College of Engineering and Technology
3
ABSTRACT
RAJENDAR, SUSHEEL KUMAR BOKDIA, M.S., March 2009, Electrical Engineering
Characterization and Modeling of Wireless Channel Transitions (161 pp.)
Director of Thesis: David W. Matolak
The thesis provides statistical characterization and modeling of wireless channel
transitions in both indoor and outdoor environments based on narrowband and wideband
measurements. We characterize delay dispersion characteristics of the wireless channel as
it transits from a line of sight (LOS) to a non-line of sight (NLOS) region. For the
narrowband indoor channel transition measurements, received power levels versus frequency were measured in the 900 MHz unlicensed ISM frequency band. The narrow band channel results quantify some fading characteristics versus frequency and distance,
and we also estimate values for the “power correlation” bandwidth. The power
correlation values of 0.5 were observed for bandwidths of approximately 7 MHz. For the
wideband channel transition measurements, power delay profiles (PDP) were measured
in indoor and outdoor environments in the 5 GHz frequency band. Several delay spread
parameters – root mean square delay spread, delay window, and channel impulse
response X, dB (CIRX,dB) duration – were obtained for LOS and NLOS regions from the
measured PDPs, and we quantify example changes in these parameters due to the
transition. As expected, the delay spread parameters for NLOS regions are larger than
those for LOS regions. Root mean-square delay spreads were found to increase from
approximately 9 ns to 18 ns in going from LOS to NLOS regions, respectively. Wideband
channel models were also developed for both regions for a bandwidth of 50 MHz. The 4 channel models define tap amplitude fading distributions and parameters, tap energies, and Markov tap persistence parameters.
Approved: ______
David W. Matolak
Associate Professor of Electrical Engineering and Computer Science 5
ACKNOWLEDGEMENTS
“Om Gurur Brahma Gurur Vishnuh
Gurur Devo Maheshawarah
Gurureva param brahma
Tasmai Shri Gurave Namah”
God is the only teacher the world has, throughout our life god takes various forms as human being and enter our life to teach us. In my life, god took different forms and entered my life with many relationships such as a mother, a father, a teacher, a fiancée, and friends. I would like to take this opportunity to thank various forms of god who walked in my life had helped me in achieving my goals. There are few compassionate, kind, helpful, understanding and caring people who have been a significant source of my motivation in completing my thesis.
First of all I would like to sincerely thank my advisor Dr. David W. Matolak. My advisor is a true teacher. He had always been available to support, teach and encourage me in all possible ways. He had helped me to be at my best and his patience is laudable.
I would also like to thank my lovable fiancée - Nisha, who has constantly been very cooperative, and understanding. Her love had given me immense energy and ability to always perform better. This would have never been possible without her.
I would like to thank my beloved parents, brother, sister in law and my loveable sister who believed in my ability and skills and allowed me to pursue my masters here in
U.S.A. It would have not been possible without their sacrifice and never ending love. 6
I would also like to thank few of my close friends namely: Arvind
Chandrasekaran, Chintan Patel, Krishna Manoharan and Najeeb Al-Hashim who supported me throughout, encouraged me when I was down, helped me when I got struck and finally made me feel at home. I would also like to thank my other friends namely
Zingtao Zhang, Qian Zhang, Nidhin Davis, Qiong Wu for lending a helping hand in discussions, measurements, analysis and etc.
I would also like to thank my committee members Dr. Jeffrey C. Dill and Dr.
Trent Skidmore for providing valuable knowledge. I also would sincerely like to thank
Dr. Sergio Lopez-Permouth.
7
TABLE OF CONTENTS
Page
ABSTRACT ...... 3
ACKNOWLEDGEMENTS ...... 5
LIST OF TABLES ...... 11
LIST OF FIGURES ...... 13
CHAPTER 1: INTRODUCTION ...... 18
1.1. Introduction ...... 18
1.2. Evolution of Modern Mobile Communications ...... 18
1.3. Channel Characterization ...... 24
1.4. Motivation for Thesis ...... 25
1.5. Thesis Scope ...... 26
1.6. Thesis Outline ...... 27
CHAPTER 2: BACKGROUND AND LITERATURE REVIEW ...... 28
2.1. Introduction ...... 28
2.2. Literature Review...... 28
2.3. Large-Scale Fading ...... 31
2.4. Small-Scale Fading ...... 33
2.4.1. Delay vs. Time ...... 35
2.4.2. Signal Time Spreading ...... 35
2.4.3. Channel Time Variation ...... 38
2.5. Amplitude Fading Models ...... 39 8
2.5.1. Rayleigh Fading Distribution ...... 39
2.5.2. Ricean Distribution ...... 41
2.5.3. Nakagami Fading Distribution ...... 42
2.5.4. Weibull Fading Distribution ...... 43
CHAPTER 3: NARROWBAND INDOOR CHANNEL TRANSITIONS ...... 45
3.1. Experimental Description ...... 45
3.1.1. Goal ...... 45
3.1.2. Test set up ...... 46
3.1.2.1. Equipment ...... 46
3.1.2.2. Set up procedure ...... 46
3.1.3. Measurement Description ...... 51
3.1.4. Environment Description ...... 54
3.2. Results ...... 56
3.2.1. Corner 1 ...... 57
3.2.1.1 3-Dimensional Bar Plot of Received power vs. frequency and distance ..
...... 57
3.2.1.2 Resultant Power vs. Frequency ...... 58
3.2.1.3. CDF of Relative Power vs. Frequency ...... 60
3.2.1.4. Resultant Power vs. Spatial Distance ...... 63
3.2.1.5. CDF of Relative Power vs. Spatial Distance ...... 65
3.2.1.6. Power Correlation Bandwidth Plots...... 68
3.2.2. Corner 2 ...... 69 9
CHAPTER 4: WIDEBAND OUTDOOR CHANNEL MEASUREMENTS ...... 71
4.1 Introduction ...... 71
4.2. Equipment Description ...... 71
4.2.1. Channel Sounder ...... 71
4.2.2. Other Equipment ...... 73
4.3. Environment Description ...... 74
4.3.1. West Green Corner ...... 76
4.3.2. Stocker Parking Lot ...... 82
4.4. Measurement Procedure ...... 84
A. Training Set Up ...... 84
B. Measurements...... 85
4.5. Analysis...... 88
4.5.1. Data Pre-Processing ...... 89
A. Format Translation ...... 89
B. Noise Thresholding ...... 90
C. Multipath Threshold...... 91
4.5.2. Parameter Extraction ...... 93
A. Mean Excess Delay ( μτ ) ...... 93
B. Root Mean Square Delay Spread (RMS-DS) ...... 93
C. CIR X,dB Duration ...... 95
D. Delay Window ...... 95
4.5.3. Tapped Delay Line Model ...... 96 10
4.5.3.1. Number of Taps ...... 98
4.5.3.2. Tap Energy ...... 98
4.5.3.3. Markov Process ...... 99
4.6. Channel Statistic and Modeling Results ...... 101
4.6.1. Stocker Parking Lot Corner ...... 101
4.6.2. West Green Corner ...... 116
CHAPTER 5: WIDEBAND INDOOR CHANNEL MEASUREMENTS ...... 127
5.1. Introduction ...... 127
5.2. Environment Description ...... 127
5.2.1. Indoor Corner 1 ...... 128
5.2.2. Indoor Corner 2 ...... 131
5.3. Measurement Procedure ...... 133
5.4. Indoor Corner Delay Spread Results and Analysis ...... 134
CHAPTER 6: SUMMARY, CONCLUSION AND FUTURE WORK ...... 146
6.1. Summary ...... 146
6.2. Conclusions ...... 146
6.3. Future Work ...... 148
REFERENCES ...... 150
APPENDIX A: MATLAB CODE FOR NARROWBAND MEASUREMENTS ...... 155
11
LIST OF TABLES
Page
Table 2.1. Example RMS-Delay spread tabulated for various environments and frequency bands ...... 31
Table 3.1. Transmitter and receiver description ...... 46
Table 3.2. Log likelihood of different distribution fits for the PDF of received power at 910 MHz vs. spatial displacement for corner 1 ...... 67
Table 4.1 Summary of channel sounder parameters ...... 73
Table 4.2. Labeling convention used for outdoor wideband measurements ...... 88
Table 4.3. Number of taps for each outdoor corner calculated using
RMS-DS method ...... 98
Table 4.4. Power delay profile, RMS-DS statistics and number of taps for
OC2-MS1 and OC2-MS2 ...... 102
Table 4.5. Channel statistics of Stocker Parking lot corner after removing
PDPs with large delay ...... 106
Table 4.6. Multipath channel statistics for OC2-MS2 ...... 110
Table 4.7. Summary of channel parameters for the two region at OC2-MS1 ...... 114
Table 4.8. Summary of channel parameters for the two region at OC2-MS1 ...... 115
Table 4.9. Tabulated channel statistics for West Green corner ...... 116
Table 4.10. Multipath channel parameter statistics for OC1-MS2 ...... 120
Table 4.11. Summary of channel parameters for the two region at OC1-MS1 ...... 124
Table 4.12. Summary of channel parameters for the two region at OC1-MS2 ...... 125 12
Table 4.13. Summary of channel parameters for the two region at OC1-MS3 ...... 126
Table 5.1. Delay domain channel statistics for indoor corners ...... 135
Table 5.2. Channel statistics for indoor corners after removing PDPs with large delay spreads ...... 136
Table 5.3. LOS and NLOS delay spread parameter statistics for OC1...... 142
Table 5.4. Summary of channel parameters for the two regions at IC1 ...... 145
13
LIST OF FIGURES
Page
Figure 2.1. Small-Scale fading channel manifestations [1], [2] ...... 35
Figure 2.2. Plot of Rayleigh CDF with varying values of σ ...... 40
Figure 2.3. Plot of Ricean PDF, parameterized by different values of K [38] ...... 42
Figure 3.1. Block diagram of transmitter section...... 48
Figure 3.2. Photograph of transmitter section ...... 48
Figure 3.3. Block diagram of receiver section ...... 49
Figure 3.4. Photograph of receiver section ...... 51
Figure 3.5. Receiver path illustration ...... 52
Figure 3.6. Floor plan for 3rd floor Stoker Center ...... 53
Figure 3.7. A view of the unobstructed hallway ...... 54
Figure 3.8. View of corner C1 ...... 55
Figure 3.9. 3D Bar plot for indoor corner 1 ...... 57
Figure 3.10. Plot of relative power in dB for LOS positions vs. frequency in MHz for
IC1...... 59
Figure 3.11. Plot of relative power in dB for NLOS positions vs. frequency in MHz
for IC1 ...... 59
Figure 3.12. CDF of relative power (dB) vs. frequency for LOS positions for IC1 ...... 61
Figure 3.13. CDF of relative power (dB) vs. frequency for NLOS positions for IC1 ...... 62
Figure 3.14. CDFs of received power at a given location vs. frequency and Ricean fit
CDFs for IC1...... 63 14
Figure 3.15. Plot of relative received power at a given frequency vs. spatial displacement for IC1 ...... 64
Figure 3.16. Plot of relative received power at a given frequency vs. spatial displacement for IC1 ...... 64
Figure 3.17. CDF of relative power in dB for frequency range of 906-909 MHz vs. spatial displacement for IC1 ...... 65
Figure 3.18. CDF Plot of relative power in dB for a frequency range of 918-921 MHz vs. spatial displacement for indoor corner 1 ...... 66
Figure 3.19. Distribution fit for PDF plot of received amplitude at 910 MHz vs. spatial displacement for corner 1 ...... 67
Figure 3.20. Plots of power correlation function for LOS and NLOS regions of indoor corner 1 ...... 69
Figure 3.20. Plot of received power at a given spatial displacement vs. frequency for indoor corner 2 ...... 70
Figure 3.21. Plot of received power at a given frequency vs. spatial displacement for indoor corner 2 ...... 70
Figure 4.1. Measurement team members along with transmitter and receiver
Equipments ...... 75
Figure 4.2. A 3-dimensional view of West Green ...... 76
Figure 4.3. 160° panoramic view of the channel environment behind the transmitter location at West Green (this picture was taken when standing at the transmitter location) ...... 78 15
Figure 4.4. 150° panoramic view of the channel environment in front of the transmitter location at West Green (this picture was taken when standing at the transmitter location) ...... 79
Figure 4.5. Panoramic view of the environment around the receiver path at
West Green ...... 80
Figure 4.6. Continued panoramic view of the environment around the receiver path at
West Green ...... 81
Figure 4.7. 80° panoramic view of the channel environment in front of the transmitter location at Stocker parking lot (this picture was taken when standing at the transmitter location) ...... 83
Figure 4.8. Portable sounder Rx and ancillary equipment ...... 86
Figure 4.9. Illustrating the receiver motion on a set path ...... 87
Figure 4.10. Illustration of a sample PDP record ...... 90
Figure 4.11. PDP depicting multipath threshold ...... 92
Figure 4.12. Plot of RMS-DS vs. profile index (time) for OC2-MS2 ...... 94
Figure 4.13. Illustration of calculation of CIR X, dB duration for a given PDP ...... 96
Figure 4.14. Block diagram of tapped delay line model ...... 97
Figure 4.15. Example persistence process ...... 100
Figure 4.16. State transition diagram of the example discussed ...... 101
Figure 4.17. Plot of RMS-DS vs. Profile Index along with moving average
for OC2-MS2 ...... 103 16
Figure 4.18. Plot of RMS-DS vs. profile index along with moving averages, for OC2-
MS1 ...... 104
Figure 4.19. Illustrating loss of Rx synchronization (left) and correctly synchronized
PDP (right) ...... 104
Figure 4.20. Plot of RMS-DS vs. profile index for OC2-MS1 ...... 107
Figure 4.21. Plot of RMS-DS vs. profile index for OC2-MS2 ...... 107
Figure 4.22. Histogram of RMS-DS for Stocker Parking lot corner ...... 108
Figure 4.23. CIR25dB duration vs. profile index for Stocker Parking lot corner ...... 109
Figure 4.24. Plot of delay window (DW90) in ns vs. profile index for Stocker Parking lot corner ...... 110
Figure 4.25. Tap amplitudes in dB vs. profile index plot for Stocker Parking lot corner...... 111
Figure 4.26. LOS and NLOS cumulative energy plot for measurement conducted at
Stocker Parking lot ...... 112
Figure 4.27. Plot of Probability of having a tap vs. Tap index for LOS and NLOS
regions for measurements conducted at Stocker Parking lot ...... 113
Figure 4.28. Plot of RMS-DS vs. profile index (time) for OC1-MS1 ...... 118
Figure 4.29. Plot of RMS-DS vs. profile index (time) for OC1-MS2 ...... 118
Figure 4.30. Plot of RMS-DS vs. profile index (time) for OC1-MS3 ...... 119
Figure 4.31. Plot of CIR25dB vs. profile index (time) for OC1-MS2 ...... 119
Figure 4.32. Plot of delay window (DW90) in ns vs. profile index for OC2-MS1 ...... 121
Figure 4.33. Histogram of RMS-DS for OC2-MS1 in LOS region ...... 121 17
Figure 4.34. Histogram of RMS-DS for OC2-MS1 in NLOS region ...... 122
Figure 4.35. Tap amplitude in dB vs. profile index for West Green Corner
OC1-MS2...... 123
Figure 4.36. Cumulative tap energy vs. tap index for OC1-MS2 ...... 123
Figure 5.1. Floor plan of 3rd floor Stocker Engineering Center illustrating marked
positions of transmitter, corner 1, and corner 2 ...... 129
Figure 5.2. Illustration of receiver trajectory at IC2 ...... 130
Figure 5.3. The view of indoor channel environment at IC2 ...... 130
Figure 5.4. The view of indoor channel environment at IC2 ...... 132
Figure 5.5. Illustration of receiver trajectory at IC2 ...... 132
Figure 5.6. Receiver unit placed on cart during measurement campaign ...... 134
Figure 5.7. Plot of RMS-DS vs. profile index (time) for IC1 along with moving average of 50 and 500 PDPs ...... 137
Figure 5.8. Plot of RMS-DS vs. profile index (time) for IC2-MS1 along with moving
average of 50 and 500 PDPs ...... 138
Figure 5.9. Histogram of RMS-DS for IC1 for LOS ...... 139
Figure 5.10. Histogram of RMS-DS IC1 for NLOS section ...... 139
Figure 5.11. Plot of CIR25 dB duration vs. profile index for IC1 ...... 140
Figure 5.12. Plot of delay window (DW90) vs. profile index for IC1 ...... 141
Figure 5.13. Plot of tap amplitude in dB vs. profile index (time) for IC1 ...... 143
Figure 5.14. Plot of probability of tap existence vs. tap index for IC1 ...... 143
Figure 5.15. Plot of cumulative tap energy vs. tap index for IC1 ...... 144 18
CHAPTER 1: INTRODUCTION
1.1. Introduction
In this chapter we briefly describe the evolution of modern mobile communication systems. We then motivate this work by discussing the importance of wireless channel characterization and modeling. This is followed by a discussion of the scope and an outline of this thesis.
1.2. Evolution of Modern Mobile Communications
During the last two decades, mankind has witnessed a tremendous growth in the cellular communication industry, which has given rise to the introduction of newer technologies designed to cater to the needs of the growing demand. All the new communications technologies focus on higher transmission data rates, an increasing number of users for a given bandwidth, higher efficiency and lower cost. Higher growth in the developing nations has resulted in the addition of more than 3 million cellular mobile subscribers on an average every month [31], [32], thanks to industry friendly policies undertaken by governments around the globe. These policies accelerated competition and yielded the advent of newer, faster and more efficient technologies for personal communication services (PCS).
We start the discussion of the evolution of modern mobile communications from second generation cellular networks, which are widespread and form the basis for future generations to come. Second generation cellular saw the use of digital modulation formats and time division multiple access (TDMA)/frequency division duplex (FDD) and code division multiple access (CDMA)/FDD techniques. The most popular second 19 generation standards include (a) Global System for Mobile communications (GSM); (b)
Interim Standard 136 (IS-136); (c) Pacific Digital Cellular (PDC); (d) Interim Standard
Code Division Multiple Access (IS-95) [2]. GSM supports eight time slots (users) per 200 kHz channel radio, whereas IS-136 supports three time slots (users) per 30 kHz channel; the IS-95 standard supports up to 64 orthogonally coded users transmitting simultaneously in a 1.25 MHz channel radio [5]. In 2001 several major carriers around the globe abandoned IS-136 in favor of emerging third generation schemes based on
GSM and TDMA platforms.
The second generation based standards were designed to handle speech based services and hence lacked the required data rates to support modern internet applications.
In order to serve this increasing demand, there came a need to develop data-centric standards based on these existing 2G standards that would increase throughput data rates to support modern internet applications such as browsing, e-mail, etc. [2]. These new standards were denoted 2.5 G, and they allowed modification of existing 2G equipment, supplemental base station add ons, and software upgrades of mobile phones to allow these faster data rates.
There were different upgrade paths developed for GSM carriers such as (a) High
Speed Circuit Switched Data (HSCSD); (b) Global Packet Radio Service (GPRS); (c)
Enhanced Data Rates for GSM evolution (EDGE). HSCSD allows the subscribers to use multiple time slots in order to obtain higher data rates of up to 57.6 kbps. GPRS supports multiuser network sharing of individual radio channels and time slots, which is well suited for non-real time internet services. The major disadvantage of GPRS is the reduced 20 data rate with an increased number of users [2]. In order to have a common technology path to 3G, high speed access EDGE was developed. EDGE uses higher order 8-PSK modulation in addition to GSM’s standard Gaussian minimum shift keying (GMSK) modulation. The high data rate is achieved by dedicating eight time slots of the GSM radio channel to a single user providing raw peak throughput data rates of up to 547.2 kbps.
Unlike the multiple upgrades in GSM based systems, CDMA had single path upgrade for ultimate third generation (3G) operations known as IS-95B (also termed
TIA/EIA-95 [28]). It allows a user to employ up to eight different Walsh-Hadamard codes simultaneously and in parallel for a throughput of up to 115.2 kbps [2]. Many practical CDMA systems employed in Korea and Japan offer 64 kbps packet switched data in addition to voice services [28]. Soft handoff procedures were also specified in the
IS-95B standard, which allowed the subscriber unit to switch between base stations to maintain signal quality.
3G mobile systems offer consumers incomparable wireless flexibility with higher transmission data rates for high speed internet access in conjunction with “always-on” access [2]. These should enable video conference calls, streaming music, simultaneous voice and data access with multiple parties, and many other applications. The standard
IS-95B formed the foundation for evolution to third generation CDMA systems, called cdma2000. Employing the same network fundamentals of GSM, the merged version of
GSM and IS-129 through EDGE paved the way for the third generation systems known as Wideband CDMA (W-CDMA) or Universal Mobile Telecommunications Services 21
(UMTS). When multiple worldwide proposals were submitted for International Mobile
Telephone 2000 (IMT 2000) standardization, several proposals were grouped with either cdma 2000 or W-CDMA. The International Telecommunication Union (ITU) IMT-2000 standards are currently divided into two organizations, the Third Generation Partnership
Project (3GPP) and 3GPP2 for 3G GSM and CDMA systems, respectively.
W-CDMA uses a core network derived from GSM and which ensures backward compatibility at the network layer and above with 2G and 2.5G TDMA technologies, but is based on a new air interface [33]. A minimum spectrum allocation of 5 MHz is required, and this allows transmission data rates in the range of 9.6 kbps – 2.048 Mbps.
W-CDMA supports up to 350 voice calls simultaneously, and will provide at least a six- fold increase in spectral efficiency compared to GSM [29], [2]. According to [30], the W-
CDMA systems can offer a data rate of 384 kbps along with voice based services. The initial cost of W-CDMA will be higher than cdma2000 as W-CDMA will require all new base stations and the procurement of expensive radio spectrum to operate (spectrum is made expensive due to large number of operators bidding to acquire the limited radio spectrum). Another reason for higher procurement cost of radio spectrum is the colossal rise in demand from the future bandwidth hungry subscribers.
On the other hand, the cdma2000 standard belongs to the family of IS-95 2G and
2.5G wireless standards and is backward compatible with them. The cdma2000 standard is also known as cdma2000 1X, and has a practical throughput of up to 144 kbps depending on the mobility of a user, propagation conditions, and number of users in a cell. The number of voice users supported by cdma2000 is twice the number supported 22 by the 2G CDMA standard. The 3G cdma2000 standard also increases the battery life of a subscriber unit by providing increased standby time. It also eliminates the need for additional RF hardware at the base station for switch over from existing IS-95 systems, hence giving cdma2000 an edge over W-CDMA with respect to cost of ownership [2],
[28]. The cdma2000 1xEV enhancement is an evolutionary advancement for CDMA with higher data rates, which is compatible with the existing cdma2000, IS-95 and IS-
95B networks; it can also work as a stand-alone system. These CDMA standards were developed by Qualcomm and were adopted as specifications by the Telecommunications
Industry Association (TIA). The standards provide service providers with the options of installing radio channels with data only (cdma2000 1xEV-DO) and with data and voice only (cdma2000 1xEV-DV) [2]. The cdma2000 1xEV-DO enhancements use the radio channel with data only services and support data transmission rates greater than 2.4 Mbps in a standard bandwidth 1.25 MHz channel.
The upcoming fourth generation systems, which are intended to be synonymous with high-speed and high capacity mobile wireless technologies, will enable subscribers to employ very-high speed broadband internet access along with superior voice clarity
[37]. With networks based on Internet Protocol (IP) technology, the 4G architecture is planned to concentrate on increasing the number of users per cell, hence increasing spectral and area efficiency and reducing operating cost.
The growth of portable, laptop computers in the past two decades, along with the popularity of the internet use has caused a large increase in the growth of wireless local area networks (WLANs). These WLANs are used for low-power transmissions in license 23 free spectrum, and essentially all standards have come from the working group of IEEE
802.11 [2]. In 1987, this IEEE 802.11 working group began the standardization of spread spectrum WLAN’s for the unlicensed Industrial, Scientific, and Medical (ISM) bands, and this took about ten years. The popular standards belonging to the IEEE 802.11 family are 802.11b, 802.11g, 802.11a and 802.11n. The 802.11 high rate standard which is also known as IEEE 802.11a provides data rates of up to 54 Mbps and operates in the
Unlicensed National Information Infrastructure (UNII) bands of 5.2 and 5.8 GHz. The
802.11b systems, operating in the 2.4 GHz ISM band, use direct sequence-spread spectrum (DS-SS) and have been named wi-fi by the Wireless Ethernet Compatibility
Alliance (WECA) [2]. The disadvantage of the IEEE 802.11b standard is that it must contend with potential interference from other electrical appliances operating in the same unlicensed band, such as microwave ovens, baby monitors, cordless phones and
Bluetooth devices.
The IEEE 802.11g standard provides data rate up to 54 Mbps in the 2.4 GHz frequency band using the 802.11a modulation scheme. This standard is backward compatible with the 802.11b standard and employs an orthogonal frequency division multiplexing (OFDM) modulation scheme [2]. The IEEE 802.11a systems accommodate a large number of users by offering 12 non-overlapping channels. A disadvantage of the
802.11a standard is its lower range compared to 802.11b due to the higher operating frequency; also, most devices support 802.11b in preference to 802.11a [34].
The IEEE 802.11n standard is a newer standard based upon on previous standards and includes multiple input multiple output (MIMO) processing. A MIMO system is 24 attained via multiple antennas at both transmitter and receiver. These multiple antennas can utilize multipath propagation to increase the receiver’s ability to recover the transmitted message [34]. The 802.11n standard has a dual radio channel operating in the frequency bands of 2.4 GHz and 5 GHz, and hence it is backward compatible with existing WLAN standards.
With the advent of newer and more efficient wireless communication technologies such as the cellular and WLAN systems described, it is more important than ever to understand the signal propagation conditions in multiple types of environments
(e.g., city, urban, and rural) so as to enable the system designer to design superior, efficient and reliable wireless communication systems. The next section gives an overview of channel characterization and its necessity.
1.3. Channel Characterization
Channel characterization and modeling deals with understanding the propagation of a wireless signal through a given medium at a given frequency, and developing a mathematical representation of the channel’s effect upon transmitted signals. During propagation, the signal can undergo fading, multipath distortion, scattering, and other effects, hence it is necessary to have a good understanding and model for the signal propagation characteristics so as to better design transmission schemes and channel effect countermeasures. Channel modeling requires characterizing the impulse response of a wireless channel and predicting the propagation path loss. A model for path loss helps enable design of better base stations and mobile terminals with appropriate, and possibly reduced, transmission power, hence saving cost. The characterization of the channel’s 25 impulse response enables designers to predict the range of behaviors of the received signal, and this helps the design of better and more efficient transmitters and receivers.
Characterization of the channel impulse response (CIR) is typically done by quantifying the delay spread experienced by the propagating signal. When the CIR duration is on the order of signal symbol duration, the channel is termed dispersive, and knowing these dispersion characteristics enables design of effective signal processing techniques to recover the transmitted signal. CIR knowledge may also guide the choice of modulation techniques [19], [17].
Channel characterization and modeling can be carried out using (a) site measurements; and/or, (b) propagation models. The former is expensive and ultimately site-specific, and hence the latter is widely used as a suitable, low-cost and convenient alternative [19]. Propagation models can be classified into statistical models and deterministic models, and we use the former type of model in this thesis. Chapter 2 provides further details on the different statistical parameters typically employed in channel characterization.
1.4. Motivation for Thesis
Authors in the past have not done much (if any) work to explicitly model and characterize the indoor and outdoor wireless radio channel in the 5 GHz frequency band when the channel undergoes a transition, specifically when a mobile receiver transits from a line of sight (LOS) to a non-line of sight (NLOS) region. The channel models developed for this situation can help in future communication system design by providing quantifiable measures of the channel’s characteristics in this transition. These 26 characteristics can be used to specify transmitter and receiver processing (e.g., equalization) schemes that can be used to mitigate these channel effects upon transmitted signals. In addition, if geolocation information is known for a mobile receiver in future systems, such channel characteristics can be reported back to base stations to enable compilation of “propagation condition maps” that associate channel characteristics with specific geographic locations [17].
1.5. Thesis Scope
We model and characterize the wideband wireless channel in the 5 GHz frequency band, in a campus environment (both indoors and outdoors). Our main aim is to understand the channel behavior, quantified using various delay spread parameters
(root mean square – delay spread (RMS-DS), delay window, and CIRX,dB duration), as the
receiver (Rx) transits from an LOS region, around a corner to an NLOS region. We then
develop channel models based on the popular tapped delay line model for these
environments.
Our quantification of channel dispersion changes is done using measurements of
power delay profiles (PDPs), roughly equivalent to the CIR squared. The statistics of
various multipath parameters are separated into LOS and NLOS regions for each corner.
These statistics are studied to deduce the behavior of these parameters in LOS and NLOS
regions as the channel undergoes this transition from LOS to NLOS.
An attempt was also made to understand the behavior of the narrowband wireless
channel in the Industrial Scientific and Medical (ISM) frequency band of 900 MHz for an
indoor environment. This was done as a complement to our wideband measurements, to 27 gain experience in measurement techniques, and also to gather some useful data while the wideband measurement test set was out for repair. These narrowband measurements were also performed as the Rx made a transition from LOS to NLOS regions.
1.6. Thesis Outline
The thesis starts with a literature review required to understand different delay spread parameters and fading distributions, and to place our work in the context of other work. The third chapter describes our narrowband measurements and analysis for the indoor environment. Chapters four and five describe the wideband channel characterization for outdoor and indoor environments, respectively. We finally conclude the thesis with summary discussion in chapter six, where we also introduce ideas for future work.
28
CHAPTER 2: BACKGROUND AND LITERATURE REVIEW
2.1. Introduction
This chapter provides a review of some key literature required to understand the discussion in chapters 3 and 4. We also describe background information on radio propagation and channel modeling.
A radio signal traverses a medium and in doing so often encounters various obstacles (and possibly interference). In some cases the radio signal might also have to travel via a NLOS path to reach the receiver antenna. During propagation, the signal may undergo large-scale and small-scale fading, which degrades the signal quality at the receiver. When designing a radio system, a system designer needs to understand the propagation characteristics of the medium, and design the system accordingly. One such design may aim to ensure that the signal level doesn’t drop below some permissible limit.
In this chapter we discuss the concepts of large-scale and small-scale fading, followed by discussion on various fading models.
2.2. Literature Review
In the past, many authors have carried out channel characterization and modeling for different environments and frequency bands. One commonly used measure of the CIR duration is the RMS-DS – this is quantified later in this chapter, but here we describe related work using this parameter. In [27], the author characterized the wireless channel for the Ohio University campus area in the 5 GHz band. The mean RMS-DS for LOS and
NLOS regions was found to be 0.341 µs and 1.503 µs, respectively. These measurements 29 were made with the transmitter atop a building roof, whereas our measurements have both transmitter and receiver antennas at low elevation (pedestrian height).
A number of authors have also done work to characterize urban and suburban channels in the cellular bands. Cox [8] characterized the wireless channel in a suburban mobile environment for the 910 MHz frequency band, and found the delay spreads to range from 0.20 µs to 0.31 µs at one location in New Jersey, with a link distance of 5.25 km. The measurements were carried out by mounting the transmitter 100 m above the suburban area. Another author [7] carried out measurements to characterize dense urban, suburban and rural environments in the 910 MHz frequency band to understand the impact of multipath propagation on the performance of the TIA IS-54 digital standard. It was found from those results that long delay spreads were overly emphasized in prior studies, and consequently frequency flat fading had been underestimated for dense urban environments. The mean RMS-DS delay spread for urban and suburban settings was found to be 0.73 µs and 0.59 µs, respectively, with a combined mean RMS-DS of 0.66
µs.
The VHF/UHF channel bands have been extensively used by military and civilian communications and in these bands, terrain-induced multipath can be considerable in urban areas [9]. Terrain multipath includes built up structures, bridges, hills, etc. In [9], the author suggests that several tests have indicated multipath spreads lower than 1 µs for urban and suburban areas. Propagation tests conducted by [10] in the frequency band of 1
GHz in urban environments found delay spreads up to 10 µs, but these large values are atypical. 30
With the growth of airport operations, the need for reliable new wireless communication services on the airport surface has been established. In [11], the authors reported measurement results for channel characterization and modeling for airport surface areas in the 5 GHz frequency band. Measurements were conducted at several airports including large, medium, and small airports. The transmitter was placed at two locations – air traffic control tower (ATCT) and airport field sites (AFS) (on the airport surface) – and the receiver was mounted on a ground vehicle. They found mean RMS-DS values to be 1.469 µs and 0.789 µs in NLOS and NLOS-Specular (“partially obstructed”
LOS) regions at a large airport. The mean RMS-DS using the field site transmitter was found to be 1.475 µs and 0.317 µs in the NLOS and NLOS-S regions, respectively.
As the use of wireless communication is increasing in indoor environments, systems are also being used within vehicles, including aircraft. The authors of [14] conducted measurements and modeling within several aircraft of various sizes in the 5
GHz frequency band, and found mean RMS-DS for small aircraft to be on the order of 25 ns.
Experiments conducted by [16] to characterize wireless indoor radio channels in a campus environment in the frequency range of 5.15 GHz to 5.35 GHz. The RMS-DS at various indoor locations ranged from 13.95 ns to 80.75 ns. Throughout the measurements the receiver antenna remained stationary at a given location and the transmitter was mobile. In [15], the indoor channel in the unlicensed frequency and of 2.4 GHz was measured, with RMS-DS values from 22.19 ns to 30.55 ns using a measurement procedure similar to that in [16]. 31
Table 2.1. Example RMS-Delay spread tabulated for various environments and frequency bands. Environment Reference Frequency Example Delay Spread (ns) Band RMS-DS Mean RMS-DS Outdoor Campus [27] 5 GHz 341 to 1503 wide
Airport [11] 5 GHz - 1469 to 789 (NLOS) 1475 to 317 (NLOS-S) Aircraft [14] 5 GHz - 25 ns
Indoor campus [16] 5 GHz 13.95 to - 80.75
Indoor campus [15] 2.4 GHz 22.19 to - 30.55 Dense Urban, [7] 910 MHz - 730 to 590 suburban and rural
Table 2.1 shows the example RMS-DS for different environments and frequencies. As we have noted, we have found no references that quantify channel dispersion changes when the mobile receiver causes a transition of the propagation environment from a LOS to a NLOS region, in any frequency band. Although many authors have measured and reported results for both types of regions, none have studied the actual transition.
2.3. Large-Scale Fading
A radio signal undergoes average signal power attenuation or path loss for any distance. Variation in this path loss is represented by large-scale fading. This phenomenon is affected by local physical features such as hills, forests, billboards, etc. 32
The statistics of large-scale fading helps us to determine a useful statistical relationship between path loss and distance. Propagation models indicate that the mean path loss
Lp (d) as a function of d, the distance between the transmitter and receiver, can be approximated as a function of the nth power of distance d relative to a reference distance d0 0:
⎛ d ⎞ ⎜ ⎟ L p (d)dB = Ls ()d 0 (dB) +10n log⎜ ⎟ (2.1) ⎝ d 0 ⎠ where n is the path loss exponent and the reference distance d0 varies based on the extent of the system under consideration. For example, d0 can be 1 m for indoor settings or 1 km for large cellular settings. For free space, propagation loss follows an inverse-square law and the path loss exponent n is equal to 2. In the presence of strong wave guiding structures, the path loss exponent can often be less than 2. In contrast, in the presence of obstructions, path loss exponents are typically greater than 2.
Strictly speaking, path loss itself is not fading. As noted, in free space, where there is by definition no obstruction, signal strength decays with distance because a traveling electromagnetic wave’s power density decreases with distance. This is sometimes termed “spreading loss.” The large scale fading effect is embodied in the
another term that we add to (2.1). This term is typically a Gaussian random variable Xσ with zero mean and standard deviation σ, hence the large scale power attenuation equation becomes 0.
Lp (d)(dB) = Ls (d 0 )(dB) +10nlog10 (d / d 0 ) + X σ (dB) (2.2) 33
Thus, the required parameters to statistically describe path loss due to large-scale fading are as follows: (1) a reference distance d0, (2) the path loss exponent n, and, (3) the standard deviation of Xσ. This variable, Gaussian in dB, is lognormally distributed, and its presence is most often attributed to obstruction of the signal by large obstacles, hence the term Xσ is often referred to as a lognormal shadowing random variable.
2.4. Small-Scale Fading
Small scale fading is used to describe propagation of an electromagnetic wave experiencing “rapid” fluctuation of amplitude, phase or multipath delay [2] over a small spatial extent, typically on the order of one-half wavelength. Small scale fading is generally caused by the destructive interference between two or more multipath signals arriving within a small duration of each other. These multipath components have different path lengths, leading to constructive and destructing addition of multipath components. For an unmodulated carrier signal with carrier frequency fc, the received baseband signal can be expressed as [1]
− jθn (t) Z(t) = ∑α n (t)e (2.3) n
th where τn is the delay of the n multipath component and θn is found from the carrier
th frequency fc via θn (t) = − j2πfcτ n (t) . Whenever the delay τ n for the n multipath signal
arriving at the receiver changes by 1/fc, θn will change by 2π radians. The received baseband signal Z(t) hence varies in space and if the receiver is mobile, it also varies in time. The resultant received envelope can be expressed as [1]: 34
Z(t) = α (t)e− jθ (t) (2.4) where α(t) and θ (t) are the resultant amplitude and resultant phase, respectively.
The effects of small scale fading are as follows [2]:
1. Variation in received signal strength over a small distance.
2. Delay in multipath causes time dispersion of the signal.
3. Varying Doppler shifts of multipath components leads to random frequency
modulation.
The factors influencing small scale fading are multipath propagation, the speed of the mobile receiver, the relative speed of surrounding scattering and reflecting objects, and the bandwidth of the transmitted signal [2]. Multipath propagation lengthens the time required for a baseband signal to reach the receiver and can give rise to inter-symbol interference. Relative motion between a mobile receiver and transmitter (mobile or not) with stationary surrounding objects gives rise to random frequency modulation; even without multiple transmission paths, relative motion causes Doppler shifts. The random
FM can be viewed as characterizing the range of these Doppler shifts. A diagram of the effects of small scale fading is shown in Figure 2.1 [1], [2].
35
Figure 2.1. Small-Scale fading channel manifestations [1], [2].
2.4.1. Delay vs. Time
In characterizing a channel, the term delay is used to represent the extent of the channel’s impulse response. In this sense, delay is a “local” time scale, since typical impulse response durations are short for terrestrial communications (ns or μs). The time variable is used to represent longer term variation (typically ms or longer)
2.4.2. Signal Time Spreading
For a wide-sense stationary uncorrelated scattering (WSS-US) channel, signals with different delays arriving at the receiver antenna are uncorrelated [18]. The multipath components cause time dispersion of the received signal, which results in either flat or 36 frequency selective fading, depending upon the signal bandwidth relative to the reciprocal of the spread of multipath delays. The term excess delay is often used to quantify the delay of the “last” multipath component, and the time duration between the first and last arriving multipath signal is known as delay spread Tm.
The relationship between delay spread and symbol time Ts gives rise to two categories of degradation, namely flat and frequency selective fading. A channel is said to exhibit flat fading if Tm < Ts. Flat fading gives rise to reduction in SNR (SNR is the ratio of desired signal power to the receiver noise power) as all the multipath components are in essence smeared together as one; the different phases of each component results in destructive addition of these “unresolved” phasor components [1].
A channel is said to exhibit frequency selective fading if Tm > Ts, that is the delay spread exceeds the symbol time1. This gives rise to inter symbol interference (ISI). Some of the multipath components are resolved and these yield distinct “echoes” of the transmitted signal at the multipath delay values.
The “absolute” delay spread Tm is not the best indicator of the time dispersive property of a wideband channel, typically because the multipath components are not of equal strength, and signal to noise ratios are finite in real systems. In addition, the delay spread changes in space (and time). Hence we often use a different parameter known as
the root mean square delay spread (RMS-DS), represented by στ . The RMS-DS is the square root of second central moment of the power delay profile [2] and this is explained in detail in chapter 4.
1 Some frequency selectivity is seen for Tm as small as ~0.1Ts. 37
Signal time spread can also be viewed in the frequency domain, and this is typically done using the spaced frequency correlation function R(Δf), which represents the correlation between the channel’s response to two signals with frequency separation
Δf.
The coherence (or, correlation) bandwidth f0 is a statistical measure of the range of frequencies over which the channel amplitude responses are comparable. In [19], the authors define coherence bandwidth as the bandwidth with 10% of signal amplitude variation, but this is not the only definition. For correlation values above 0.9 another measure of correlation bandwidth is [2]
1 f 0 ≈ (2.5) 50σ τ
If the frequency correlation function is above 0.5, then yet another approximate correlation bandwidth is [2]
1 f 0 ≈ (2.6) 5σ τ
It can be noted that the parameters in equations (2.5) and (2.6) do not depend on the signal characteristics. The signaling rate determines the transmission bandwidth W.
Based on the relationship between the transmission bandwidth and the coherence bandwidth we can classify the fading as either flat or frequency selective. A channel is said to exhibit flat fading if f0 is greater than W and this results in performance degradation due to loss of SNR. Frequency selective fading is exhibited by the wireless channel if W is greater than f0. A frequency selective fading channel gives rise to ISI. 38
2.4.3. Channel Time Variation
The time variation of a channel is caused in most instances by the relative rate of change of motion of a receiver with respect to the transmitter. Motion of reflecting and scattering objects can also cause this. A channel is said to be time invariant if the impulse response function is constant over time. The channel’s time variation can be described using the frequency and time domain parameters of Doppler spread and coherence time, respectively.
Doppler spread Bd is a statistical measure of spectral broadening, as noted, most often caused by motion of a transmitter or receiver with respect to each other and/or the reflecting/scattering objects [2]. This amount of spectral broadening depends on the relative velocity between the Tx and Rx, and the angle θ between the direction of motion of the receiver and the angle of arrival of the multipath component [2]. The amount of
frequency broadening for a transmitted bandpass signal with center frequency fc is ± fm ,
where f m is the maximum value of Doppler shift. Based on the relationship between the
Doppler spread and bandwidth of the transmitted baseband signal W, we deduce two categories of degradation: fast fading and slow fading.
A channel will exhibit fast fading if the Doppler spread is large relative to the transmitted signal bandwidth, that is when Bd is on the order of W (or larger). A fast fading channel induces frequency dispersion due to Doppler spread and this causes signal distortion. A channel induces slow fading if the Doppler spread is much smaller than the transmitted signal bandwidth Bd< The time variation of the channel can also be explained in the time domain using the parameter known as coherence time Tc. Coherence time is defined as a statistical measure of the time duration over which the channel is considered to be time invariant. For a correlation value above 0.5 we can approximate Tc using the expression [2] 9 Tc = (2.7) 16πfm where the maximum value of Doppler shift fm is given by v f = (2.8) m λ As with the other parameters, the value of coherence time can be used to describe two categories of channel degradation, fast and slow fading. If the rate of change of the channel impulse response is on the order of the symbol duration Ts then the channel is said to exhibit fast fading. Slow fading is when the coherence time is much greater than the symbol time, Tc>>Ts (typically two orders of magnitude or more in practice). Both fast and slow fading can be either frequency flat or frequency selective. 2.5. Amplitude Fading Models In this section we describe popular statistical models used to characterize the distribution of wireless channel amplitude fading. These models all pertain to fading caused by multipath propagation. 2.5.1. Rayleigh Fading Distribution The Rayleigh distribution statistically describes the variation of the envelope of a received signal for a flat fading channel or an individual multipath signal [2], [19] i.e., the variation of α(t) in (2.4). It is derived from the Central Limit Theorem, in which the in- 40 phase and quadrature components of the channel are modeled as Gaussian. A received signal is Rayleigh distributed if it does not contain any dominant (often LOS) component and has a probability density function given by ⎧ r ⎛ r 2 ⎞ exp⎜− ⎟ ⎪ 2 ⎜ 2 ⎟ (0 ≤ r ≤ ∞) p(r) = ⎨σ ⎝ 2σ ⎠ (2.9) ⎪ ⎩0 (r < 0) where σ is the rms value of the received signal voltage. The probability that the received envelope voltage r does not exceed a given value R is given by the corresponding cumulative distribution function (cdf) [2], [19] ⎛ R 2 ⎞ P(R) = Pr(r ≤ R) = 1− exp⎜− ⎟ (2.10) ⎜ 2 ⎟ ⎝ 2σ ⎠ 1 0.9 sigma=4 sigma=3 0.8 sigma=2 sigma=1.5 0.7 sigma=1 0.6 0.5 0.4 0.3 Cumulative density function P(R) function density Cumulative 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Envelope of received signal (R) Figure 2.2. Plot of Rayleigh CDF with varying value of σ. 41 Plots of Rayleigh cdfs for values of σ ranging from 1 to 4 in (2.10) are shown in Figure 2.2. The mean of Rayleigh distribution is 1.2533σ and the variance is 0.4292σ 2 . It is often easiest to compare the different distributions using their median values rather than the mean values, so sometimes median values will be cited for both analytical and measured distributions. 2.5.2. Ricean Distribution The statistical variation of a received envelope is Ricean distributed if a dominant non fading signal component (such as a line of sight component) is present along with weaker multipath components that can be modeled as Rayleigh. The composite received signal in the absence of a dominant LOS component resembles a noise signal and the envelope is the Rayleigh distribution [19]. The probability density function of a Ricean distribution is given by [19] ⎧ r ⎛ r 2 + A2 ⎞ ⎛ Ar ⎞ exp⎜− ⎟I ⎪ 2 ⎜ 2 ⎟ 0 ⎜ 2 ⎟ A ≥ 0, r ≥ 0 p(r) = ⎨σ ⎝ 2σ ⎠ ⎝σ ⎠ (2.11) ⎪ ⎩0 r < 0 where A denotes the peak amplitude of the dominant component and the mean power is 2 given by 2σ . The function I0(·) is the modified Bessel function of first kind and zero order. The Ricean distribution is described using the parameter known as the Ricean K factor, which is the ratio of the dominant component power to the scattered component power, given by A 2 K = (2.12) 2σ 2 42 ⎛ A 2 ⎞ K(dB) =10 log⎜ ⎟ (2.13) ⎜ 2 ⎟ ⎝ 2σ ⎠ As A tends to 0, K tends to − ∞ dB and this results in the Ricean distribution (2.11) reducing to the Rayleigh distribution. We plot the Ricean PDF for values of K ranging from 1 to 5 in Figure 2.3. Envelope of received energy (r) Figure 2.3. Plot of Ricean PDF, parameterized by different values of K [38]. 2.5.3. Nakagami Fading Distribution The Nakagami fading distributions were developed by Nakagami in the 1940’s, and are known to characterize fast fading in long distance High Frequency (HF) channels. The distribution was selected to fit empirical data and provides a better approximation to 43 experimental data than the Rayleigh and Ricean distributions [3] in many cases. The probability density function of a Nakagami distribution is given by ⎛ m ⎞ 2mmr 2m−1 exp⎜− r 2 ⎟ Ω p(r) = ⎝ ⎠ (2.14) Γ(m)Ωm The received signal envelope amplitude is r, the received signal’s time averaged power is represented by Ω=E(r2), Γ(•) is the gamma function, and m is the inverse of the normalized variance of r2 [19] and is also known as Nakagami shape factor: r 2 m = (2.15) ()r 2 − r 2 with ⋅ denoting expectation. The Nakagami distribution is often used because it can model fading conditions that are better or worse than Rayleigh fading, that is for m =1 the distribution becomes the Rayleigh distribution and for m>1, the Ricean distribution can be closely approximated by the Nakagami using the relation between the Nakagami shape factor m and the Ricean factor K [3]: m 2 − m K ≅ m >1 (2.16) m − m 2 − m ()K + 1 2 m ≅ (2.17) (2K + 1) 2.5.4. Weibull Fading Distribution In this thesis we fit our measured power delay profile component amplitude statistics with the Weibull distribution for all taps (components). The Weibull fading 44 distribution has often been found to better characterize fading distributions, and also provides flexibility in modeling a range of fading conditions, just as does the Nakagami distribution. (As with the Nakagami, the Weibull also lacks a theoretical basis [19]) The probability density function for the Weibull distribution is [19] ⎧ ⎡ β ⎤ β β −1 ⎛ r ⎞ (r ≥ 0) ⎪ β r exp⎢− ⎜ ⎟ ⎥ p(r, β) = ⎨a ⎣⎢ ⎝ a ⎠ ⎦⎥ (2.18) ⎪ r < 0 ⎩0 () where β, the shape factor, is analogous to the Ricean K and Nakagami m factors. The parameter a is the scale factor, related to the signal mean-square value Ω [11] Ω a = (2.19) ⎡⎛ 2 ⎞ ⎤ Γ⎢⎜ ⎟ +1⎥ ⎣⎝ β ⎠ ⎦ For β = 2 the Weibull distribution is the Rayleigh, and for b<2 the fading is worse than Rayleigh. 45 CHAPTER 3: NARROWBAND INDOOR CHANNEL TRANSITIONS In this chapter we model the response of an indoor narrowband wireless channel when it undergoes a transition from a LOS position to a NLOS position around corners. Wideband measurements are the focus of this thesis, but narrowband measurements were also conducted, primarily to gain experience in measurement procedures and statistical data analysis and interpretation. The chapter describes the equipment used to carry out the narrowband channel measurements, followed by a description of the measurement procedures. We also describe the specific channel environments around the corners. Finally, we describe results from our analysis of these channel transitions. 3.1. Experimental Description 3.1.1. Goal The goal of this experiment was to measure the received power level in a band of frequencies as the wireless channel underwent a transition. Specifically, the transition we imposed was a change from a LOS to NLOS condition, around several corners indoors, on the 3rd floor of Stocker Center. These measurements can help us quantify how a wireless channel changes in this indoor environment when such a transition occurs. Our narrowband indoor measurements were taken in the Industrial, Scientific and Medical (ISM) band ranging from 902-928 MHz. Our ultimate aim is to model the behavior of received RF signals when subjected to these transitions. 46 3.1.2. Test set up 3.1.2.1. Equipment The equipment used as transmitter and receiver for the measurements is described below, and some detailed specifications for the two main components are shown in Table 3.1. Table 3.1. Transmitter and receiver description. TRANSMITTER RECEIVER EQUIPMENT Signal Generator Spectrum Analyzer Agilent E4432B ESG-D Agilent E4404B ESA-E MODEL NUMBER series Signal Generator series Spectrum Analyser SERIAL NUMBER US40240983 US40053897 SETTINGS Tx Power = +20dBm Frequency Span = 27 MHz The receiver unit was placed on a cart of approximately 1 meter in height and was made to travel along an “L-shaped” path around each corner. The entire path was divided into several segments of equal length. Antennas were connected to the signal generator and spectrum analyzer using 50 Ω RG-58 RF cables. We used the procedures based on the work done by. 3.1.2.2. Set up procedure Transmitter The transmitter consists of a signal generator connected directly to an omni directional monopole antenna through a short section (~1m) of co-axial cable. The entire 47 900 MHz ISM frequency band from 902-928 MHz was covered by stepping a tone across the band in 1 MHz increments. For these experiments, we set the transmit power level to +20 dBm. The signal generator outputs a tone for the “dwell time” of 500 ms, then steps or “hops” to the next frequency. The sequence of steps followed for configuring the signal generator was derived from [24], [25] and is as follows: 1. Switch on the signal generator. 2. Select the sweep/list from the menu, and then select the following options: a. Sweep type step b. Sweep repeat cont c. Configure step sweep: Start frequency : 902 MHz Stop frequency : 928 MHz Start Amplitude : +20 dBm Stop Amplitude : +20 dBm No. of points : 27 Step dwell : 500 ms Press return to return to previous menu d. Sweep ON and select frequency and amplitude to start sweeping. 3. Attach the monopole antenna at the RF output. 4. Start the frequency and amplitude sweep. 5. Select RF ON to transmit. 48 A block diagram of the transmitter section is shown in Figure 3.1. This set up is shown in the photograph of Figure3.2. MONOPOLE ANTENNA SIGNAL GENERATOR Figure 3.1. Block diagram of transmitter section. Antenna Signal Generator Figure 3.2. Photograph of transmitter section consisting of signal generator and antenna. 49 Receiver Our receiver was a spectrum analyzer, omni directional monopole antenna, and connecting RF cable, all also placed on an equipment cart. The spectrum analyzer measured the received power level at different spatial locations. The Omni directional monopole antenna was connected to the spectrum analyzer through a short section (~1m) of 50 Ω RG-58 co-axial cable. The received power level was recorded manually, at each of the tone frequencies within the frequency band, at every spatial location along the trajectory of travel around each corner. The block diagram in Figure 3.3 depicts the connection of the receiver unit. MONOPOLE ANTENNA SPECTRUM ANALYZER RF CABLE Figure 3.3. Block diagram of receiver section. We derived the sequences of steps for configuring the spectrum analyzer (SA) from [24], [25] and these were as follows: 1. Switch on the spectrum analyzer. 50 2. Select start frequency as 901 MHz. 3. Select stop frequency as 929 MHz. 4. Select amplitude from the control menu and set attenuation manually to 0 dB. 5. Select BW/Avg from the control menu and set resolution bandwidth and video bandwidth to 300 kHz. Finally regarding the test procedure, the sequence of steps followed for recording the measured received power level on the spectrum analyzer was as follows: 1. Select view/trace from the control menu. A. Select Clear Write B. Select Max Hold C. Wait until the entire frequency spectrum is scanned. This took exactly 13.5 seconds. (The scan duration is obtained by multiplying the dwell time (500 ms) by the difference between the start and stop frequencies.) D. Select View to freeze the image on the screen of the spectrum analyzer. 2. Obtain the power level for each frequency point using the SA marker A photograph of the receiver section is shown in Figure 3.4. 51 Antenna Spectrum Analyzer RF Cable Figure 3.4. Photograph of Receiver section consisting of spectrum analyzer, RF cable and antenna. 3.1.3. Measurement Description As noted, the spectrum analyzer was placed on a cart and was moved slowly along the path around the corner. Each “leg” of the L-shaped path measured 1m. The entire path along the corner was split into equidistant intervals of length λ/4, where the wavelength λ is 0.327 m at f =915 MHz c λ = f where c = 3×108 m/sec is the speed of light, and f is the center frequency of the 900 MHz ISM band. 52 The receiver was moved along the path as shown in Figure 3.5 and at each measurement location, corresponding to an interval end point, the received power level over the entire frequency band was measured and recorded. Figure 3.5 illustrates the receiver path. Points 1 to 13 represents LOS conditions. The entire LOS path length from point 1 to point 13 is 96 cm, and it was divided into 13 spatial segments each of length 8 cm (λ / 4 ). Point 7 to point 17 is approximately where the transition from LOS to NLOS occurs. We denote the path from point 13 to point 25 the NLOS section. 1 λ / 4 2 Receiver Trajectory To 7 Transmitter 25 17 13 Figure 3.5. Receiver path illustration. 53 Figure 3.6 shows the floor plan of the third floor of Stocker Engineering and Technology Center located in the West Green, Ohio University. The Stocker Center houses the College of Engineering. Point T1 is the location of the transmitter. The transmitter was placed at the end of the hallway as seen in Figure 3.7. The long unobstructed hallway behaves as a waveguide that directs the transmitted signal. Corners C1 and C2 indicate the corners around which the receiver was moved along the path as illustrated in Figure 3.5. T1 C1 C2 Figure 3.6. Floor plan for 3rd floor Stocker Center. 54 3.1.4. Environment Description The aim of the experiment was to model the narrowband channel as accurately as possible with the equipment employed. This meant that we wanted to encounter a minimal amount of interference at the receiver. To get these results the experiment was conducted in the indoor environment free from any human or RF interference during “quiet” times. The experiments could not be carried out during the day time as students, faculty, opening and closing of doors, etc., could easily influence the measured data. Hence we measured at night, and made sure that all people involved with the experiment remain stationary when the data were collected. Transmitter location Figure 3.7. A view of the unobstructed hallway indicating the location of the transmitter. 55 The received power level at corner C1 was measured to be stronger than the power level measured at corner C2. This is due to the fact that the corner C1 was closer to the transmitter than corner C2. There also arises a possibility of back reflections contributed by the closed door along the end of corner C1 as seen in Figure 3.8; this could have reflected signals back to the receiver, adding to the LOS power at corner C1. Closed door Corner C1 Figure 3.8.View of corner C1 56 Corner C2 is an open L-shaped corridor with many labs and rooms that remain open most of the time. This can be observed in Figure 3.6. Hence the back reflections are minimal. 3.2. Results The measured received power levels were recorded and input into a computer. We used MATLAB® to analyze our measurement data. Our transmitted signal was subjected to various types of distortions due primarily to multipath propagation in the channel. Different propagation mechanisms that the signal encounters can be scattering, reflection, and diffraction. As the wave propagates through an indoor channel, the signal arriving at the receiver has multiple components. All these components could not be resolved since we are sending a narrowband signal (tone). To illustrate results we show the following plots for each corner. i. 3-Dimensional bar plot of Received power vs. frequency and distance ii. Relative power at a given spatial distance vs. frequency iii. Cumulative distribution plot (CDF) of relative power at a given spatial location vs. frequency iv. Relative power for a given frequency vs. distance (time) v. CDF plot of relative power for a given frequency vs. spatial location (time) We first discuss these plots of measured power at corner 1, followed by a similar discussion for corner 2. 57 3.2.1. Corner 1 3.2.1.1 3-Dimensional Bar Plot of Received power vs. frequency and distance The bar plot illustrates the variation in received signal power due to multipath fading versus both frequency and distance. Clearly frequency selective fading is evident from the 3D bar plot in Figure 3.9. Another point to be noted is the drop in received power level is significant in the frequency range of 902-920 MHz, when the receiver enters N-LOS region from LOS. This may be due to significant back reflections generated in the NLOS region in corner 1 due to the closed door as noted in Figure 3.8. The signal strength is substantial since corner 1 is located close to the transmitter, and the 10 5 Relative Power (dB) 0 25 25 NLOS 20 20 15 15 LOS 10 Distance 10 5 Frequency (901+y) MHz (Each unit on distance 5 axis = 8 cms) 0 Figure 3.9. 3D Bar Plot for indoor corner 1. 58 hallway between the transmitter and receiver acts as a waveguide. At some frequencies there is a gradual increase in received power level for a given spatial location as the receiver moves closer into the NLOS region. 3.2.1.2 Resultant Power vs. Frequency The resultant power measured at each location around the receiver path is plotted against the entire frequency span. The plot aids in analyzing the frequency selective fading behavior of the channel for every location around the corner. As discussed in section 3.1.3, we classify our spatial positions as either LOS or NLOS based on the distance relative to the corner. Figure 3.5 shows this as our “distance index.” Thus if the distance index is less than 14 then we consider the area LOS, else it is considered to be in the NLOS region. Figure 3.10 illustrates plots of the received power vs. frequency for LOS positions indexed from 5 through 9. Deeper fading was observed at 924 MHz for 5th position. Lower frequency selective fading was observed at positions 6 through 9. 59 0 -5 -10 -15 Relative Power in dB Position5 Position6 -20 Position7 Position8 Position9 -25 900 905 910 915 920 925 930 Frequency in MHz Figure 3.10. Plot of relative power in dB for LOS positions vs. frequency in MHz for IC1. 0 -2 -4 -6 -8 Relative Power in dB in Power Relative Position20 -10 Position21 Position22 -12 Position23 Position24 -14 900 905 910 915 920 925 930 Frequency in MHz Figure 3.11. Plot of relative power in dB for NLOS positions vs. frequency in MHz for IC1. 60 Figure 3.11 illustrates the plot of relative received power for NLOS positions vs. the entire frequency span. Position 22 and 23 shows similar fading patterns with deeper fading in the frequency range of 910-915 MHz. Large fading was observed at most of the positions in the frequency range of 905-914 MHz. Most clear is that the NLOS area, due to a larger number of multipath components and no dominant LOS component, has deeper fading overall than the LOS area. 3.2.1.3. CDF of Relative Power vs. Frequency The CDF of relative power vs. frequency for different locations is plotted and is compared with the chi-squared CDF whose mean is normalized to 0 dB [20]. The reason why we compare the CDF of received power with the CDF of a chi square is because the commonly used Rayleigh amplitude distribution yields a chi-square distribution when we convert to power. The chi-squared probability density function (PDF) is given by (3.1) ⎧ xn / 2−1 −x / 2 x ≥ 0 ⎪ n / 2 e f x (x) = ⎨2 Γ(n / 2) ⎪ (3.1) ⎩0 otherwise where n is the number of degrees of freedom. For two degrees of freedom (our Rayleigh model) the PDF and CDF of chi-squared distribution is given as in (3.2) and (3.3) respectively exp(−x / 2a2 ) f (x) = (3.2) x 2a2 61 2 (3.3) Fx (x) = 1− exp(−x / 2a ) The mean of the chi-squared distribution is E[x] = 2a2 for our normalization unity mean power. The normalized chi-squared CDF is then (3.5) Fx (x) = 1− exp(−x) 0 10 -1 10 Cumulative Density Function LOCATION 8 LOCATION 9 LOCATION 10 LOCATION 11 -2 Chi Square CDF 10 -8 -6 -4 -2 0 2 4 Relative Power in dB Figure 3.12. CDF of relative power (dB) vs. frequency for LOS positions for IC1. 62 0 10 -1 10 LOCATION 20 Cumulative DensityFunction LOCATION 21 LOCATION 22 LOCATION 23 Chi Square CDF -2 10 -10 -5 0 5 Relative Power in dB Figure 3.13. CDF of relative power (dB) vs. frequency for NLOS positions for IC1. We also normalized the mean of our measured received power over the entire frequency span to 0 dB and plotted the CDF of this normalized relative power along with the normalized chi squared CDF plot for both LOS and NLOS locations. These can be seen in Figure 3.12 and 3.13. It can be observed that the measured data CDFs are better than the chi-squared CDF for both LOS and NLOS locations. It can also be noticed that CDFs’ of higher indexed positions (i.e., NLOS points) are closer to the chi-squared CDF than are those of the LOS locations. Hence the NLOS case is closer to Rayleigh fading, whereas the LOS case is closer to Ricean. Using the distribution fit tool in MATLAB® 63 1 Location 1 0.9 Ricean;k=0.449;location 1 Location 14 0.8 Ricean;k=0.646;location 14 Location 24 0.7 Ricean;k=0.779 ;location 24 0.6 0.5 0.4 Cumulative probability 0.3 0.2 0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Power inPower milliwatts Figure 3.14. CDFs of received power at a given location vs. frequency and Ricean fit CDFs for IC1. we fit the CDF’s of power levels recorded at locations 1, 14 and 24 with a Ricean CDF as shown in Figure 3.14. This gave us estimates of the Ricean K-factor (in linear units), the ratio of power in the dominant component to that in the scattered components. 3.2.1.4. Resultant Power vs. Spatial Distance Relative power received at a given frequency is plotted against spatial displacement. As discussed, the receiver unit placed on the cart makes a step displacement of λ /4 (~8 cm) and at every position we measure and record the relative power. Figures 3.15 and 3.16 depict the plots for portions of the frequency band, specifically 907-911 MHz and 917-921 MHz, respectively. It can be inferred from the plots that over some small range of frequencies the channel can be considered “frequency 64 0 -2 -4 -6 -8 Relative Power in dB in Power Relative -10 F=907MHz F=908MHz F=909Hz -12 F=910MHz F=911MHz -14 0 5 10 15 20 25 SpatialS pDisplacement(Lamba/4atial Displacement (λ /4) cm) Figure 3.15. Plot of relative received power at a given frequency vs. spatial displacement for IC1. 0 -2 -4 -6 -8 -10 Relative Power in dB F=917MHz -12 F=918MHz F=919MHz F=920MHz -14 F=921MHz -16 0 5 10 15 20 25 SpatialSpatial DisDisplacement(Lamba/4placement (λ /4 cm) cm) Figure 3.16. Plot of relative received power at a given frequency vs. spatial displacement for IC1. 65 flat,” or in other words, the signal experiences little difference in amplitude fading over this range of frequencies; this is related to a statistical measure called coherence bandwidth. We further investigate this in section 3.2.1.6 where power correlation bandwidth plots are studied for LOS and NLOS data. 3.2.1.5. CDF of Relative Power vs. Spatial Distance It can be noticed that the CDFs of relative power at a given frequency vs. spatial distance, plotted in Figure 3.17 and 3.18, are also better than chi square fading. 0 10 -1 10 F=906 MHz Cumulative Density Function F=907 MHz F=908 MHz F=909 MHz Chi Square CDF -2 10 -10 -5 0 5 Relative Power in dB Figure 3.17. CDF of relative power in dB for frequency range of 906-909 MHz vs. spatial displacement for IC1. 66 0 10 -1 10 F=918 MHz Cumulative DensityFunction F=919 MHz F=920 MHz F=921 MHz Chi Square CDF -2 10 -10 -5 0 5 Relative Power in dB Figure 3.18. CDF Plot of relative power in dB for a frequency range of 918-921 MHz vs. spatial displacement for indoor corner 1. To better understand the closeness of different distributions to our set of data we plot the probability density function (PDF) of square root of received power at 910 MHz vs. distance against various other distributions including the Ricean, Rayleigh, Nakagami and Weibull using “dfittool” function in MATLAB® The closeness of a fit was decided based on the log likelihood of a distribution that is higher the log likelihood of a distribution fit closer it resembles to the data set. As seen from Table 3.2 and Figure 3.19, the Ricean distribution was found to be the best fit for the data set under discussion with highest log likelihood of -0.7577 and Rayleigh distribution was worst fit with log likelihood of -9.943. 67 3 910MHz Ricean 910MHz Rayleigh 910MHz 2.5 Weibull 910MHz Nakagami 910MHz 2 1.5 Density 1 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Received amplitudeData Figure 3.19. Distribution fit for PDF plot of received amplitude at 910 MHz vs. spatial displacement for corner 1. Table 3.2. Log likelihood of different distribution fits for the PDF of received power at 910 MHz vs. spatial displacement for corner 1. Distributions Log Likelihood Ricean -0.75771 Nakagami -8.52877 Weibull -9.94105 Rayleigh -9.94349 68 3.2.1.6. Power Correlation Bandwidth Plots A sense of the coherence bandwidth can be obtained from the resultant power vs. spatial distance plot in section 3.2.14. Strictly, the coherence bandwidth refers to the channel transfer function, but since the spectrum analyzer measures only amplitude (squared), we can’t compute this directly. We can though investigate the channel’s correlation in the frequency domain by plotting a “power correlation bandwidth” (PCB) plot for a respective set of data. To compute the PCB, we use the formula R(Δf , Δt) = E[H 2 ( f ,t)H 2 ( f + Δf ,t + Δt)] (3.6) 1 R(Δf ,0) = H 2 ( f )H 2 ( f + Δf ) (3.7) N ∑ where N is total number of samples. We plot the normalized power correlation bandwidth for each region (LOS, NLOS) separately. It can be observed from Figure 3.20 that the PCB for LOS and NLOS regions are comparable. It can be noticed that the power correlation becomes 0.5 at a frequency difference of 6 MHz and 8 MHz for LOS and NLOS areas. 69 1 LOS 0.9 N-LOS 0.8 0.7 0.6 0.5 0.4 0.3 0.2 NORMALIZED POWER CORRELATION POWER NORMALIZED 0.1 0 -30 -20 -10 0 10 20 30 Delta F in MHz Figure 3.20. Plots of power correlation function for LOS and NLOS regions of indoor corner 1. 3.2.2. Corner 2 The results for indoor corner 2 are comparable to those discussed for corner 1. We discuss only plots of received power vs. frequency and vs. spatial displacement as these are most distinct from those of corner 1. In the LOS region less fading was observed for corner 2 than compared with corner 1 for the upper portion of the band, as seen in Figure 3.21 and Figure 3.10 for corner 1. This may be due to the presence of fewer multipath signals. As expected the received signal strength measured at corner C2 decreases as the receiver enters the NLOS region and hence deeper fading along with comparable amplitude fading were observed in the NLOS region for the plot of received power for a given frequency vs. spatial displacement as seen in Figure 3.22 and Figure 3.11 for corner 1.. 70 0 -1 -2 -3 -4 Position5 Position6 Relative Power in dB -5 Position7 Position8 Position9 -6 -7 900 905 910 915 920 925 930 Frequency in MHz Figure 3.20. Plot of received power at a given spatial displacement vs. frequency for indoor corner 2. 0 -2 -4 -6 -8 Relative Power in dB -10 F=917MHz F=918MHz F=919MHz -12 F=920MHz F=921MHz -14 0 5 10 15 20 25 Spatial Displacement(Lamba/4 cm) Figure 3.21. Plot of received power at a given frequency vs. spatial displacement for indoor corner 2. 71 CHAPTER 4: WIDEBAND OUTDOOR CHANNEL MEASUREMENTS 4.1 Introduction This chapter discusses in detail about the characterization and modeling of wideband outdoor channel. We extract delay spread parameters such as RMS-DS, Delay window and CIR X, dB from the measured PDPs. The PDP’s are separated into two different sets of LOS and NLOS region and each set is statistically analyzed. Channel models for each region is developed and defined in terms of number of tap, tap persistence process and fading distribution. A part of the chapter has been selected to be published in IEEE Radio Wireless Conference 2009 which is due to be held on January, 2009 at San Diego, California [23]. Various topics discussed in this chapter include description of the equipment used, environment, and the also introduces to the necessary background required to understand the various analysis carried out. 4.2. Equipment Description 4.2.1. Channel Sounder The channel is considered to be a linear time-variant system, which depends on multiple features of the environment, including the positions of transmitter (Tx) and receiver (Rx) antennas. To provide a complete description of the channel requires determination of certain parameters. These parameters are obtained from experimental data that is gathered using measuring equipment called channel sounder [4]. These parameters are then used by engineers to predict the performance, or performance limits of a communication system that may operate in the channel [4]. For our application we used a modified “Raptor” model wireless channel sounder, manufactured by Berkeley 72 Varitronics Systems (BVS) [39]. The channel sounder was custom built to operate in the 5 GHz band with a selectable center frequency and chip rate. This channel sounder utilizes the stepped time-delay cross-correlation method; hence the sounder uses direct sequence (DS) spread spectrum modulation. This type of sounding provides a detailed estimate of the multipath channel via its impulse response. In this technique, a sinusoidal signal is modulated with high frequency chip sequence of length m using BPSK modulation. The “chips” are elements of a pseudo noise (PN) sequence of length m, with chip duration Tc. The channel sounder can be operated with two values of bandwidth, either 50 MHz or 25 MHz. For a bandwidth of 50 MHz, the chip duration is Tc=20 nsec, and for the 25 MHz bandwidth, the chip duration is 40 nsec. For either value of bandwidth, the maximum unambiguous delay range Td is calculated by multiplying chip duration by the length of PN sequence (m=255), hence Td is 10.2 µsec for a bandwidth of 25 MHz, and 5.1 µsec for the 50 MHz bandwidth. The channel sounder Tx transmits a maximum 2-Watt BPSK signal modulated by the PN sequence of length 255 chips. The channel sounder Rx unit demodulates the received signal, samples at 100 MHz, and can resolve multiple received components (“paths”) down to 20 nsec. Table 4.1 shows the specifications of the channel sounder. 73 4.2.2. Other Equipment Various additional equipment was also used in our measurements. The transmitter related equipment consisted of the following: 1. Channel sounder Tx unit 2. Uninterruptible power supply (UPS): required to safely transfer sounder Tx unit from the Mobile Multiuser Communications (MMCL) lab to the measurement site without losing power to the Tx (the sounder Tx unit was powered by the UPS during this transition). 3. Extension cord: The measurement site did not have an AC power socket nearby, so a 100-foot extension cord was used to connect to the nearest AC supply socket. 4. Antenna: Omni directional monopole antenna, above a ground plane, with gain of 1.5 dBi, used to transmit the SS signals generated by sounder Tx Table 4.1 Summary of channel sounder parameters. Characteristics Value Transmit power +5 to 33 dBm (increment of 1 dB) Center frequency 5.12-5.22 GHz Chip rate 50 Mcps or 25 Mcps Unambiguous delay range 5.1 μsec 99% Power Bandwidth 52.76 MHz Measurement rate 2-60 PDPs/sec Sampling frequency 100 MHz 74 5. RF cable and connectors: Low loss RF cable and connectors were used to connect the antenna to the sounder Tx. The receiver related equipment consisted of the following: 1. Channel sounder Rx unit 2. Lead-Acid battery pack: the sounder Rx was designed to be portable, and can easily be powered using a battery pack. The battery pack can power the receiver for approximately 3 hours and hence sufficed for our measurements. 3. Antenna: Identical to the Tx antenna, an omni directional monopole above a ground plane, with gain of 1.5 dBi, used to receive direct and multipath RF signals. 4. RF cable and connectors: Low loss RF cable and connectors were used to connect the antenna to the sounder Rx. 5. Laptop: To continuously record every power delay profile (PDP), a laptop was connected to the sounder Rx through the serial communication port using an RS- 232 cable. The laptop was also used to configure the receiver unit. Figure 4.1 shows all the instruments and equipment used during the measurement campaign. 4.3. Environment Description To better understand measurement results, we need to have a description of the environment in which the measurements were conducted. The environment description helps us to potentially correlate results with local environment features. The first task was 75 Me Arvind Tx Antenna Sounder Tx Sounder Rx UPS Figure 4.1. Measurement team members along with transmitter and receiver equipments to choose appropriate corners around which we could conduct measurements. The corners were chosen such that the effect of transition from LOS to NLOS would be direct and complete. We choose two corners for LOS to NLOS transitions in one environment surrounded by buildings and trees and in the other environment the channel undergoes the transition in comparatively open space. The locations of the two corners around which we made channel transition measurements were as follows: (1) West Green Corner; (2) Stocker Parking Lot corner. These are more precisely specified subsequently. The channel parameters we measure are directly related to the local environment. The channel characteristics will depend upon the transmitter and receiver location and antenna heights, and the size and composition of objects in the environment, including 76 buildings, trees, etc. For our complex environment, we have three main propagation mechanisms: (a) reflection, (b) diffraction, and (c) scattering. 4.3.1. West Green Corner The measurements were conducted during the summer break of June, 2008. The building corner around Wilson Hall was chosen in the West Green area of the campus. Wilson Hall is numbered as building number 104 in Figure 4.2. The environment around the corner was almost free of human presence (except the three member team conducting the measurements) and there are many trees and buildings. The various multipath components in the environment include those reflected/diffracted from buildings, the ground, railings, a dustbin, tree trunks, etc.. Foliage and tree branches acted as multipath attenuators. Figure 4.2. A 3-dimensional view of West Green. 77 Reflections generally emanate from obstacles with dimensions greater than the wavelength λ (5.88 cm). Diffractions occur when the propagating signal impinges on a corner or sharp edge, e.g., from the building corner under discussion, or metal railings. The motion of humans could cause dynamic scattering whereas non-moving obstacles (buildings, tree trunks, air conditioners) could be classed up as static scatterers. The distance between the transmitter and receiver was approximately 81.26 m. The transmitter was placed on a cart at a location outside the Stocker Engineering Center near the bicycle parking stand, close to the Wilson Hall Research building (building number 104) on the right side, with Stocker Center behind the Tx. The west green has a number of paved pathways and grassy areas, an array of tall trees (deciduous) on either sides of the pathway near Wilson Hall. There were no major obstructions between the Tx and Rx, i.e., an LOS path existed for the first half of the measurements. Figures 4.3 and 4.6 illustrate the features present in the environment around the transmitter location. 78 . Irvine Hall (181) Stocker Engineering Center (103) Figure 4.3. 160° panoramic view of the channel environment behind the transmitter location at West Green (this picture was taken when standing at the transmitter location). 79 Receiver location Irvine Hall (181) Pathway Figure 4.4. 150° panoramic view of the channel environment in front of the transmitter location at West Green (this picture was taken when standing at the transmitter location). 80 Irvine Hall (181) Figure 4.5. Panoramic view of the environment around the receiver path at West Green. 81 Wilson Hall Grosvenor (104) Hall (96) Receiver path Figure 4.6. Continued panoramic view of the environment around the receiver path at West Green. 82 4.3.2. Stocker Parking Lot This corner was chosen around Stocker Engineering Center (building number 103 in Figure 4.2) facing the Stocker parking lot on one side and Lausche Heating Plant (building number 108) on the other side. It can be seen clearly from Figure 4.2 that the environment around Stocker parking lot corner was more open than the Wilson Hall corner at West Green. The various components in the environment that contributed towards multipath propagation of the transmitted signal were similar to those of the first corner, e.g., buildings, the ground, vehicles, humans, signboard, lamp posts, tree trunks, etc. Diffraction of the transmitted signal may have resulted from the building corner under discussion and the signboards. These features can be observed in Figure 4.7. Movements of humans and vehicles (on the road) could have caused dynamic scattering, whereas the parked cars, tree trunks, buildings, and sign boards were static scatters [23]. The distance between transmitter and receiver was approximately 26.5 meters. The transmitter location was chosen outside a side door of Stocker Engineering Center leading to the parking lot. The Tx unit placed on the cart was positioned very close to the wall on the right side. Behind the Tx unit there was a road leading to Grosvenor Hall (building number 97 as seen in Figure 4.2), and on both sides of this road are buildings. Fewer trees were present around this corner than in the West Green corner. The parking lot was located on the left side of the transmitter unit position. The parking lot had only a few cars present. A view of Stocker parking lot can be seen in Figure 4.7. 83 . Stocker Parking lot Receiver location Figure 4.7. 80° panoramic view of the channel environment in front of the transmitter location at Stocker parking lot (this picture was taken when standing at the transmitter location). 84 4.4. Measurement Procedure To estimate the channel impulse response (CIR) for a given channel, we record the PDP and multipath component phases with our channel sounder. The measurement procedure to record PDPs is carried out in two phases, a sounder training phase and a measurement phase. A. Training Set Up It is required to calibrate the sounder to ensure that the sounder Tx-Rx pair is synchronized and they are frequency locked. The Rubidium oscillators in the Tx and Rx are highly precise and stable, but can drift over time. The longer the pair is calibrated, the longer the pair will remain synchronized before beginning to drift. The manufacturer suggests training (i.e., calibrating) the sounder for a time period of at least 2Tt minutes where Tt is the desired measurement time [12]. Generally we would estimated a measurement time of at least 45 minutes, but to allow for any unforeseen delays in measuring, we trained the sounder for a longer period, overnight. This gave us a measurement time of close to 120 minutes. During the sounder training, we connect the Tx and Rx unit “back to back” using a low loss RF cable and a 40 dB attenuator. The Tx power is set to +5 dBm in order not to overload the Rx front end. The receiver is also connected to a laptop using an RS-232 cable. On the laptop, the manufacturer “Raptor” sounder control software is invoked and the receiver is set to the training mode. Reference [12] explains the training procedure in detail. 85 B. Measurements It may be necessary to scan the spectrum to sense any spurious signal in the desired frequency band of interest (5.090-5.250 GHz) before starting with any measurements. Spectrum scanning enables us to determine if any undesired signal may interfere with our measurements. For our measurements we set the Tx RF frequency at 5.120 GHz. Ohio University campus is a complete “WiFi” enabled zone which supports the IEEE 802.11b/g/a WLAN standards. IEEE 802.11 b/g operates at a frequency band of 2.4 GHz and hence it could be ruled out as a possible source of interference. The IEEE 802.11a standard though operates in the frequency band of 5 GHz and the lower frequency band is 5.15-5.25 GHz with center frequencies spaced 20 MHz from the edges [35]. The lower operating frequency band does not overlap with sounder Tx operating frequency for our measurement campaign (5.120 GHz). Moreover according to [36], the IEEE 802.11a standard was supported only in a few specific locations on campus thereby making the probability of interference with our signal of interest low; we did not do any spectrum scanning. Finally on this point, when measuring, our observed results were as expected, i.e., power delay profiles were observed to be what one would predict for our setting, thus we were confident that no interference of any significant level corrupted our measurements. Our measurement routes ensured that the transmitter antenna had a direct line of sight with the receiver antenna for the first part of each measurement run. The PDPs were then recorded as the receiver unit moved away from the transmitter to enter the NLOS region around the building corner. This is explained in detail in the following section. 86 After the overnight training, the transmitter along with uninterruptible power supply (UPS), antenna and Tx power supply, were placed on a cart and moved to the transmitter location as quickly as possible. The UPS could support the transmitter unit for approximately 9 minutes. The transmitter power supply at the transmitter location was then transferred to an AC power source through the UPS. The receiver unit was powered by the lead acid battery pack. The receiver unit and its battery pack, antenna, and laptop was worn by one of the Rx team members using a back pack for outdoor measurements, as shown in Figure 4.8. The Rx team then moved to the Rx measurement location and took position. When the Rx team was ready to start measurements, it signaled the Tx team via voice or walkie talkie to begin transmission. The Rx team then invoked the Raptor software on the laptop, Antenna Laptop Sounder Rx Battery pack Figure 4.8. Portable sounder Rx and ancillary equipment. 87 and started measuring after confirming transmission by the sounder Tx unit. The laptop then started recording the data measured by the Rx. This data is then stored in the laptop after measurement for each corner was completed. A complete description of the procedure to carry out channel sounding can be found in [12]. For every corner, the Rx unit was moved around a building corner on a predetermined path, as in Figure 4.9. The Rx unit moved from the LOS region to the NLOS region with an approximately constant velocity. The total length of the Rx path was 6 meters, with LOS and NLOS paths of lengths 3 meters each. The receiver was moved very slowly along the path. At every corner, two different sets of measurements were carried out. The first set of measurements was conducted with the Rx antenna placed at shoulder height (approximately 150 cm from the ground) and the second set with the antenna placed at waist height (approximately 90 cm from ground). Rx Path 3 m NLOS Stop 3 m LOS BUILDING Towards Tx Start Figure 4.9. Illustrating the receiver motion on a set path. 88 To commence measurements, after invoking the Rx Raptor software the receiver team also set the desired delay span. After the Rx was moved along the path, the data file was saved with a name containing the details of the location, date, and measurement type. To distinguish all corners without ambiguity it was necessary to label every corner based on the type of environment (indoor or outdoor), corner number and antenna position. In the nomenclature we use, the first letter represents the type of environment, outdoor (O) or indoor (I). The second and third letters refer to the building corner, i.e., West Green corner is C1 and Stocker parking lot corner is C2). The last three letters after the hyphen stand for the antenna position, with shoulder height represented by MS1 and waist height represented by MS2. Table 4.2 summarizes this labeling convention. Table 4.2. Labeling convention used for outdoor wideband measurements. OUTDOOR ANTENNA POSITION CORNER Shoulder height Waist height West Green OC1-MS1 OC1-MS2 corner Stocker parking OC2-MS1 OC2-MS2 lot corner 4.5. Analysis After measurements we needed to analyze the data, and we started our analysis with several pre-processing steps, followed by extraction of the desired channel parameters from which we generate the channel models. For every corner we have a set of measured data and for each data set we follow the same steps for analysis. 89 4.5.1. Data Pre-Processing Data pre-processing consists of a series of steps to convert a raw data file (obtained directly from the measurements) into a format from which we could extract channel parameters and generate channel models. The first step in data pre-processing is to translate the proprietary BVS format data (.rap) from the sounder into a format — ASCII — that could be used to perform statistical analysis using mathematical software. We then removed the effects of thermal noise induced by the receiver electronics via a noise thresholding algorithm. Finally we remove the insignificant multipath using multipath thresholding. A. Format Translation The set of PDP’s measured for a particular corner was recorded by the sounder Rx and sent to the laptop, which stored the data in a file in a proprietary .rap format. We converted the .rap format files into a standard ASCII format via the BVS “Chameleon” software. The Chameleon software enables us to choose the required fields during the format translation. The fields that we have used are (1) RTC time, (2) magnitude (dBm), (3) phase (radians), and (4) RSSI (dBm). Figure 4.10 illustrates the output file format with the required fields after the conversion for an arbitrary ith PDP record [26]. Every PDP record consists of n samples. For a 50 MHz bandwidth, each sample in a PDP record is spaced by 20 ns. For a full span measurement the total number of samples recorded per PDP is 510 samples, for a bandwidth of 50 MHz or 1020 samples for a bandwidth of 25 MHz. For our measurement 90 campaign we used a reduced delay span of ~1 μs hence we obtained approximately 100 samples per PDP. Magnitude Phase Magnitude Phase …. Magnitude Phase RSSI (dBm) for (Rads) for (dBm) for (Rads) for …. (dBm) for (Rads) (dBm), 1st sample, 1st sample, 2nd sample, 2nd …. nth for nth for ith ith PDP ith PDP ith PDP sample, ith …. sample, ith sample, PDP record record record PDP …. PDP ith PDP record record record record Figure 4.10. Illustration of a sample PDP record. B. Noise Thresholding The measured PDPs can be significantly affected by the thermal noise induced by the receiver electronics. We mitigate the effect of thermal noise using the algorithm developed by [7]. The algorithm separates a valid echo from “likely noise.” This algorithm was refined for our sounder by [26]. The algorithm determines a noise threshold (NTi) which is determined using a constant false alarm rate (CFAR) and 2 estimated noise variance (σ N). We estimate the level of background noise, assumed to be Gaussian and hence with Rayleigh distributed amplitude. For this, the probability that the noise amplitude exceeds a given level N0 is given by 2 N0 P(N0 ) = exp(− 2 ) (4.1) 2σ N 91 The estimated median level σm is found by equating N0 = σm and setting P(N0 ) in (4.1) to 0.5, and we obtain [7], σ σ = m = 0.85σ (4.2) N ln 4 m We then separate noise samples that are below a user selected threshold of 25 dB [26] to i th calculate the median value σ m for every i PDP record. From the median value th i calculated for the i PDP record, we then find σ N using (4.2). Our last step is to find a noise threshold corresponding to a desired false alarm probability, and the equation for this threshold is given by j NTj =ησ N (4.3) where η for the 50 MHz mode is found to be 3.52 for 510 samples per PDP [26]. For th every i PDP record, we set all the samples that are below the noise threshold NTj to a minimum value of -130 dBm (essentially “zeroing” them in comparison to the stronger multipath components). C. Multipath Threshold The sampling frequency of the sounder receiver is 100 MHz but the chip rate of the sounder transmitter unit was set to be 50 MHz. The receiver oversamples the incoming signal by a factor of two. Hence we must combine the consecutive samples vectorially. This is done by first converting the power samples into voltage samples and then creating I and Q samples using the voltage and phase information. For a 50 MHz bandwidth channel model, consecutive I and Q samples are added and a resultant chip 92 voltage value is obtained. This resultant voltage value is squared to obtain the power for PDP generation. We then set a multipath threshold at a level so as to remove the weaker multipath components. This multipath threshold is set at a level so as to capture most of the energy of a given PDP and neglect the weakest components. For our analysis we set this threshold at 25 dB. The threshold level was calculated iteratively by noticing that using larger values of multipath threshold did not significantly affect the channel statistics [26]. -60 RMS-DS 79.89 ns -70 -80 25 dB -90 d -100 Power in dBm in Power Samples below this -110 Multipath Threshold are set to -125 dBm -120 -130 0 200 400 600 800 1000 1200 Delay in ns Figure 4.11. PDP depicting multipath threshold. Multipath thresholding is carried out by retaining all multipath components whose power levels are within 25 dB of the maximum (main) component and setting those multipath components with power levels below the threshold to be -130 dBm, as shown in Figure 4.11. 93 4.5.2. Parameter Extraction As mentioned, we employ statistical tools to model the unknown wireless channel in order to capture the channel effects concisely. A wideband channel is more dispersive than a narrow band channel (it “resolves” more multipath components in the delay domain) and hence a wideband signal sent over this channel is dispersed in time [13]. After segregating the entire valid multipath using noise and multipath thresholding, we then determine certain channel parameters, including the mean excess delay, root mean- square delay spread (RMS-DS), channel impulse response X,dB (CIRX,dB) duration, and delay window A. Mean Excess Delay ( μτ ) Excess delay is the delay of any multipath sample in a power delay profile with respect to the first arriving multipath sample [19]. Mean excess delay is the first moment of excess delay. The value of mean excess delay ( μτ ) for each PDP is obtained from N −1 2 2 ∑τ k α k k =0 μτ = N −1 (4.1) α 2 ∑k =0 k th th where τ k is the time delay of the k sample in a given PDP, α k is the amplitude of the k sample, and N is the number of samples per PDP. B. Root Mean Square Delay Spread (RMS-DS) RMS-DS (στ ) is regarded as an excellent measure to quantify multipath spread in a wireless channel. According to [19], it also provides an indication of the nature of inter- symbol interference (ISI) and can be used to estimate the maximum possible data rate for 94 transmission. In a PDP, the stronger multipath samples with large delay are major contributors to RMS-DS. Channel dispersion can be quantified effectively using RMS- DS [13]. It is the square root of the second central moment of a power delay profile. For a single PDP the στ can be calculated by N −1 2 2 ∑τ k α k k =0 2 (4.2) σ τ = N −1 − μτ α 2 ∑k =0 k where τk and αk are as defined for mean energy delay. 120 RMS-DS for OC2-MS2 Moving Average= 50 NLOS 100 Moving Average= 150 80 60 RMS-DS inns LOS 40 20 0 0 100 200 300 400 500 600 700 800 900 1000 Profile index (time) Figure 4.12. Plot of RMS-DS vs. profile index (time) for OC2-MS2. Figure 4.12 is a plot of RMS-DS vs. time for OC2-MS2. A total of 976 PDP’s were collected at this corner and each PDP consisted of 50 samples. The PDPs are 95 segregated into LOS and NLOS components with the 488th PDP set as threshold. It can be clearly seen that as the receiver moves towards the NLOS from the LOS region, the RMS-DS increases significantly, and this is more clearly seen from the moving average plots with window lengths of 50 and 150 PDPs. The mean RMS-DS for the LOS region was found to be 58.68 ns compared to a mean value of 75.64 ns in the NLOS region. C. CIR X,dB Duration This parameter is defined as the time duration between the first multipath sample and the last multipath sample that are both within X dB of the maximum amplitude sample. This parameter is also sometimes known as maximum excess delay [2] or delay interval as proposed by [21]. From [2] CIRX,dB duration is calculated using the expression below CIRX,dB Duration = τX - τ0 (4.3) Where, τX is the maximum delay of the multipath component within the X dB threshold and τ0 is the first arriving multipath component for a given PDP, also within 25 dB of the maximum sample. The plot of a single PDP in Figure 4.13 illustrates the calculation of CIRX,dB duration. The CIRX,dB for the PDP in Figure 4.13 discussion was found to be 220 ns. D. Delay Window Delay window is defined as the width of the PDP in terms of the time duration that contains x% of total energy for a given PDP. We represent delay window by DWx , where x is the percentage of total energy enclosed in the delay window. 96 90 80 X= 5 Y= 85.1003 70 25 dB down 60 X= 2 Y= 63.7908 50 CIRX,dB =220 nsec 40 Samples in a PDP Relative Power in dB 30 whose power level are within 25dB 20 below the maximum power 10 (sample 5) 0 0 100 200 300 400 500 600 700 800 900 1000 Delay in nsec Figure 4.13. Illustration of calculation of CIR X, dB duration for a given PDP. 4.5.3. Tapped Delay Line Model We now focus on how we model our wireless channel in a way that could be used by wireless system designers to evaluate system performance. Since the channel is linear and time-variant, we employ the most commonly used tapped delay line (TDL) model [6] and [11]. This model is illustrated in Figure 4.14, with the x’s and y’s the inputs and outputs of the TDL model, respectively, Tc the chip duration, and the C’s are the CIR random amplitude coefficients, given by [11] jφk (t) Ck (t) = zk (t)αk (t)e (4.4) 97 x k+1 x k x k-1 x k-L-1 T T Tc c c C (t C2(t C L(t 1 × × × y k Figure 4.14. Block diagram of tapped delay line model. We denote k the multipath component index, or the channel tap index, and αk is th the k tap amplitude and θk its phase. The value of k ranges from 0 to L for our TDL model with L+1 the number of channel taps. In (4.4) the variable zk is the tap persistence process. This tap persistence process enables us to model the presence or absence of a valid multipath component over time. When the multipath component amplitude is above our threshold, the value of zk is set to 1 and when it is below our threshold, the value of zk is set to 0. The presence or absence of a valid multipath in a given PDP is determined by the noise and multipath threshold algorithms, and zk is dynamic due to movement and obstructions in the environment. 98 4.5.3.1. Number of Taps The number of taps in our channel model can be calculated using different criteria; here we calculate the total number of taps based on RMS-DS [26]. The number of taps is calculated using (4.5) [26]. Table 4.3 shows the number of channel taps computed for each of our corners. ⎡max(RMS − DS ⎤ L = ⎢ ⎥ + 1 (4.5) ⎢ Tc ⎥ Table 4.3. Number of taps for each outdoor corner calculated using RMS-DS method. Outdoor OC1-MS1 OC1-MS2 OC1-MS3 OC2-MS1 OC2-MS2 Corner No. of Taps (L) 25 24 24 21 24 4.5.3.2. Tap Energy th The tap energy of the j tap, Ej, is the average energy of the tap over time (over PDPs), so if the amplitude of tap k is αk, we find the average energy by computing the average of the square of αk for each tap. In our case where we have a persistence process, we consider only those tap amplitude values whose persistence equals one. N 2 ∑ ()α j,i × z j,i E = i=1 (4.7) j N where j is the tap index, i is the PDP index, N is the total number PDPs and zj,i is the persistence for the jth tap and ith PDP. 99 4.5.3.3. Markov Process A Markov process (or Markov chain) is a process that can be in one of several (numbered) states, and can pass from one state to another at each time step according to certain probabilities. The Markov process parameters for our case are the persistence values for each tap. These can be represented as a vector of samples, with each sample being a 1 if the tap amplitude in that PDP is above threshold, else the sample is 0. For any given PDP the threshold is set 25 dB below the maximum power sample in that PDP. To describe the Markov chain for any tap, we require two matrices, the steady state (SS) matrix and the transition (TS) matrix. A. Steady State (SS) Matrix The size of the matrix depends on the number of states in a Markov process. For our case we have two states (1 or 0) and hence the size of our SS matrix is 1× 2. The first element of the SS matrix represents the probability that the tap is in state 0 (below threshold) and the second element is the probability that the tap is in state 1 (above threshold). This is illustrated using the following example. Consider that our vector of z samples is of length N=10, as shown in Figure 4.15. The number of zeros is 2 and number of ones is 8 and hence our SS matrix is SS = [0.2 0.8]. 100 1 0.5 0 0 1 2 3 4 5 6 7 8 9 10 Sample Figure 4.15. Example persistence process. B. Transition (TS) Matrix The Markov chain can be described by means of a state transition diagram, which is a diagram showing all the states and transition probabilities. The TS matrix consists of elements that are the probabilities of going from one state to another during a time step. Each tap in our model has two states, zero or one, and during each time step, the persistence value z can stay the same or change value. Hence each TS matrix is two by two, with elements Pij denoting the probability of going from state i to state j, i,j ∈{0,1}. The calculation of the TS matrix elements can be explained with a simple example shown in Figure 4.16. We use the sequence illustrated in Figure 4.15. From this sequence, we find that P00 =0, because while in state 0, we never transition back to state 0. The value of P01=1 because while in state 0, we always transition to state 1. For the second row, the sequence is in state 1 for 8 samples, but only 7 of these count since the last one at the end of the sequence cannot make any transition. Out of the 7 possible transitions from state 1, only 2 go to state 0, and the other five go to state 1, hence P10=2/7 and P11=5/7. The state transition diagram is shown in Figure 4.16 and the TS matrix is 101 To 0 1 0 ⎡P00 = 0 P01 = 1 ⎤ ⎢ ⎥ From 2 5 ⎢P = P = ⎥ 1 ⎣ 10 7 11 7⎦ P01 = 0 0 1 P10 = 2/7 P00 = 0 P11 = 5/7 Figure 4.16. State transition diagram of the example discussed. 4.6. Channel Statistic and Modeling Results Based on our analysis, we obtained model results for the two corners, as explained in the following sections. We divide our results into two sections, channel parameters and channel models. For the channel parameters, our intuition based on the environment and Rx travel path would be that the delay spread parameters would be larger in the NLOS region than in the LOS region. As for the channel amplitude characteristics, we would expect more fading in the NLOS region than in the LOS region. 4.6.1. Stocker Parking Lot Corner We conducted two sets of measurements at Stocker parking lot corner during our measurement campaign. The first measurement set was conducted with the Rx antenna 102 facing the Tx antenna during Rx motion in the LOS region, with the Rx antenna at waist height (approximately 90 cm above ground level). The second measurement set was conducted with the Rx antenna held at shoulder height (approximately 150 cm above ground level). As explained previously, the receiver path was divided into two sections, the LOS region and the NLOS region, each of length 3 m. During our measurement campaign, a total of 1760 PDPs were collected for the corner under discussion using a delay span of 1.0 µs. The channel statistics for both measurements are shown in Table 4.4. It can be noticed from the table that the mean RMS-DS for both measurements are comparable and the minimum RMS-DS are below 6 ns. The maximum RMS-DS for OC1-MS2 is higher than that for OC2-MS1 and hence OC1-MS2 will have a larger number of taps for its model (based on (4.5)). Table 4.4. Power delay profile, RMS-DS statistics and number of taps for OC2-MS1 and OC2-MS2. OC2-MS1 OC1-MS2 Total Number of PDPs 783 976 Power Delay Number of sample per PDP 50 50 Profiles Delay Span (μs) 1.0 1.0 Minimum 5.51 3.61 Maximum 394.61 457.32 RMS- Delay Spread (ns) Mean 45.15 42.51 Standard Deviation 25.56 32.44 Number of Taps 21 24 103 Figure 4.17 is a plot of RMS-DS vs. profile index for all PDPs collected at OC2- MS2. Figure 4.17 also illustrates moving average plots for window sizes of 50 and 150. An increase in RMS-DS in clearly evident for the higher indexed profiles, particularly from the moving average plots. Some PDPs in the plot have very high RMS-DS values compared to other PDPs. The PDPs with index values of 595, 705, 766, 899 and 916 have RMS-DS greater than 120 ns and these may be due to movements of the measurement team, or Rx malfunction (intermittent). This was also observed in the RMS-DS vs. profile index plot for OC2-MS1, as seen in Figure 4.18. The left PDP plot in Figure 4.19 shows a loss of Rx synchronization, in which early-arriving multipath components are “wrapped” at the end of the profile, and this explains the large value of RMS-DS for PDP index 916. The PDP plot on the right of Figure 4.19 is more typical. Since there were so few of these “wrapped” PDPs, we were able to neglect them without substantially affecting the 500 RMS-DS for OC2__MS2 450 Moving Average= 50 Moving Average= 150 400 350 300 250 Threshold set at 120 ns to 200 RMS-DS in ns remove PDPs with high RMS-DS 150 100 50 0 0 100 200 300 400 500 600 700 800 900 1000 Profile Index (time) Figure 4.17. Plot of RMS-DS vs. Profile Index for OC2-MS2. 104 400 RMS-DS for OC1__MS1 Moving Average= 50 350 Moving Average= 150 300 250 200 Threshold set at 96 ns to remove RMS-DS in ns 150 PDPs with high RMS-DS 100 50 0 0 100 200 300 400 500 600 700 800 Profile Index (time) Figure 4.18. Plot of RMS-DS vs. profile index along with moving averages, for OC2-MS1. 70 100 916th PDP;OC2-MS2 90 1st PDP;OC2-MS2 60 80 50 70 40 60 RMS-DS = 433.76 ns RMS-DS = 25 ns 50 30 40 20 30 Relative power in dB in power Relative Relative power in dB in power Relative 20 10 10 0 0 0 200 400 600 800 1000 0 200 400 600 800 1000 Delay in ns Delay in ns Figure 4.19. Illustrating loss of Rx synchronization (left) and correctly synchronized PDP (right). 105 computed channel statistics. We now determine the channel parameters for the Stocker Parking lot corner with the large RMD-DS PDPs removed. For simplicity we excised these PDPs by visually inspecting the plots of RMS-DS vs. profile index, and selected a suitable threshold such that the probability of occurrence of a PDP with abnormally large delay is small. The threshold was set to 100 ns and 120 ns for measurement sets OC2-MS1 and OC2-MS2, respectively. The probability of occurrence of PDP with delay greater than 100 ns for OC2-MS1 is given by 100 0.0064 (4.7) and the probability of occurrence of a PDP with delay greater than 120 ns for OC2-MS2 is given by 120 0.0051 (4.8) The channel statistics for both corners after ignoring these PDPs with larger delay are given in Table 4.5. It can be seen that the mean and standard deviation of RMS-DS for both measurement sets are comparable. With a maximum RMS-DS of 95.48 ns and 117.80 ns for OC2-MS1 and OC2-MS2, respectively, the number of taps using (4.5) was found to be 6 and 7, respectively. 106 Table 4.5. Channel statistics of Stocker Parking lot corner after removing PDPs with large delay. OC2-MS1 OC2-MS2 Power Delay Total Number of 781 971 Profiles PDPs Minimum 5.51 3.615 RMS- Delay Maximum 95.58 117.80 Spread (ns) Mean 44.11 40.943 Standard Deviation 20.49 22.694 Number of Taps 6 7 The RMS-DS vs. profile index along with moving average plots with windows of 50 and 150 PDPs are plotted for OC2-MS1 and OC2-MS2 in Figures 4.20 and 4.21, respectively. It can be noticed most clearly from the moving average plots that the RMS- DS for both measurement sets increases significantly as the receiver transits from the LOS region to the NLOS region. In the OC2-MS2 RMS-DS plot of Figure 4.21, the RMS-DS shows a slight decreasing trend in the LOS region, but as the receiver enters the NLOS region, the mean RMS-DS increases significantly to 75.64 ns from the value of 58.68 ns for the LOS region. An overall increasing trend in RMS-DS is noticed for OC2- MS1 as the receiver moves towards the NLOS region. The mean RMS-DS for the NLOS region for this corner is 59.01 ns in contrast to 29.24 ns for the LOS region. Hence our intuition is confirmed regarding the higher delay spread in the NLOS region. This is also evident if we plot other channel dispersion parameters such as delay window or CIRX,dB. 107 100 RMS-DS; OC1__MS1 90 Moving Average= 50 Moving Average= 150 80 70 LOS 60 50 40 RMS-DS in ns in RMS-DS NLOS 30 20 10 0 0 100 200 300 400 500 600 700 800 Profile Index (time) Figure 4.20. Plot of RMS-DS vs. profile index for OC2-MS1. 120 RMS-DS for OC2__MS2 Moving Average= 50 100 Moving Average= 150 80 60 LOS RMS-DS in ns in RMS-DS 40 NLOS 20 0 0 100 200 300 400 500 600 700 800 900 1000 Profile index (time) Figure 4.21. Plot of RMS-DS vs. profile index for OC2-MS2. 108 All the measurements conducted at the Stocker Parking lot have similar channel parameter statistics (i.e., RMS-DS) and an increasing trend in RMS-DS from LOS to NLOS, thus we restrict discussion to results of OC2-MS2 henceforth. The histogram of RMS-DS is plotted in Figure 4.22 for OC2-MS2. This histogram has two modes, one corresponding to the LOS region with lower delay spreads and the other corresponding to the NLOS region with higher delay spreads. The delay spreads larger than 45 ns are classified as belonging to the NLOS region. 120 LOS OC2__MS2 100 80 NLOS 60 40 Number of Occurrence 20 0 0 20 40 60 80 100 120 RMS-DS in ns Figure 4.22. Histogram of RMS-DS for Stocker Parking lot corner. Figure 4.23 shows a plot of CIR25dB vs. profile index for OC2-MS2 along with moving average plots with window sizes of 50 and 150 samples, as before. The moving average plots again clearly depict the increasing trend of CIR duration as the receiver 109 enters the NLOS region and this is comparable to the trend seen in the RMS-DS plot of OC2-MS2 in Figure 4.21. The mean CIR25dB duration for the LOS region is 222.83 ns, and the mean is 419.67 ns for the NLOS region. 600 CIR, 25 dB; OC2-MS2 550 Moving Average= 50 Moving Average= 150 500 450 LOS 400 350 300 NLOS CIR delayfor X dBin nS 250 200 150 100 0 100 200 300 400 500 600 700 800 Profile index(time) Figure 4.23. CIR25dB duration vs. profile index for Stocker Parking lot corner. The delay window containing 90% of the CIR energy (DW90) for OC2-MS2 is plotted against profile index in Figure 4.24. This plot is also comparable with those for the other dispersion parameters; there is an increase in the delay window in the NLOS region as compared to that in the LOS region, as expected. The mean delay window value for the NLOS region was 169.66 ns, and the mean for the LOS region was 48.48 ns. The detailed multipath statistics for OC2-MS2 are listed in Table 4.6. 110 300 Moving Average = 50 Moving Average= 150 RMS-DS for OC2__MS2 250 200 LOS 150 100 Delay Window 90) in (DW ns NLOS 50 0 0 100 200 300 400 500 600 700 800 900 1000 Profile Index (time) Figure 4.24. Plot of delay window (DW90) in ns vs. profile index for Stocker Parking lot corner. Table 4.6. Multipath channel statistics for OC2-MS2. Multipath Statistic LOS NLOS Parameters Mean 21.748 60.715 RMS Delay Maximum 94.143 117.80 Spread (ns) Minimum 3.615 17.983 Standard Deviation 7.306 13.981 Mean 331.25 441.08 CIR25 dB Maximum 380.00 720.00 Duration (ns) Minimum 100.00 140.00 Standard Deviation 56.080 117.41 Mean 48.48 169.66 Delay Window Maximum 120.00 300 (ns) Minimum 20.00 40.00 Standard Deviation 32.82 46.03 111 In Figure 4.25 we show a plot of tap amplitudes in dB vs. profile index for OC2- MS2 for the 1st and 2nd taps, along with moving averages with the same window sizes as used previously. Deeper fading on the 2nd tap is evident from the moving average plots. The tap amplitudes can also be divided into LOS and NLOS regions with threshold set at the 486th PDP. The deep fading of tap 2 in the LOS region is believed to be attributable to obstructions. In the NLOS region, the 2nd tap clearly fades more than the first. Since in the LOS region the 1st tap represents a direct path, and in the NLOS, it likely represents a diffracted path, the weak fading on the 1st tap is as expected. 5 0 -5 -10 Tap Index=2; OC2__MS2 -15 Tap Index=1; OC2__MS2 Moving Average= 50 Moving Average= 150 -20 Normalized Tap EnergydB in -25 -30 -35 0 100 200 300 400 500 600 700 800 900 1000 PDP index (time) Figure 4.25. Tap amplitudes in dB vs. profile index plot for Stocker Parking lot. corner. 112 The number of taps found based upon RMS-DS, after removing the PDPs with abnormally large values, was found to be seven for OC2-MS2. Each tap has a tap energy associated with it, and the tap energy is the average energy of the tap over time (over all PDPs). For OC2-MS2, the composite PDPs are segregated into LOS and NLOS PDPs and we plot cumulative tap energy vs. tap index for both regions as shown in Figure 4.26. It can be observed that the first LOS tap contains about 94% of the total energy, whereas the first tap in the NLOS section contains approximately 53% of the total energy. About 90% of the total energy was contained in the first 5 taps in the NLOS region. The probability 1 0.9 LOS;OC2-MS2 NLOS;OC2-MS2 0.8 0.7 Cumulative energy 0.6 0.5 0.4 1 2 3 4 5 6 7 Tap index Figure 4.26. LOS and NLOS cumulative energy plot for measurement conducted at Stocker Parking lot. 113 of having a tap above threshold (P(z=1)) is higher in the NLOS region than in the LOS region, and this is shown in Figure 4.27. 1 0.95 0.9 LOS;OC2-MS2 0.85 NLOS;OC2-MS2 0.8 0.75 Probabilityof having a tap 0.7 0.65 0.6 1 2 3 4 5 6 7 Tap Index Figure 4.27. Plot of Probability of having a tap vs. Tap index for LOS and NLOS regions for measurements conducted at Stocker Parking lot. Channel models developed for the Stocker Parking lot corner are shown in Tables 4.7 and 4.8 for OC2-MS1 and OC2-MS2, respectively. By noting the Weibull distribution’s shape factor (b), deeper fading was observed in the LOS region when compared to the NLOS region channel parameters in both measurement sets. We hypothesize this may be due to two-wave diffuse power fading [22]. 114 Table 4.7. Summary of channel parameters for the two region at OC2-MS1. Weibull SS TS Matrix Shape Matrix Tap Tap Factor Index Energy (b) P(z=1) P(01) P(10) Line of Sight (LOS) 1 0.7662 1.8334 1.0000 NaN 0 2 0.0544 2.3670 0.9086 0.58824 0.05952 3 0.0116 3.1496 0.77957 0.4878 0.13889 4 0.0419 2.3125 0.85484 0.66667 0.11392 5 0.0292 2.4823 0.83333 0.48387 0.097403 6 0.0220 2.7215 0.85484 0.57692 0.09434 Non Line of Sight (NLOS) 1 0.4840 2.3444 1 NaN 0 2 0.1068 2.5349 0.99475 1 0.005291 3 0.0878 2.7713 0.98163 1 0.018767 4 0.0571 2.5970 0.96063 0.8 0.032877 5 0.0600 3.0019 0.97638 0.88889 0.021563 6 0.0567 2.8383 0.94488 0.80952 0.047354 115 . Table 4.8. Summary of channel parameters for the two region at OC2-MS2 Weibull SS TS Matrix Tap Tap Shape Matrix Index Energy Factor (b) P(z=1) P(01) P(10) Line of Sight (LOS) 1 0.9391 1.3219 1.0000 NaN 0 2 0.0223 2.3262 0.78395 0.27143 0.075099 3 0.0062 2.3347 0.75000 0.48148 0.16116 4 0.0121 2.0500 0.80247 0.53125 0.13127 5 0.0074 1.9848 0.72531 0.39326 0.14957 6 0.0093 1.8527 0.76852 0.41333 0.12500 7 0.0036 1.7449 0.63272 0.36134 0.21078 Non Line of Sight (NLOS) 1 0.5349 5.0510 1.0000 NaN 0 2 0.1322 1.8688 0.9877 1.0000 0.012474 3 0.0809 3.5075 0.96721 0.8125 0.027601 4 0.0762 2.6859 0.97541 1.0000 0.025263 5 0.0713 2.7313 0.96107 0.94737 0.038462 6 0.0578 2.7575 0.94672 0.69231 0.039046 7 0.0467 3.6131 0.90574 0.69565 0.072562 116 4.6.2. West Green Corner West Green Corner was chosen to be one of the corners for measurements due to its high density of trees and buildings surrounding the corner as discussed in section 4.3. During our measurement campaign at West Green corner we collected approximately 2550 PDPs with three sets of measurements. The first two sets of measurement (OC1- MS1 and OC1-MS2) were conducted using an L-shaped trajectory for the receiver along the building corner, and the third set (OC1-MS3) was conducted by moving from the LOS to the NLOS region in a straight line perpendicular to the direct line to the transmitter. The channel parameters were analyzed from the measured PDPs as discussed in section 4.6.1 for the Stocker Parking lot corner. For this corner, we also neglected the PDPs with abnormally large delay spreads by setting a threshold RMS-DS of 100 ns for first two measurement sets OC1-MS1 and OC1-MS2, and a threshold of 150 ns for OC1- MS3. Table 4.9 shows the channel statistics for all measurements conducted at West Green corner. It can be observed that the mean and Table 4.9. Tabulated channel statistics for West Green corner. OC1-MS1 OC1-MS2 OC1-MS3 Power Delay Total Number of 714 798 1020 Profiles PDPs Minimum 7.175 4.479 7.171 RMS- Delay Maximum 94.55 96.20 149.98 Spread (ns) Mean 37.438 41.879 39.487 Standard Deviation 13.688 15.724 28.072 Number of TapsNumber of Taps 6 6 9 117 minimum RMS-DS for all the measurement sets are comparable. OC1-MS3 has higher maximum RMS-DS and hence a larger number of model taps. We plot the RMS-DS vs. profile index along with the moving average plots for all the measurement sets in Figures 4.28 to 4.30. As before, we can clearly see that the RMS- DS for all the measurement sets increases significantly as the receiver unit enters the NLOS region from LOS region, agreeing with expectations For OC1-MS2 the mean RMS-DS increases by 14.765 ns in the NLOS region from that in the LOS region. It can also be noticed from Figures 4.28 and 4.29 that the RMS-DS for OC1-MS1 and OC1- MS2 showed a slight decreasing trend in the LOS region as the receiver moved towards the NLOS region. In the NLOS regions, similar trends of increasing RMS-DS were observed for all the measurement sets. For brevity we only discuss the other channel parameters, CIRX,dB and delay window, for one of the measurement sets. The set we select to discuss is OC1- MS2. The plot of CIR25dB vs. profile index, along with the moving averages, is shown in Figure 4.31. The moving averages of 50 and 150 clearly illustrate that the trend of CIR25dB is similar to the corresponding RMS-DS plot. As the receiver unit heads into the NLOS region, the mean NLOS CIRX, dB delay increases to 391.42 ns from the mean LOS CIR delay spread of 289.66 ns. Table 4.10 shows the statistics of all these multipath channel parameters for OC1-MS2. 118 100 RMS-DS ;OC1__MS1 90 Moving Average= 50 NLOS Moving Average= 150 80 70 LOS 60 50 40 RMS-DS in ns 30 20 10 0 0 100 200 300 400 500 600 700 Profile Index (time) Figure 4.28. Plot of RMS-DS vs. profile index (time) for OC1-MS1. 100 RMS-DS ;OC1__MS2 90 Moving Average= 50 NLOS Moving Average= 150 80 70 LOS 60 50 40 RMS-DS in ns 30 20 10 0 0 100 200 300 400 500 600 700 800 Profile Index (time) Figure 4.29. Plot of RMS-DS vs. profile index (time) for OC1-MS2. 119 150 RMS-DS; OC1__MS3 Moving Average= 50 Moving Average= 150 NLOS 100 LOS RMS-DS in ns 50 0 0 100 200 300 400 500 600 700 800 900 1000 Profile Index (time) Figure 4.30. Plot of RMS-DS vs. profile index (time) for OC1-MS3. 600 CIR, 25 dB; OC1-MS2 550 Moving Average= 50 Moving Average= 150 500 450 LOS 400 350 300 CIR delay for X dB in ns 250 NLOS 200 150 100 0 100 200 300 400 500 600 700 Profile index(time) Figure 4.31. Plot of CIR25dB vs. profile index (time) for OC1-MS2. 120 Table 4.10. Multipath channel parameter statistics for OC1-MS2. Multipath Statistics LOS NLOS Parameters Mean 34.495 49.263 RMS Delay Spread Maximum 71.771 96.20 (ns) Minimum 18.408 4.479 Standard Deviation 6.8466 18.410 Mean 289.662 391.42 CIR25dB Duration Maximum 500.00 580.00 (ns) Minimum 160.00 100.00 Standard Deviation 52.778 113.018 Mean 100.70 130.573 Maximum 140.00 340 Delay Window (ns) Minimum 60.00 20.00 Standard Deviation 17.897 64.124 Figure 4.32 shows a plot of delay window (90% energy) for OC1-MS2 along with moving averages. It can be seen, as expected, that the delay window increases as the receiver enters the NLOS region. The mean delay window for the NLOS region was found to increase by 30%, to a value of 130.573 ns, compared to the mean delay window of 100.70 ns for the LOS region. In addition, the standard deviation in the NLOS region increases by a factor of three from that in the LOS region. A histogram of RMS-DS for each region is plotted in Figures 4.33 and 4.34. It can be seen that the histogram is centered on 35 ns for the LOS region and the mode is 49 ns for the NLOS region. 121 350 RMS-DS;OC1__MS2 Moving Average= 50 300 Moving Average= 150 NLOS 250 LOS 200 150 100 Delay 90) in ns (DW Window 50 0 0 100 200 300 400 500 600 700 800 Profile Index (time) Figure 4.32. Plot of delay window (DW90) in ns vs. profile index for OC2-MS1. 80 OC1__MS2; LOS 70 60 50 40 30 Number of Occurrence 20 10 0 10 20 30 40 50 60 70 80 RMS-DS in ns Figure 4.33. Histogram of RMS-DS for OC2-MS1 in LOS region. 122 55 OC1-MS2; NLOS 50 45 40 35 30 25 20 Number of Occurrence 15 10 5 0 0 10 20 30 40 50 60 70 80 90 100 RMS-DS in ns Figure 4.34. Histogram of RMS-DS for OC2-MS1 in NLOS region. The tap energies for the first and sixth taps are plotted for OC2-MS2 along with their moving averages in Figure 4.35. As expected, the first tap has a larger energy due to the strong LOS component. As the receiver enters the NLOS region, the higher indexed tap experiences deeper fading. The plots of cumulative tap energy vs. tap index for the LOS, NLOS and composite data sets are comparable, as seen in Figure 4.36. Channel models for these regions are provided in Tables 4.11-4.13. 123 5 0 -5 -10 -15 -20 Tap Index:1; OC1__MS2 Tap Index:6; OC1__MS2 Normalized Tap Energy dB in Moving Average= 50 -25 Moving Average= 100 -30 -35 0 100 200 300 400 500 600 700 800 900 PDP Index (time) Figure 4.35. Tap amplitude in dB vs. profile index for West Green Corner OC1-MS2. 1 OC1-MS2; LOS OC1-MS2; NLOS 0.95 OC1-MS2; Composite 0.9 0.85 0.8 0.75 Cumulative tapenergy 0.7 0.65 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Tap Index Figure 4.36. Cumulative tap energy vs. tap index for OC1-MS2. 124 Table 4.11. Summary of channel parameters for the two region at OC1-MS1. Weibull SS TS Matrix Shape Matrix Tap Tap Factor Index Energy (b) P(z=1) P(01) P(10) Line of Sight (LOS) 1 0.7553 2.4300 1 NaN 0 2 0.0676 2.4405 0.93055 0.72 0.05389 3 0.0471 2.7225 0.89166 0.46153 0.05625 4 0.0338 2.5548 0.92222 0.64285 0.05438 5 0.0369 1.8457 0.89444 0.5 0.05919 6 0.0148 1.9140 0.76388 0.34117 0.10583 Non Line of Sight (NLOS) 1 0.6553 3.8094 1 NaN 0 2 0.1161 3.5077 0.97222 0.6 0.01719 3 0.0428 2.5661 0.94166 0.714286 0.04437 4 0.0358 2.5921 0.91666 0.766667 0.06990 5 0.0592 2.9751 0.90277 0.542857 0.05864 6 0.0235 3.6790 0.84444 0.553571 0.10231 125 Table 4.12. Summary of channel parameters for the two region at OC1-MS2. Weibull SS TS Matrix Tap Tap Shape Matrix Index Energy Factor (b) P(z=1) P(00) P(10) Line of Sight (LOS) 1 0.6467 1.6319 1 NaN 0 2 0.1267 2.2575 0.99256 0 0.007519 3 0.0321 2.5210 0.94541 0.54545 0.026316 4 0.0763 1.6733 0.95285 0.66667 0.018229 5 0.0439 1.6904 0.94789 0.61905 0.020997 6 0.0312 1.5284 0.92308 0.64516 0.02965 Non Line of Sight (NLOS) 1 0.5752 2.5518 1 NaN 0 2 0.1246 2.5915 0.98263 0 0.017722 3 0.0700 2.8253 0.95037 0.3 0.036649 4 0.0656 3.6727 0.94045 0.58333 0.02381 5 0.0502 2.3447 0.89826 0.4878 0.058172 6 0.0284 3.6871 0.84615 0.62903 0.067647 126 Table 4.13. Summary of channel parameters for the two region at OC1-MS3. Weibull SS TS Matrix Tap Tap Shape Matrix Index Energy Factor (b) P(z=1) P(01) P(10) Line of Sight (LOS) 1 0.8101 1.7374 1 NaN 0 2 0.1247 1.1716 0.99803 1 0.00198 3 0.0121 1.4998 0.78698 0.36111 0.09799 4 0.0157 1.5003 0.84221 0.3125 0.058685 5 0.0055 1.9112 0.58185 0.16038 0.11565 6 0.0045 2.4066 0.61144 0.20305 0.12945 7 0.0056 2.6860 0.57199 0.14747 0.11073 8 0.0003 4.0044 0.2071 0.054726 0.20192 9 0.0002 3.2311 0.1716 0.042959 0.2069 Non Line of Sight (NLOS) 1 0.5553 2.3422 1 NaN 0 2 0.1011 2.1297 0.96325 0.47368 0.018109 3 0.0897 2.3320 0.96132 0.55 0.022177 4 0.0520 2.5860 0.94391 0.62069 0.036961 5 0.0316 2.2405 0.82979 0.48864 0.10047 6 0.0288 2.7665 0.8472 0.41026 0.075342 7 0.0143 2.8617 0.74662 0.31298 0.10649 8 0.0137 1.7791 0.82205 0.34783 0.075472 9 0.0138 1.6555 0.74081 0.29851 0.10209 127 CHAPTER 5: WIDEBAND INDOOR CHANNEL MEASUREMENTS 5.1. Introduction Similar to our outdoor wideband transition measurements, we also conducted some wideband measurements around indoor corners to assess the behavior of the wireless indoor channel when moving from a LOS to a NLOS region. The results reported in this chapter are similar to those for the outdoor case, hence our treatment here is more concise, and we do not provide equipment descriptions, descriptions of measurement procedures and analysis, etc. In this chapter we describe the channel environment surrounding the indoor corners and discuss the derived results and channel models. 5.2. Environment Description Indoor wideband measurements were carried out on the third floor of Stocker Engineering and Technology center at Ohio University. We carried out the measurements during the day time on a regular weekday, and hence there was human movement present. The indoor environment was also made more complicated by the presence of open doors in the corridor in which measurements were taken. Three set of measurements were taken around two corners. The transmitter was placed at the end of the hallway as seen in Figure 5.1. The corners around which the measurements were carried out were chosen such that the first corner was closer to the transmitter location than was the second corner. As in the outdoor case, we also employ a specific labeling convention. The indoor corner closest to the transmitter location was labeled corner 1 and the corner farther from the transmitter 128 location was labeled corner 2. Two sets of measurements were made at corner 2, and these are labeled IC2-MS1 and IC2-MS2, respectively, and the sole measurement made at corner 1 was labeled IC1. 5.2.1. Indoor Corner 1 The corridor between the transmitter and corner 1 can be considered a wave guide. The doors to the rooms along the corridor between the transmitter and corner 1 were closed most of the time during the measurement period. As seen in Figure 5.1, the NLOS section of corner 1 is a long corridor consisting of a path with closed doors and administrative offices whose doors remained open during regular hours of the day. It can be seen from Figure 5.1 that corner 1 is located at a 4-way juncture with one side of the corner leading to a laboratory (room number 315) whose door was closed during the measurement period. The height of the ceiling is roughly 2.26 m and the width of the hallway is about 5 feet. The distance between the transmitter and receiver at corner 1 was 25 m. The length of the path along which the Rx unit was moved from the LOS to NLOS region was about 1.5 m. A view of channel around IC1 can be seen in Figure 5.2. The receiver L-shaped trajectory can be seen in Figure 5.3. 129 Administrative offices Corner 1 Elevator Corner 2 Transmitter Laboratory Figure 5.1. Floor plan of 3rd floor Stocker Engineering Center illustrating marked positions of transmitter, corner 1, and corner 2. 130 NLOS LOS Figure 5.2. Illustration of receiver trajectory at IC2. Transmitter Location IC1 Figure 5.3. The view of indoor channel environment at IC2. 131 5.2.2. Indoor Corner 2 The environment around corner 2 is in the vicinity of several laboratories (rooms numbered 302, 303, 304) whose doors were closed during the measurement time. Apart from the 3 member receiver team conducting the measurements, there were other people moving about on the floor. An elevator is located adjacent to corner 2, whose doors would of course open when people used the elevator. This corner was located at a 3-way juncture with the NLOS region of the corner leading to another L-shaped corridor. The entire floor is carpeted, with the walls covered with wall paper. The height of the ceiling is roughly 2.42 m and the widths of the corridor in the LOS region and NLOS region were 2.4 m and 1.9 m, respectively. The separation between the transmitter and receiver at corner 2 was about 44 m, and the length of the trajectory along which the Rx unit travelled from the LOS to the NLOS region of the corner was about 1.5 m. The Figure 5.4 gives a view of channel around the IC2 and Figure 5.5 illustrates the L-shaped receiver trajectory. 132 Transmitter Location IC2 Figure 5.4. The view of indoor channel environment at IC2. NLOS LOS Figure 5.5. Illustration of receiver trajectory at IC2. 133 5.3. Measurement Procedure The measurement procedures are very similar to those discussed in chapter 4 and hence we only briefly summarize them here. During the indoor measurement campaign we mounted the sounder receiver unit on a cart as shown in Figure 5.6 in contrast to the outdoor measurements where the receiver was worn by a member of the receiver team. The transmitter team had one member, and the receiver team had 3 members. The sounder transmitter unit (consisting of sounder Tx, UPS, Tx AC power supply, and antenna) were mounted on the cart and moved to the transmitter location near one end of the corridor (Figure 5.1). The Tx unit position remained fixed for both corner 1 and corner 2 measurements. At the Tx location, the sounder Tx was powered by an AC wall socket through the UPS. The sounder Rx unit (consisting of sounder Rx, lead acid battery, laptop, and antenna) was mounted on another cart as shown in Figure 5.6, and moved to the corner. The Rx team set up the sounder Rx unit as explained in Chapter 4. The Rx team signaled the Tx team to start transmitting after setting the Rx sounder and laptop for recording PDPs. The receiver cart was then moved from the LOS to the NLOS region along the specified trajectory with a velocity of approximately 10 cm/sec. During our measurement campaign we recorded ~5500 PDPs and ~5400 PDPs at corners 1 and 2, respectively, both using a reduced delay span of 1 μs. 134 Nidhin Antenna Sounder Rx Unit Cart Figure 5.6. Receiver unit placed on cart during measurement campaign. 5.4. Indoor Corner Delay Spread Results and Analysis Background information for the results and analysis is provided in section 4.5. We discuss the channel parameters obtained from the recorded PDPs, and develop channel models for both LOS and NLOS regions based on the TDL model. The mean RMS-DS for IC2-MS1 and IC2-MS2 are comparable at 31.47 ns and 32.78 ns, respectively. For brevity, we restrict our discussion to IC2-MS1 for corner 2. The channel statistics for IC1 and IC2-MS1 are tabulated in Table 5.1. It can be noticed that the mean RMS-DS for IC1 is 12.2 ns lower than the mean RMS-DS for IC2-MS1. The standard deviation of RMS- 135 DS was also found to be lower by 6.19 ns when compared to that for IC2-MS1. The total number of taps calculated from (4.5) is comparable for both corners. Table 5.1. Delay domain channel statistics for indoor corners. IC1 IC2-MS1 Total Number of PDPs 5511 5398 Power Delay Number of sample per PDP 58 58 Profiles Delay Span (μs) 1.17 1.16 Minimum 3.0183 4.95 Maximum 446.9043 475.79 RMS- Delay Spread (ns) Mean 19.2775 31.47 Standard Deviation 13.8449 20.04 Number of Taps 24 25 As in the outdoor measurements, we also found some abnormally large delay spreads, and we similarly removed those anomalous results by setting an RMS-DS threshold of 100 ns and 140 ns for IC1 and IC2-MS2, respectively. The thresholds were set by conducting a visual inspection of the RMS-DS plots. It was found that the probability of occurrence of a PDP with delays greater than these thresholds were 0.00054 and 0.0015 for IC1 and IC2-MS1, respectively, hence removal of these PDPs does not significantly affect the delay spread statistics. Table 5.2 shows the channel statistics for IC1 and IC2-MS1 after removing the PDPs with higher RMS-DS. 136 Table 5.2. Channel statistics for indoor corners after removing PDPs with large delay spreads. IC1 IC2-MS1 Power Delay Total Number of 5511 5390 Profiles PDPs Minimum 3.0183 4.95 RMS- Delay Maximum 97.9682 138.90 Spread (ns) Mean 19.0092 31.01 Standard Deviation 10.92 15.44 Number of Taps 6 8 The The mean RMS-DS values for both corners are essentially unchanged by removal of the “outlier” PDPs. With a maximum RMS-DS of 97.968 ns and 138.90 ns for IC1 and IC2-MS1, respectively, the number of channel model taps using (4.5) reduced to 7 and 8, respectively. Plots of RMS-DS vs. profile index for IC1 and IC2-MS1 are shown in Figures 5.7 and 5.8, respectively. To track the trend of RMS-DS we plot moving averages of RMS- DS for 50 and 500 PDPs. It can be clearly observed from the moving averages of 50 and 500 PDPs in Figure 5.7 that the RMS-DS for IC1 increases consistently as the receiver unit moves from the LOS to the NLOS region around the corner. 137 100 IC1;RMS-DS 90 Moving Average: 50 Moving Average: 500 NLOS 80 70 LOS 60 50 40 RMS-DS in ns 30 20 10 0 0 1000 2000 3000 4000 5000 6000 Profile Index (time) Figure 5.7. Plot of RMS-DS vs. profile index (time) for IC1 along with moving average of 50 and 500 PDPs. The plot of RMS-DS for IC2-MS1 along with moving averages of 50 and 150 PDPs is Figure 5.8 shows a less substantial increase in RMS-DS as the receiver unit enters the NLOS region than for corner 1. Given that this corner was more distant than the first, the signal strength of multipath components in the NLOS region was generally lower than that in corner one. 138 140 RMS-DS; IC2-MS1 Moving Average= 50 500 120 Moving Average= 150 NLOS 100 LOS 80 60 RMS-DS in ns 40 20 0 0 1000 2000 3000 4000 5000 6000 Profile Index (time) Figure 5.8. Plot of RMS-DS vs. profile index (time) for IC2-MS1 along with moving average of 50 and 500 PDPs. For brevity we discuss the other channel dispersion parameters, CIRX,dB duration and delay window, only for IC1. We split the PDPs (with larger PDPs removed) measured at IC1 into two equal sets and denote the former set the LOS section and the latter set the NLOS section. Histograms of RMS-DS for the LOS and NLOS sections of IC1 are shown in Figures 5.9 and 5.10, respectively. 139 600 IC1 LOS 500 400 300 200 Number ofNumber Occurrence 100 0 0 10 20 30 40 50 60 70 80 90 100 RMS-DS in ns Figure 5.9. Histogram of RMS-DS for IC1 for LOS. 600 IC1 N-LOS 500 400 300 200 Number ofNumber Occurrence 100 0 0 10 20 30 40 50 60 70 80 90 100 RMS-DS in ns Figure 5.10. Histogram of RMS-DS IC1 for NLOS section. 140 It can be observed that the LOS mode of RMS-DS is approximately 12 ns as compared with the NLOS mode of 20 ns. Hence a clear increase in RMS-DS is evident as the Rx unit enters the NLOS section. We next plot the CIR25 dB duration along with moving averages of 50 and 500 PDPs for IC1 in Figure 5.11. It can be observed from the moving average plot of 500 PDPs that the CIR25dB duration increases for higher indexed PDPs, or in other words there is an increase in this duration as the receiver enters the NLOS region. The mean CIR25 dB duraion for the NLOS section was 254.304 ns compared to 174.17 ns for the LOS section, whereas the maximum CIR25 dB duration for the LOS and NLOS sections was found to be 460 ns and 580 ns, respectively. 600 CIR, 25 dB; IC1 Moving Average= 50 Moving Average= 500 NLOS 500 400 LOS 300 200 CIR delay for X dB in ns 100 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 ProfilePDP Profile Index (time) Figure 5.11. Plot of CIR25 dB duration vs. profile index for IC1. 141 Figure 5.12 shows a plot of delay window for IC1, and as expected the delay window containing 90% of the PDP energy increases, but only marginally. The mean delay window for the NLOS section was ~20 ns higher than in the LOS section. The maximum delay window in the NLOS section was 340 ns, in contrast with 100 ns in the LOS section. 350 RMS-DS for IC1 Moving Average= 50 300 Moving Average= 150 NLOS 250 LOS 200 150 100 Delay 90) in ns (DW Window 50 0 0 1000 2000 3000 4000 5000 Profile Index (time) Figure 5.12. Plot of delay window (DW90) vs. profile index for IC1. Table 5.3 shows the detailed delay spread statistics tabulated for the measurement set IC1’s LOS and NLOS sections. 142 Table 5.3. LOS and NLOS delay spread parameter statistics for IC1. Multipath LOS NLOS Statistics Parameters (ns) (ns) Mean 12.4755 21.3787 RMS Delay Maximum 47.0851 97.9682 Spread (ns) Minimum 4.0280 3.0183 Standard Deviation 4.3469 13.4080 Mean 174.170 254.304 CIR25 dB Maximum 460.00 580.00 Duration (ns) Minimum 80.000 60.000 Standard Deviation 46.843 125.093 Mean 29.6369 40.1380 Delay Window Maximum 100.000 340.00 (DW90) (ns) Minimum 20.000 20.000 Standard Deviation 13.1249 28.470 Tap amplitude plots for the first and fifth taps for IC1 are plotted along with their respective moving averages in Figure 5.13. As noticed from the moving average, the fifth tap experiences deeper fading in the LOS region than in the NLOS region. We hypothesize this possibly due to human movement during measurement at Corner 1. In Figure 5.14, the probability of tap existence (P(z=1)) for each tap is plotted vs. tap index for the LOS and NLOS regions of IC1. As expected, there is a higher probability of tap existence for the NLOS region than the LOS region. The cumulative energy plots for the taps in Figure 5.15 show that for both LOS and NLOS regions, the first two taps contain more than 90% of the entire energy. It can also be seen from Figure 5.15 that as expected, the cumulative tap energy for the first four taps is larger in the LOS region than in the NLOS region . 143 10 Tap Index:1; IC1 Tap Index:5; IC1 5 Moving Average= 50 Moving Average= 150 0 -5 -10 -15 -20 Normalized Tap Energy in dB -25 -30 -35 0 1000 2000 3000 4000 5000 6000 PDP Index (time) Figure 5.13. Plot of tap amplitude in dB vs. profile index (time) for IC1. 1 LOS; IC1 NLOS; IC1 0.9 0.8 0.7 0.6 0.5 0.4 Probability of having a tap a having of Probability 0.3 0.2 0.1 0 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Tap Index Figure 5.14. Plot of probability of tap existence vs. tap index for IC1. 144 1 0.98 LOS; IC1 NLOS; IC1 0.96 0.94 0.92 0.9 0.88 0.86 Cumulative tap energy 0.84 0.82 0.8 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Tap Index Figure 5.15. Plot of cumulative tap energy vs. tap index for IC1. The channel model parameters developed for both regions of IC1 are as shown in Table 5.4. As before, the table consists of Weibull distribution fits, and Markov persistence TS matrix and SS matrix parameters. 145 Table 5.4. Summary of channel parameters for the two regions at IC1. Weibull Nakagami SS TS Matrix Shape shape Matrix Tap Tap Factor Parameter Index Energy (b) (M) P(z=1) P(01) P(10) Line of Sight (LOS) 1 0.8824 1.6400 23.5636 1.000 NA 0 2 0.1006 1.8250 0.3771 0.9437 0.4583 0.0274 3 0.0113 2.5684 0.0986 0.6466 0.2102 0.1138 4 0.0052 1.9176 0.2064 0.6935 0.2474 0.1084 5 0 2.6238 0.0722 0.0766 0.0381 0.4536 6 0.0005 1.6520 0.1014 0.3557 0.1590 0.2885 Non Line of Sight (NLOS) 1 0.8012 0.5519 15.632 1.000 NA 0 2 0.1490 0.4924 0.7352 0.9800 0.5091 0.0104 3 0.0363 0.4694 0.5354 0.9442 0.3268 0.0193 4 0.0111 0.5325 0.2784 0.8014 0.1963 0.0487 5 0.0011 0.5100 0.1190 0.3462 0.0864 0.1633 6 0.0013 0.5803 0.1260 0.3921 0.1079 0.1674 146 CHAPTER 6: SUMMARY, CONCLUSION AND FUTURE WORK 6.1. Summary In this thesis we dealt with wireless channel characterization and modeling of wideband outdoor and indoor channels. We also address channel characterization for an indoor narrow band channel. The first two chapters discussed relevant literature and background information. We explained the procedure for narrowband measurements, in which we measured power levels vs. frequency for a transition from LOS to NLOS conditions. The narrow band indoor measurements employed the unlicensed ISM frequency band of 902-928 MHz, and we gathered and analyzed statistics of .received power vs. frequency and distance, and also computed power correlation bandwidths. In the wideband channel transition measurements we collected PDPs as the receiver moved around the corners from LOS to NLOS regions. The channel dispersion characteristics were described using RMS-DS, delay window and CIR X,dB durations. We also separated the measured PDPs into LOS and NLOS regions, and analyzed channel statistics for each region. Channel models were developed for a 50 MHz channel bandwidth, and these specify fading amplitude distributions as well as tap persistence processes for modeling the appearance and disappearance of multipath components. 6.2. Conclusions The primary aim of this thesis was to characterize and model the multipath delay dispersion trends for a channel transition from LOS to NLOS. Our literature review revealed that although significant work has been conducted to characterize wireless 147 channels in multiple types of environments in various frequency bands, no authors have attempted to characterize wideband channel transitions from LOS to NLOS regions. For the narrow band measurements, the received signal strength was larger in the LOS region than in the NLOS region, as expected, due to the strong LOS component. From measurements of received power vs. frequency, some flat amplitude fading was observed for bandwidths on the order of a few MHz. The power correlation bandwidths were comparable for the LOS and NLOS region and power correlation values of 0.5 were observed for bandwidths of approximately 7 MHz. Cumulative distribution functions of received power vs. frequency show that fading was not as severe as Rayleigh for either the LOS or NLOS regions. For the wideband outdoor channel measurements, corner OC1 experienced comparable fading in the LOS and NLOS regions, whereas multipath delay dispersion in the NLOS region was larger than in the LOS region, as expected. The LOS taps also generally persist longer than the NLOS taps. In contrast, the LOS region in OC2 experienced deeper fading than in the NLOS region, even though the NLOS delay dispersion was still larger than in the LOS region. The RMS-DS for IC1 clearly showed an increase in delay spread as the receiver entered the NLOS region. Deeper fading was observed in the LOS region for higher indexed taps. As expected, the multipath delay dispersion statistics in NLOS region were higher than compared to that of LOS region. The mean RMS-DS in NLOS region was found to be approximately 9 ns higher than the delay in LOS region. In the case of IC2, 148 the delay spread increases as the channel makes a transition from LOS region to NLOS region. The mean RMS-DS in NLOS region is slightly higher than in LOS region. We conclude from the analysis of wideband channel characteristics that the delay spread parameters (RMS-DS, delay window and CIRX,dB duration) increase as the receiver transits into the NLOS region from the LOS region. Although we can quantify the increase in dispersion between these regions, e.g., with a linear or other polynomial fit, results would likely pertain only to our specific environments. For these environments, we have quantified the delay dispersion values. 6.3. Future Work Future work could involve measuring and gathering more data from various other building corners involving different sizes and structures so as to validate our results, and possibly enable a polynomial fit to model delay dispersion trends. We could also gather more data in these environments in the presence of human and vehicular movements. This would make the model more practical, but would also likely complicate it. Our work involved transitions from a LOS to NLOS region along corners in an L-shaped trajectory, but further measurements could be carried out to investigate other types of transitions, e.g., from LOS to partially obstructed regions. It would also be interesting to characterize the wireless channel transitions as the receiver transits from an outdoor to an indoor environment and vice-versa. Measurement analysis for OC2 found that the LOS region experienced deeper fading than the NLOS region and our hypothesis for this result is the two-wave diffuse power model of [22]. Further work could be done to validate this hypothesis by 149 comparing PDF’s of measured data at OC2 with those obtained analytically using the two-wave diffuse power PDFs. This work would be the first of its kind that provides empirical justification for the PDFs developed in [22]. 150 REFERENCES [1] B. Sklar, Digital Communications Fundamentals and Applications, 2nd ed., Upper Saddle River, New Jersey, Prentice-Hall, 1995. [2] T. S. Rappaport, Wireless Communications: Principles & Practice, 2nd ed., Upper Saddle River, New Jersey, Prentice Hall, 2005. [3] G.L. Stuber, “Propagation Modeling”, in Principles of Mobile Communications, 2nd ed., Springer, Norwell, MA, 2001. [4] J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., John Wiley & Sons, New York, NY, 2000. [5] R.L. Perterson, R.E. Zeimer, D.E. Borth, “Introduction to Spread Spectrum Communications”, Upper Saddle River, New Jersey, Prentice-Hall,1995. [6] J.G. Proakis, “Digital Communication”, 4th ed., McGraw Hill, New York, NY, 2000 [7] E. S. Sousa, V. M. Jovanovic, C. Daigneault, “Delay Spread Measurements for the Digital Cellular Channel in Toronto,” IEEE Trans. Veh. Tech., vol. 43, no. 4, pp. 837-847, Nov. 1994. [8] D.C. Cox, “Delay Doppler characterization of multipath propagation at 910 MHz in a suburban radio environment,” IEEE Trans. Antennas Propagat., vol. 20, no. 5, pp. 625–635, Sep. 1972. [9] S. Stein, “Fading Channel Issues in System Engineering,” IEEE Journal on Selected Areas in Comm., vol. SAC-5, no. 2, February 1987. 151 [10] D.L. Neilson, “Microwave propagation measurements for mobile digital radio applications,” in Proc. EASCON 77, paper 14-2. [11] D. W. Matolak, "Wireless Channel Characterization in the 5 GHz Microwave Landing System Extension Band for Airport Surface Areas," NASA ACAST Final Project Report, Grant no. NNC04GB45G, May 2006. [12] D. W. Matolak, “ACAST 5 GHZ Wireless Channel Characterization: Test Plan,” Version 3, May 2005. [13] D.W. Matolak. (2008, May). Chanel Modeling for Vehicle-to-Vehicle Communications. IEEE Communications Mag. pp. 76-83. [14] D.W. Matolak and A. Chandrasekaran, “Aircraft Intra-Vehicular Channel characterization in the 5 GHz Band”, May 2008, ICNS Conference 2008. [15] T.Wysocki, H.-J.Zepernick: “Characterisation of the Indoor Radio Propagation Channel at 2.4 GHz,” Journal of Telecommunications and Information Technology, No. 3-4, vol. 1, pp.84-90, 2000. [16] M.Carroll, T.A.Wysocki: “Characterization of Indoor wireless Channel at 5 GHz U-NII Bands,” Elsevier Computers and Electrical Engineering Journal, vol.30, pp.331-345, 2004 [17] Y. Zhao, J. Gaeddert, K. K. Bae, J. H. Reed, “Radio Enviromnent Map Enabled Situation-Aware Cognitive Radio Learning Algorithms,” Proc. Software Defined Radio Tech.Conf., 2006. [18] P. Bello, “Characterization of Random Time-Variant Linear Channels,” IEEE Trans. Comm., vol. 11, pp. 360-393, December 1963. 152 [19] Tapan K. Sarkar, Zhong Ji, Kyungjung Kim, Abdellatif Medouri and Magdalena Salazar-Palma, "A Survey of various propagation models for mobile communication", IEEE Antennas and Propagation Mag., Vol. 45, No. 3, pp. 51- 82, Jun., 2003. [20] J. Frolik, “A case for considering Hyper-Rayleigh fading channels,” IEEE Trans. Wireless Comm., vol. 6, no. 4, April 2007. [21] ITU-R Rec. P. 1407-1, ”Multipath propagation and parameterization of its characteristics”, 1999-2003. [22] G. D. Durgin, T. S. Rappaport, D. A. de Wolf, “New Analytical Models and Probability Density Functions for Fading in Wireless Communications,” IEEE Trans. Comm., vol. 50, no. 6, pp. 1005 – 1015, June 2002. [23] D.W. Matolak, S. Rajendar and Q. Zhang, “Modeling Wireless Channel Delay Spread Trends” to appear in IEEE Radio Wireless Symposium 2009, San Diego, CA. [24] J. Vig, “ISM Band indoor wireless channel amplitude characteristics: path loss vs. distance and amplitude vs. frequency,” M.S. thesis, Ohio University, Athens, Ohio, U.S., Jun. 2004. [25] P. Sundaram, “New Results for characterization of Indoor Channels in two ISM bands,” M.S. thesis, Ohio University, Athens, Ohio, U.S., Nov.2005. [26] I. Sen, “5 GHz Channel Characterization for airport surface areas and vehicle – vehicle communication systems,” Ph.D. dissertation, School of EECS, Ohio University, July 2007. 153 [27] Pai, Guruprasad, 5 GHz Wirelss Channel Characteristics on The Ohio University Campus, Master of Science (MS), Ohio University, Athens, Ohio, U.S, Nov.,2007. [28] CDMA developer group, website: http://www.cdg.org/technology/2g.asp, December 2008. [29] UMTS World, website: http://www.umtsworld.com, December 2008. [30] GSM World, website http://www.gsmworld.com/technology/3gsm/index.htm, December 2008. [31] International Telecommunication Union, website: http://www.itu.int/osg/spu/newslog/India+Publishes+New+Stats+On+Mobile+Gr owth.aspx, December 2008. [32] International Telecommunication Union, website: http://www.itu.int/newsroom/press_releases/2008/29.html, December 2008. [33] 3rd Generation Partnership Project (3GPP), website: http://www.3gpp.org/article/w-cdma, December 2008. [34] About.com, website: http://compnetworking.about.com/cs/wireless80211/a/aa80211standard.htm, December 2008. [35] VOCAL Technologies, Ltd., website http://www.vocal.com/data_sheets/802.11a_fre.html, November 2008. [36] Ohio University Information Technology website http://technology.ohio.edu/wireless/faq.html#2, November 2008. 154 [37] The Future Generations of Mobile Communications Based on Broadband Access Technologies, Shingo Ohmori, Yasushi Yamao and Nobuo Nakajima, Dec 2000, IEEE Communications. [38] Website of Duke University, http://dukemil.egr.duke.edu/Ultrasound/k- space/node5.html, December 2008. [39] Berkeley Varitronics, Inc., website, http://www.bvsystems.com/, April 2008. 155 APPENDIX A: MATLAB CODE FOR NARROWBAND MEASUREMENTS Routine to calculate and plot the CDF of Received Power versus. Frequency and Distance. % ROUTINE TO CALCULATE CDF OF RECEIVED POWER V/S FREQUENCY OR DISTACE) clear all; clc; z=1; j=1; t=0.06 clc; M1=corner1(1); Power_dB=M1; Power_W= 10.^(Power_dB/10); zz=[1,5,9,13,17,21,25]; z=zz(1); k=z; Power_W_location= Power_W(k,1:27); Power_mean= mean(Power_W_location) %Normalize mean norm= 1/Power_mean; Power_norm_W= Power_W_location.*norm; % Compute CDF for i=min(Power_norm_W):t:max(Power_norm_W) cdf(j)=(length(find(Power_norm_W<=i)))/length(Power_norm_W); j=j+1; end; x=min(Power_norm_W):t:max(Power_norm_W); x_dB= 10.*log10(x); semilogy(x_dB,cdf,'ko-','LineWidth',1.5,'MarkerSize',3) hold on; x=0;j=1;Power_norm_W=0;norm=0;x_dB=0;cdf=0 k=z+1; Power_W_location= Power_W(k,1:27); Power_mean= mean(Power_W_location) % Normalize mean norm= 1/Power_mean; Power_norm_W= Power_W_location.*norm; %Compute CDF for i=min(Power_norm_W):t:max(Power_norm_W) cdf(j)=(length(find(Power_norm_W<=i)))/length(Power_norm_W); 156 j=j+1; end; x=min(Power_norm_W):t:max(Power_norm_W); x_dB= 10.*log10(x); semilogy(x_dB,cdf,'b-','LineWidth',1.5,'MarkerSize',3); hold on; x=0;j=1;Power_norm_W=0;norm=0;x_dB=0;cdf=0 k=z+2; Power_W_location= Power_W(k,1:27); Power_mean= mean(Power_W_location) %Normalize mean norm= 1/Power_mean; Power_norm_W= Power_W_location.*norm; %Compute CDF for i=min(Power_norm_W):t:max(Power_norm_W) cdf(j)=(length(find(Power_norm_W<=i)))/length(Power_norm_W); j=j+1; end; x=min(Power_norm_W):t:max(Power_norm_W); x_dB= 10.*log10(x); semilogy(x_dB,cdf,'g<:','LineWidth',2,'MarkerSize',4); hold on; x=0;j=1;Power_norm_W=0;norm=0;x_dB=0;cdf=0; k=z+3; Power_W_location= Power_W(k,1:27); Power_mean= mean(Power_W_location) %Normalize mean norm= 1/Power_mean; Power_norm_W= Power_W_location.*norm; %Compute CDF for i=min(Power_norm_W):t:max(Power_norm_W) cdf(j)=(length(find(Power_norm_W<=i)))/length(Power_norm_W); j=j+1; end; x=min(Power_norm_W):t:max(Power_norm_W); x_dB= 10.*log10(x); semilogy(x_dB,cdf,'cv--','LineWidth',2,'MarkerSize',4); hold on; x=0;j=1;Power_norm_W=0;norm=0;x_dB=0;cdf=0 157 %PLOT OF RAYLEIGH CDF a=0:.01:3; F=1-exp(-a); A=10*log10(a); semilogy(A,F,'r-.','LineWidth',2,'MarkerSize',3) grid on; legend('LOCATION 0 ','LOCATION 1','LOCATION 2','LOCATION 3','Chi Square CDF'); xlabel('Relative Power in dB'); ylabel('Cumulative Density Function'); xlim([-10 5]) ylim([0.01 1]) Routine to develop Power Correlation Bandwidth for LOS and NLOS regions %TO PLOT POWER CORRELATION BANDWIDTH V/S DELTA F %same as matlab's xcorr function using biased option clc; clear; Power_corr=0; N= 27; %bandwidth sum=0; Power_corr_avg=0;Power_corr_avg_NLOS=0 M1=corner2(1); %Corner 1 is a function consisting of all datas of 1st corner %For LOS for z=1:1:14 M1_902= M1(z,1:27); for delta_f=0:26 %In MHz for i=1:(27-delta_f) H1= M1_902(i); H2= M1_902(i+delta_f); sum=sum+(H1*H2); end; Power_corr_location(delta_f+1)=sum/N; sum=0; end; Power_corr_avg=Power_corr_avg+Power_corr_location; Power_corr_location=0; end; Power_corr_avg=Power_corr_avg/14; %To find the average power correlation;14 is the Number of LOS points %NORMALIZATION 158 Norm_factor= 1/max(Power_corr_avg); Power_corr_avg_normalized= Power_corr_avg*Norm_factor; Power_corr_avg_normalized=[Power_corr_avg_normalized(27:-1:2) Power_corr_avg_normalized] %Power_corr_avg=[Power_corr_avg(27:-1:2) Power_corr_avg] delta_f= -26:1:26; plot(delta_f,Power_corr_avg_normalized,'r--') hold on grid on %For N-LOS sum=0; for z=15:1:25 data= M1(z,1:27); for delta_f=0:26 %In MHz for i=1:(27-delta_f) H1= data(i); H2= data(i+delta_f); sum=sum+(H1*H2); end; Power_corr_location(delta_f+1)=sum/N; sum=0; end; Power_corr_avg_NLOS=Power_corr_avg_NLOS+Power_corr_location; Power_corr_location=0; end; Power_corr_avg_NLOS=Power_corr_avg_NLOS/11; %11 is the number of NLOS points %NORMALIZATION Norm_factor1= 1/max(Power_corr_avg_NLOS); Power_corr_avg_normalized_NLOS= Power_corr_avg_NLOS*Norm_factor1; Power_corr_avg_normalized_NLOS=[Power_corr_avg_normalized_NLOS(27:-1:2) Power_corr_avg_normalized_NLOS] %Power_corr_avg_NLOS=[Power_corr_avg_NLOS(27:-1:2) Power_corr_avg_NLOS] delta_f= -26:1:26; plot(delta_f,Power_corr_avg_normalized_NLOS) legend('LOS','N-LOS') title('POWER CORRELATION BANDWIDTH V/S DELTA F') ylabel('NORMALIZED POWER CORRELATION') xlabel('Delta F in MHz') 159 Routine to generate CIR X, dB % To plot the CIR_X dB clear x_150; clear x_50; clear MV_50; clear MV_150; clear A; A=RMSDelSpr; XdB = 25 % In dB for i=1:length(PowerdBMN); PDP=PowerdBMN(i,:); temp=find(PDP>(max(PDP)-XdB)); CIR_X_Tap_Index=temp(length(temp)); Delay_CIR_X(i)= Del(CIR_X_Tap_Index)*(10^9); clear PDP;clear temp;clear CIR_X_Tap_Index; end; %plot(Delay_CIR_X); A=Delay_CIR_X(find(Delay_CIR_X<600)); figure;plot(A);xlabel('Profile index(time)');ylabel('CIR delay for X dB in ns') hold on; %Moving Average for j=1:(length(A)-50) MV_50(j)= mean(A(j:j+49)); end; for j=1:(length(A)-150) MV_150(j)= mean(A(j:j+149)); end; x_50=51:length(A); x_150=151:length(A); plot(x_50,MV_50,'r--','LineWidth',2);hold on;plot(x_150,MV_150,'k--','Linewidth',3) grid on; legend('X= 25 dB', 'Moving Average= 50', 'Moving Average= 150'); xlim([0 length(A)]) 160 Routine to generate moving average %Moving Average clc clear MV_50; clear MV_150 for j=1:(length(A)-50) MV_50(j)= mean(A(j:j+49)); end; for j=1:(length(A)-150) MV_150(j)= mean(A(j:j+149)); end; x_50=51:length(A); x_150=151:length(A);hold on; plot(x_50,MV_50,'r--','LineWidth',2);hold on;plot(x_150,MV_150,'k--','Linewidth',3) grid on; legend('RMS-DS for OC1__MS2', 'Moving Average= 50', 'Moving Average= 150'); %xlim([0 5150]) Routine to plot tap amplitude % To plot Tap Amplitudes along with moving average clc; for i=1:6 A1= DempSqrdB(i,:); figure;plot(A1);ylim([-47 5]); hold on; %Moving Average Calculations for j=1:(length(A1)-50) MV_50(j)= mean(A1(j:j+49)); end; for j=1:(length(A1)-150) MV_150(j)= mean(A1(j:j+149)); end; x_50=51:length(A1); x_150=151:length(A1); plot(x_50,MV_50,'r--','LineWidth',2.5); plot(x_150,MV_150,'k','LineWidth',3) 161 grid on; legend('Tap Index: ', 'Moving Average= 50', 'Moving Average= 150'); xlim([0 length(A1)]); ylabel('Tap amplitude in dB');xlabel('Profile index (time)') end; Tap1= DempSqr(1,:); Tap2= DempSqr(2,:); Tap3= DempSqr(3,:); Tap4= DempSqr(4,:); Tap5= DempSqr(5,:); Tap6= DempSqr(6,:);