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Radio Wave Diffraction and Scattering Models for Wireless Channel Simulation

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Radio Wave Diffraction and Scattering Models for Wireless Channel Simulation Radio Wave Diffraction and Scattering Models For Wireless Channel Simulation by Mark D. Casciato A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Electrical Engineering) in The University of Michigan 2001 Doctoral Committee: Associate Professor Kamal Sarabandi, Chair Associate Professor Brian Gilchrist Professor Linda P.B. Katehi Professor Thomas B.A. Senior Professor Wayne E. Stark c Mark D. Casciato 2001 All Rights Reserved ACKNOWLEDGEMENTS First I would like to acknowledge my parents, Rose and Dan Casciato for their support throughout these last 5 years, without which attending graduate school would have been much more difficult. I would also like to acknowledge all of my committee members, but most especially my thesis advisor, Professor Kamal Sarabandi for his guidance and mentorship, both academically and personally. I would also like to thank Professor Thomas Senior for the interesting and enlightening discussions on diffraction theory. The students and colleagues at the University of Michigan Radiation Laboratory, where to begin. I would like to thank and acknowledge all of the students, faculty, and staff for your help and support over my stay here at Michigan, I consider all of you good friends. I would most especially like to thank my very close friends here, St´ephane Legault, Lee Harle, J.D. Shumpert, Dejan Filipovich, Olgica Milenkovic, Leland Pierce, Katherine Herrick, Mark Fischman, Dan Lawrence, Sergio Pacheco, Dimitris Peroulis, Ron Reano, Helena Chan, Mohamed Abdelmoneum, and of course Bettina K¨othner for all the good company. I apologize in advance for anyone that I may have missed. Finally I would like to thank the Army Research Office for their support, without which this project would not have been possible (contract DAAH04-96-1-037). ii TABLE OF CONTENTS ACKNOWLEDGEMENTS .............................. ii LIST OF TABLES ................................... v LIST OF FIGURES .................................. vi LIST OF APPENDICES ............................... xii CHAPTER 1 Introduction . ................................ 1 1.1Motivation.............................. 2 1.2 Research Approach . ..................... 3 1.2.1 Methodology . ..................... 4 1.2.2 Initial Concentration . .............. 4 1.3 Relevant Assumptions & Definitions . .............. 6 1.4 Chapter Outline & Introduction . .............. 7 2 Fields of an Infinitesimal Dipole Above an Impedance Surface: Effect of theHomogeneousSurface.......................... 10 2.1 Introduction: The Sommerfeld Problem .............. 12 2.2ExactImageFormulation...................... 16 2.2.1 Transforms & Identities . .............. 18 2.2.2 VerticalElectricDipole................... 21 2.2.3 HorizontalElectricDipole................. 22 2.3Analysis&Results:ExactImageTheory.............. 28 2.4ChapterSummary:ExactImageTheory.............. 39 3 Fields of an Infinitesimal Dipole Above an Impedance Surface: Effect of an Impedance Transition . ..................... 41 3.1 Introduction: Impedance Transition . .............. 42 3.2PlaneWaveExcitation........................ 44 3.2.1 IntegralEquationFormulation............... 44 3.2.2 Iterative Solution . ..................... 48 3.2.3 Scattered Field Expressions: Plane Wave . ....... 51 iii 3.2.4 SaddlePointEvaluation:PlaneWaveIntegral....... 52 3.3ShortDipoleExcitation....................... 53 3.3.1 StationaryPhaseEvaluation:ShortDipole......... 54 3.3.2 Near-fieldObservation................... 57 3.3.3 Error Bound . ..................... 58 3.4Validation&Results:PerturbationTechnique........... 59 3.4.1 PlaneWaveExcitation................... 60 3.4.2 DipoleExcitation:Land/SeaInterface........... 66 3.5 Chapter Summary: Impedance Transition .............. 75 4 Diffraction from Convex Surfaces: Right Circular Cylinders . ....... 80 4.1 Introduction: Diffraction from Convex Surfaces . ....... 82 4.2 Development of Macromodel . .............. 86 4.2.1 FockTheory......................... 88 4.2.2 2-DCase,NormalIncidence................ 90 4.2.3 ObliqueIncidence...................... 97 4.3Validation:PECCylinder......................100 4.3.1 Direct Evaluation of Fock Type Integrals . .......103 4.4 Application of Macromodel .....................105 4.5OtherApplications.........................106 4.6 Chapter Summary: Diffraction from Right Circular Cylinders . 107 5 Diffraction from Convex Surfaces . .....................114 5.1 Introduction . ............................115 5.2 Induced Surface Currents: General Convex Surface . .......116 5.3 Results: Diffraction from Convex Surfaces . .......118 5.3.1 Ellipse............................118 5.3.2 Knife-edge (Kirchhoff) Diffraction . .......129 5.4 Chapter Summary: Diffraction from Convex Surfaces .......133 6 Summary&FutureWork..........................134 6.1 Summary: Scattering & Diffraction from Impedance Surfaces . 135 6.1.1 Fields of a Small Dipole Above an Impedance Surface . 136 6.1.2 Scattering from an Impedance Transition . .......136 6.2 Summary: Diffraction from Convex Surfaces . .......138 6.3FutureWork.............................139 6.3.1 Future Work: Fields of a Dipole Above an Impedance Sur- face.............................140 6.3.2 Future Work: Diffraction From Convex Surfaces . 141 APPENDICES .....................................142 BIBLIOGRAPHY ...................................151 iv LIST OF TABLES Table 3 = 1.1 Soil parameters for San Antonio gray loam with a density of 1:4 g cm ,for varying gravimetric moisture content at 30MHz (from Hipp [1]). 7 2.1 Speed-up in computation time of exact image calculation over Sommerfeld type integrals for normalized surface impedance of 0.3-i0.1, eleven data ! φ = points from D = 10 10010m, 0 and varying source/observation heights. 36 2.2 Speed-up in computation time of exact image calculation over Sommerfeld type integrals for varying complex impedance, η. Source and receiver are 2m above surface for all cases. Eleven data points are calculated from ! φ = D = 10 10010m, 0........................... 36 4.1 Optimized parameters for Sigmoidal transition functions . ....... 95 4.2 Speed-up, Macromodel to Fock Integrals . ..............104 v LIST OF FIGURES Figure 1.1 Flowchart - Physics-based Methodology . .............. 5 1.2 Rural Terrain Scenario ............................ 5 2.1Problemgeometry,dipoleaboveanimpedanceplane............ 16 2.2 Exact image in z-plane............................ 22 2.3 x-component of total electric fields (diffracted only for this case) for a ver- tical (ˆz) electric dipole, exact image (———–) compared with Sommer- = = = feld (¥¥¥¥¥). Dipole is located at x0 y0 0, z0 2m and operating at = φ = 30 MHz. Observation is at z = 2m, D 10 10010m, along the 0(x η : : axis). Normalized Surface impedance value is = 0 3 i0 1......... 30 ÆÆÆÆÆ 2.4 z-component of diffracted (exact image ( ¥¥¥¥¥) and Sommerfeld ( )) and total electric fields (exact image (———–) and Sommerfeld ( )) = = for a vertical (ˆz) electric dipole. Dipole is located at x0 = y0 0, z0 2m = and operating at 30 MHz. Observation is at z = 2m, D 10 10010m, φ η = along the = 0(x axis). Normalized Surface impedance value is : 0 :3 i0 1.................................... 31 2.5 y-component of total electric fields for a horizontal (ˆy) electric dipole, exact image (———–) compared with Sommerfeld ( ). Dipole is = = located at x0 = y0 0, z0 2m and operating at 30 MHz. Observation is = φ = at z = 2m, D 10 10010m, along the 0(x axis). Normalized Surface η : : impedance value is = 0 3 i0 1....................... 33 2.6 Time (in seconds) to calculate all electric field components, at each obser- vation point, for a vertical (ˆz) electric dipole, exact image (———–) and = = = Sommerfeld ( ). Dipole is located at x0 y0 0, z0 2m and = operating at 30 MHz. Observation is at z = 2m, D 10 10010m, along φ η = : : the = 0(x axis). Normalized Surface impedance value is 0 3 i0 1. 34 2.7 Time (in seconds) to calculate all electric field components, at each obser- vation point, for a horizontal (ˆy) electric dipole, exact image (———–) and = = = Sommerfeld ( ). Dipole is located at x0 y0 0, z0 2m and = operating at 30 MHz. Observation is at z = 2m, D 10 10010m, along φ η = : : the = 0(x axis). Normalized Surface impedance value is 0 3 i0 1. 35 vi 2.8 Effect of varying soil moisture on z-component of total electric fields for a vertical (ˆz) dipole located at the origin, 2m above an impedance sur- = ; = face, (x0 = y0 0 z0 2m) and operating at 30 MHz. Observation is also 2m above the surface and extends radially from the source along the φ = = 0(x axis) from D 10 10010m. Results are for soil moisture of 0% η : η = : : ¥¥¥¥¥ η = : : ( = 0 53, (———–)), 2.5% ( 0 38 i0 09, ( )), 5% ( 0 3 i0 1, η = : : ÆÆÆÆÆ η = : : ( )), 10% ( 0 15 i0 09, ( )) and 20% ( 0 12 i0 07, (¡ ¡ ¡ ¡))................................. 37 2.9 Comparison of the magnitude of the frequency response of the direct field (———–) to total field ( ), for a vertical (ˆz) dipole located at the = ; = : origin, 2.0m above the impedance surface (x0 = y0 0 z0 2 0m) with real ε ¼ 2 : σ = ¢ permittivity r = 22 0, conductivity 8 10 . Frequency sweep is from 30 to 130 MHz in steps of 142.86 KHz. Observation is also 2.0m above the φ = surface along the = 0(x axis) and 300m from the source (D 300m). 38 2.10 Comparison of the phase of the frequency response of the direct field (—— —–) to total field ( ) (in radians), for a vertical (ˆz) dipole located at = ; = : the origin, 2.0m above the impedance surface (x0 = y0 0 z0 2 0m) with ε ¼ 2 : σ
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