IMPERIAL COLLEGE OF SCIENCE AND TECHNOLOGY (UNIVERSITY OF LONDON) DEPARTMENT OF ELECTRICAL ENGINEERING. The Propagation of Millimetric Radio Waves through the Clear Atmosphere. by Michael Raymond Inggs A Thesis Submitted for the Degree of Doctor of Philosophy in the Faculty of Engineering, University of London. July, 1979. ABS TRRCT. Millimetre—wave propagation through a tenuous, random medium is investigated by means of practical observations and a computer simulation. The measurements obtained are in agreement with a theory of propagation based on the degradation of coherence of the propagating wave. The practical measurements were taken on a 12 km link operating at 38 GHz. The receiver was designed as a variable spacing interferometer, allowing measurements of the spatial structure of the phase and amplitude of the perturbed wavefront. These fluctuations proved to be small and a great deal of care was required in the design and implementation of the experiment. The important aspects of this equipment are discussed in detail. A large amount of data is produced by this type of investigation, ani.-an efficient data analysis system was devised. This involved a. purpose—built, multi—channel device, as well as micro— and minicomp- uters. The impact of microprocessor technology on data. collection, experimental control and other aspects of laboratory work is assessed in the light of practical experience with a number of systems. The computer simulation is based on Fejer's. slab model of propagation. The field over successive planes is obtained by..a numerical implementa- tion of Fresnel diffraction. At each plane the field is perturbed by computer—generated psuedo—random numbers, correlated using a novel technique. This phase screen represents the effect of the irregular- ities of the previous slab. This simulation is fully multiple scatter and can deal simply with anisotropic irregularities. The results are presented graphically as plots of the phase and amplitude of the field over successive planes. The degradation of the field coherence is clearly visible. This simU- lation technique shows great promise, and is directly applicable to related fields such as sound propagation in the atmosphere or ocean. CONTENTS.. ABSTRACT 1 CONTENTS 2 ACKNOWLEDGEMENTS 10 INTRODUCTION 12 Appendix I1 Current Earth/Satellite Millimetre—wave Propagation Experiments 21 REFERENCES FOR INTRODUCTION 22 CHAPTER ONE THEORETICAL ASPECTS OF RANDOM PROPAGATION 24 1.1 General Definitions 25 1.1.1 Coordinate Systems 25 1.1.2 Vector Functions 25 113 Maxwell's Equations 25 1.1.4 The Wave Equation 26 1.1.5 Duality 26 1.2 Solutions of the Wave Equation 27 1.2.1 Infinite Plane Wave 27 1.2.2 The Magnetic Field 27 1.2.3 A More General Solution 28 1.2.4 Determining the Angular Spectrum 28 1.2.5 The Far Field 29 1.2.6 Transverse Electromagnetic Fields 30 1.2.7 Polarization 30 1.2.8 The Poynting Vector 31 1.2.9 The Intensity 31 1.2.10 Standard Defintions of Aperture Antenna 32 Performance 1.2.11 Coupling between Antennas and Plane Waves 33 1.2.12 Directive Gain 35 3 1.2.13 Effective Area of an Antenna 36 1.2.14 Power Gain 36 1.2.15 Coupling between Two Antennas 36 1.3 A Slab Model of Propagation 38 1.3.1 The Model 38 1.3.2 A Single Refractive Inhomogeneity 39 1.3.3 The Equivalent Statistics of a Slab 41 1.4 A Random Phase Screen 43 1.4.1 The Average Angular Spectrum 44 1.5 Coherence Theory 46 1.5.1 Mathematical Formulation 47 1.5.2 The Lateral Coherence Function for a 48 Random Phase Screen 1.5.3 The Coherence Function for Multi—slab 50 Propagation 1.6 Coupling between Antennas Immersed in Random Media 52 1.7 Statistics of the Fluctuations 54 APPENDICES FOR CHAPTER ONE 57 A1.1 Coordinate Systems 57 A1.2 Definitions of Antenna Performance 58 A1.3 Antenna/Plane Wave Coupling 60. A1.4 The Effective Area of an Antenna 63 A1.5 Coupling between Antennas 64 A1.6 The Gaussian Antenna 66 A1.7 The Characteristic Function 71 A1.8 - The-van Cittert—Zernike Theorem 72 A1.9 Equivalent Planar Statistics of a Slab 74 A1.10 A Solution for Many Slabs 76 A1.11 The Equivalence of the Fejer and Bramley models 77 REFERENCES FOR CHAPTER ONE 78 4 CHAPTER TWO THE PHYSICS OF THE LOWER TROPOSPHERE 80 2.1 The Radio Refractive Index Refractivity 81 2.2 Statistical Description of the Random Refractivity 82 2.2.1 Basic Definitions 83 2.2.2 Stationarity 85 2.2.3 Structure Functions 85 2.2.4 Refractivity Wavenumber Spectrum 87 2.2.5 Forms of the Autocovariance Function 87 2.3 Elements of Turbulent Flow 89 2.3.1 Spectral Decomposition and Taylor's 89 Hypothesis 2.4 Turbulence in the Lower Troposphere 92 2.4.1 Energy Sources 93 2.4.2 Static Stability 93 2.4.3 Mixing Processes 94 2.4.4 Wind Shear as a Mixing Process 96 2.4.5 Surface Roughness as a Mixing. Process 96 2.4.6 Convective Mixing 99 2.5 Refractivity Measurements 101 2.5.1 The General Situation 102 2.5.2 Surface Values of Refractivity 104 Fluctuations 2.5.3 Refractivity Fluctuations in an 104 Urban Environment 2.5.4 Spectra when the Scale Sizes have a 110 Distribution 2.5.5 Stationarity of the Refractivity 111 Fluctuations 112 2.6 Conclusions 5 APPENDICES FOR CHAPTER TWO 115 A2.1 Other Processes Affecting Millimetre—waves 115 A2.1.1 Rainfall 115 A2.1.2 Fog 117 A2.1.3 Snow 118 A2.1.4 Attenuation by Atmospheric Gases 118 and Vapours A2.1.5 Multipath Propagation 120 REFERENCES FOR CHAPTER TWO 122 CHAPTER THREE AN EXPERIMENTAL 38 GHZ LINK IN AN 125 URBAN ENVIRONMENT 3.1 Description of the Path and Planning 125 3.2 Transmitter and Receiver Design 125 3.3 Receiver Performance 135 3.3.1 Determination of the Detector Power Law 135 3.3.2 Short Term Amplitude Stability 13B 3.3.3 Phase Difference Measurements 138 3.3.4 Receiver Mounting Arrangements 141 3.4 Installation and Preliminary Results 141 3.4.1 Pre—installation Calibrations 142 3.4.2 Installation of Link. 142 3.4.3 Early Results 148 3.4.4 Transmitter Antenna Wind Loading 149 3•5 Environmental Sensors and Data Recording System 149 3.5.1 Synoptic Recording System 149 3.5.2 Environmental Sensors 151 3.6 Analysis of Synoptic Data 152 3.7 The Self Oscillating Mixer 153 3.7.1 Waveguide Oscillators 155 3.7.2 The Self Oscillating Mixer 155 6 3.8 Propagation Experiment Equipment: Some Suggestions 158 APPENDICES FOR CHAPTER THREE 162 A3.1 The Receiver 162 A3.2 Automatic Frequency Control: an Analysis 171 A3.3 Crystal Palace Transmitter 179 A3.4 Local Oscillator 186 A3.5 The Influence of the Transmitter Antenna Movement 187 on Amplitude and Phase Difference Measured on a Distant Plane A3.5.1 General 187 A3.5.2 Tower Movement 187 A3.5.3 Antenna Panning Frame Movement 188 A3.5.4 Amplitude Effects of Antenna Movement 190 A3.5.5 Phase Difference Measurements of 191 Antenna Movement A3.6 Synoptic Recording System 193. A3.7 Wind Vane 194 A3.8 Electronic Thermometer 196 A3.9 Rain Gauge 197 A3.9.1 Circuit Operation 197 A3.10 Analysis of Synoptic Data 201 A3.11 Clock 204 A3.12 Published Work 208 REFERENCES FOR CHAPTER THREE 208 CHAPTER FOUR EXPERIMENTAL DATA 209 4.1 Phase Effects: Theoretical Predictions 209 4.1 .1 Phase Difference 210 4.1 •2 Calibration of the Interferometer 212 4.1.3 Practical Measurements 214 4.1.4 Results from Other Workers 214 7 4.2 Millimtere—wave Angle of Arrival Fluctuations 218 4.2.1 The Magnitude of Angle of Arrival 218 4.2.2 Antenna Performance during Angle of 220 Arrival 4.3 Amplitude Scintillation 221 4.3.1 Theoretical Predictions 221 4.3.2 Practical Measurements 225 4.3.3 Comparison with other Experimental Data 227 4.4 Signal Conditioning 229 4.5 Amplitude Fluctuation Frequency Spectra 240 4.5.1 Theoretical Predictions 240 4.5.2 Measured Scintillation Spectra 242 4.6 Gain Reduction in the Practical Situation 245 4.7 Scintillation Spectra during Rain 247 ' 4.7.1 Practical Measurements 247 4.7.2 A Possible Explanation 247 4.8 Conclusions 251 APPENDICES FOR CHAPTER FOUR 253 A4.1 Determination of the Phase Centre of 253 an Aperture A4.2 Statistics of the Field Received during 255 Angle of Arrival Fluctuations A4.3 More Exact Analysis of Angle of Arrival 258 Statistics REFERENCES FOR CHAPTER FOUR 259 CHAPTER FIVE A COMPUTER SIMULATION OF PROPAGATION 262 THROUGH A RANDOM MEDIUM 5.1 Theoretical Considerations 263 5.1.1 Practical Difficulties with the 263 Fejer and Bramley Model 8 5.1.2 Basic Theory of the Simulation 265 5.2 Model Details 267 5.2.1 The Gaussian Beam 267 5.2.2 Numerical Techniques: Scaling' 268 5.2.3 Numerical Techniques: the..-Angular Spectrum 271 -5.3 Random Number Generators 275 5.3.1 Generation of Normally Distributed Numbers 276 5.3.2 The -Generation of Uniformly Distributed 277 Random Numbers 5.4 The Generation of Correlated Random Numbers 279 5.4.1 Adjacent Summing Algorithm 280 5.5 Conclusions 284 APPENDIX FOR CHAPTER FIVE 287 A5.1 Convergence to a Gaussian Autocovariance 287- Function REFERENCES FOR CHAPTER FIVE 289 CHAPTER SIX SIMULATION RESULTS 290 6.1 Introduction 290 6.2 Program SIMUL 290 6.3 Program PLOTN 292 6.4 Model Tests: Deterministic Case 294 6.5 Simulation Runs 297 6.5.1 Strong Perturbation versus Free Space 304 Conditions 6.5.2 The Effect of the Medium Scale Size 310 6.5.3 Strong Fluctuation Case 321 APPENDICES FOR CHAPTER SIX-.