Theory of stochastic local area channel modeling for wireless communications

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Theory of stochastic local area channel modeling for wireless communications

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Tài liệu tham khảo chuyên ngành viễn thông Theory of stochastic local area channel modeling for wireless communications

THEORY OF STOCHASTIC LOCAL AREA CHANNEL MODELING FOR WIRELESS COMMUNICATIONS by Gregory D Durgin Final Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPY in Electrical Engineering Theodore S Rappaport(Chairman) David A de Wolf Gary S Brown Jeffrey H Reed Werner Kohler Robert J Boyle December 2000 Blacksburg, Virginia Keywords: Fading, Mobile Radio Propagation, Wireless Communications Copyright 2000, Gregory D Durgin THEORY OF STOCHASTIC LOCAL AREA CHANNEL MODELING FOR WIRELESS COMMUNICATIONS Gregory D Durgin (ABSTRACT) This report was written to satisfy the final dissertation requirements toward a doctoral degree in electrical engineering The dissertation outlines work accomplished in the pursuit of this degree This report is also designed to be a general introduction to the concepts and techniques of small-scale radio channel modeling At the present time, there does not exist a comprehensive introduction and overview of basic concepts in this field Furthermore, as the wireless industry continues to mature and develop technology, the need is now greater than ever for more sophisticated channel modeling research Each chapter of this preliminary report is, in itself, a stand-alone topic in channel modeling theory Culled from original reports and journal papers, each chapter makes a unique contribution to the field of channel modeling Original contributions in this report include joint characterization of time-varying, space-varying, and frequency-varying channels under the rubric of duality rules and definitions for constructing channel models that solve Maxwell’s equations overview of probability density functions that describe random small-scale fading techniques for modeling a small-scale radio channel using an angle spectrum overview of techniques for describing fading statistics in wireless channels results from a wideband spatio-temporal measurement campaign Together, the chapters provide a cohesive overview of basic principles The discussion of the wideband spatio-temporal measurement campaign at 1920 MHz makes an excellent case study in applied channel modeling and ties together much of the theory developed in this dissertation ii Contents (ABSTRACT) ii Introduction 1.1 1.2 1.3 The Need for Improvement in Channel Modeling Theory 1.1.1 Higher and Higher Data Rates 1.1.2 Ubiquity of Wireless Devices 1.1.3 Smart Antennas 1.1.4 Faster, Smaller, Cheaper Hardware 1.1.5 Frequency Congestion 1.1.6 Multiple-Input, Multiple-Output Systems Key Topics in Small-Scale Channel Modeling 1.2.1 Spatial, Temporal, and Frequency Coherence 1.2.2 Rigorous Application of Physics to Channel Models 1.2.3 Physically-Based Small-Scale Fading Distributions 1.2.4 Characterization and Analysis of Angle Spectra 1.2.5 Channel Statistics of Rayleigh Fading 1.2.6 Spatio-Temporal Peer-to-Peer Measurements How to Read This Dissertation Foundations of Stochastic Channel Modeling 2.1 2.2 10 Baseband Representation 11 2.1.1 Signal Modulation 11 2.1.2 The Baseband Channel 15 2.1.3 Time-Invariant vs Time-Varying Channels 15 2.1.4 Detection 18 Channel Coherence 2.2.1 20 Coherence vs Selectivity 20 iii 2.3 2.2.2 Temporal Coherence 20 2.2.3 Frequency Coherence 22 2.2.4 Spatial Coherence 23 26 2.3.1 Spectral Domain Representations 26 2.3.2 General Signal Transmission 28 2.3.3 Static Channel Transmission 28 2.3.4 Mobile Receiver Transmission 29 Stochastic Channel Characterization 30 2.4.1 Autocorrelation Relationships 30 2.4.2 Power Spectrum 32 2.4.3 RMS Power Spectrum Width 36 2.4.4 Channel Duality Principle 41 Chapter Summary 43 2.A Functions of Three-Dimensional Space 44 2.A.1 Vector Notation for Fourier Transforms 44 2.A.2 Scalar Collapse of Position Vectors 45 2.A.3 Scalar Collapse of Wavevectors 46 2.4 2.5 Using the Complete Baseband Channel The Physics of Small-Scale Fading 3.1 3.2 3.3 49 Plane Wave Representation 50 3.1.1 Electromagnetic Fields and Received Signals 50 3.1.2 The Maxwellian Basis 51 3.1.3 Homogeneous Plane Waves 53 3.1.4 Inhomogeneous Plane Waves 53 3.1.5 Physics of Homogeneous vs Inhomogeneous Plane Waves 55 The Local Area 60 3.2.1 Definition of a Local Area 60 3.2.2 Scatterer Proximity 60 3.2.3 A Wideband Plane Wave 62 3.2.4 The Bandwidth-Distance Threshold 64 Wave Groupings 67 3.3.1 Specular Wave Component 67 3.3.2 Non-specular Wave Component 67 3.3.3 Diffuse Wave Component 68 3.3.4 Reduced Wave Grouping 68 iv 3.4 3.5 The Stochastic Local Area Channel (SLAC) Model 70 3.4.1 Stochastic Model 70 3.4.2 Random Phase Models 71 3.4.3 Fourier Transforms 73 3.4.4 Autocorrelation Functions 74 3.4.5 Heterogeneous Scattering 75 3.4.6 Power Spectrum 76 Chapter Summary 80 3.A Wavevector Criterion for Free Space Plane Waves First-Order Statistics of Small-Scale Channels 4.1 4.2 4.3 4.4 4.5 81 82 Mean Received Power 83 4.1.1 Stationarity 83 4.1.2 Mean U-SLAC Power 85 4.1.3 Frequency and Spatial Averaging 85 4.1.4 Ergodicity 86 Envelope Probability Density Functions 89 4.2.1 Notes and Concepts 89 4.2.2 Characteristic Functions 89 4.2.3 Specular Characteristic Function 90 4.2.4 Diffuse, Non-specular Characteristic Function 91 4.2.5 The I-SLAC PDF Generator 92 Closed-Form PDF Solutions 93 4.3.1 The One-Wave PDF 93 4.3.2 The Two-Wave PDF 93 4.3.3 The Three-Wave PDF 96 4.3.4 The Rayleigh PDF 96 4.3.5 The Rician PDF 98 Two-Wave with Incoherent Power (TIP) PDF 100 4.4.1 Approximate Representation 100 4.4.2 Graphical Analysis 102 4.4.3 Rayleigh and Rician Approximations 102 4.4.4 Final Comments on Reduced Wave Groupings 108 4.4.5 TIP PDF Applications 110 4.4.6 Closing Remarks on TIP Fading 110 Chapter Summary 112 v 4.A Derivation of Envelope Characteristic Functions 113 4.B Derivation for TIP Fading PDF’s 115 4.B.1 Approximate Representation 115 4.B.2 Property as a PDF 116 4.B.3 Proper Limiting Behavior 117 4.B.4 Preservation of the Second Moment 117 The Angle Spectrum 5.1 5.2 5.3 5.4 5.5 118 Angle Spectrum Concepts 119 5.1.1 Definition of the Angle Spectrum 119 5.1.2 Mapping Angles to Wavenumbers 120 5.1.3 From-the-Horizon Propagation 121 5.1.4 Summary of Angle Spectrum Concepts 124 Fading Rate Variance 127 5.2.1 Definition of a Rate Variance 127 5.2.2 Fundamental Spectral Spread Theorem 129 Multipath Shape Factors 130 5.3.1 Definition of Shape Factors 130 5.3.2 Basic Wavenumber Spread Relationship 131 5.3.3 Comparison to Omnidirectional Propagation 132 Illustrative Examples 134 5.4.1 Two-Wave Channel Model 134 5.4.2 Sector Channel Model 134 5.4.3 Double Sector Channel Model 136 5.4.4 Rician Channel Model 138 Chapter Summary 140 5.A Derivation of Shape Factors Rayleigh Fading Channel Statistics 6.1 6.2 The Level-Crossing Problem 142 144 145 6.1.1 Level-Crossing Rate 145 6.1.2 Average Fade Duration 146 6.1.3 Level Crossing in Frequency 146 6.1.4 Level Crossing in Space 147 Envelope Unit Autocovariance 6.2.1 148 Temporal Unit Autocovariance 148 vi 6.3 6.4 6.2.2 Frequency Unit Autocovariance 149 6.2.3 Spatial Unit Autocovariance 150 6.2.4 Joint Unit Autocovariance 151 Revisiting Classical Spatial Channel Models 153 6.3.1 Classical Spatial Channel Models 153 6.3.2 Channel Model Solutions 154 6.3.3 Additional Comments 155 Chapter Summary 158 6.A Approximate Spatial Autocovariance Function Spatio-Temporal Measurements 7.1 7.2 159 161 Previous Measurement Campaigns 162 7.1.1 Contribution of this Work 162 7.1.2 Comparison to Other Measurement Campaigns in the Literature 162 164 7.2.1 Measured Locations 164 7.2.2 Channel Sounding Hardware 164 7.2.3 Automated Antenna Positioning 166 7.2.4 Antenna Specifications 169 7.2.5 Sources of Error in the Experiment 169 173 7.3.1 Delay Dispersion Results 173 7.3.2 Angle Dispersion Results 175 7.3.3 Joint Angle-Delay Statistics 178 Conclusions 180 7.A Description of Measured Parameters 181 7.A.1 Noncoherent Channel Measurements 181 7.A.2 Power Spectra 182 7.A.3 Time Delay Parameters 182 7.A.4 Angle-of-Arrival Parameters 184 7.3 7.4 Overview of Measurement Campaign Results Conclusions 8.1 185 Future Areas of Research 186 8.1.1 Theoretical Framework 186 8.1.2 Specific Analytical Problems 186 8.1.3 Applications to Wireless Technology 187 vii 8.1.4 Measurement Theory 187 8.1.5 Computer Simulation 187 Vitae 189 Bibliography 190 viii List of Tables 2.1 Received signal functions used in complex baseband analysis 19 2.2 Fourier transform definitions for each channel dependency 27 2.3 Channel duality relationships between time, frequency, and space 3.1 Maximum size of a local area according to the bandwidth-distance threshold for example wireless applications 42 66 3.2 Reduced Wave Grouping Algorithm 69 4.1 Summary of envelope PDF’s in different fading environments 94 4.2 Exact coefficients for the first five orders of the approximate Two-Wave with Incoherent Power (TIP) fading PDF 4.3 100 The TIP PDF contains the Rayleigh, Rician, One-Wave, and Two-Wave PDF’s as special cases 4.4 102 Three examples of Two-Wave with Incoherent Power (TIP) fading that may simplify to Rayleigh or Rician PDF’s 107 7.1 Summary of dispersion statistics calculated from track measurements 174 7.2 Summary of spatial multipath parameters calculated from spatially-averaged azimuthal sweeps of a horn antenna ix 176 List of Figures 2.1 The many different bandwidths defined for a baseband signal 2.2 Baseband-Passband transformations in the time domain (inner cycle) and the frequency domain (outer cycle) 2.3 12 13 Block diagram of baseband and passband channel models for SISO transmission 16 2.4 Spectral diagram of baseband and passband signals and channel 17 2.5 Example of a time-varying channel 21 2.6 Example of a frequency-varying channel 2.7 Example of a space-varying channel (one-dimensional cut) 2.8 Example of small-scale and large-scale fading 2.9 Autocorrelation and power spectrum relationships for time and frequency 22 23 24 2.10 Autocorrelation and power spectrum relationships for space and frequency 33 35 2.11 Autocorrelation and power spectrum relationships for space, time, and frequency 37 2.12 Relationship between (x, y, z) and (r, θ, ϕ) coordinates ˜ r ), to a scalar baseband 3.1 An antenna maps the complex electric field vector, E( 45 ˜ r ) channel voltage, h( 50 3.2 Homogeneous and inhomogeneous plane waves 54 3.3 Rules-of-thumb for homogeneous and inhomogeneous plane wave propagation 3.4 57 An example linear circuit contains capacitors, inductors, resistors and an AC source 3.5 58 A linear circuit solution may be broken into a steady-state and transient solution 3.6 The size of a local area decreases closer to significant scatterers 3.7 Illustration of the basic quantities of time-harmonic wave propagation through a scattering environment x 59 61 63 ... type Chapter discusses the basic form that a stochastic local area channel model must take Great care is taken in defining a local area and a stochastic local area channel, clearly stating the assumptions.. .THEORY OF STOCHASTIC LOCAL AREA CHANNEL MODELING FOR WIRELESS COMMUNICATIONS Gregory D Durgin (ABSTRACT) This report was written... trends in wireless communications which emphasize the need for improved and expanded channel modeling theory 1.1.1 Higher and Higher Data Rates The capacity for data transmission of current wireless

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