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MOBILE RADIO CHANNELS
Contents
Preface to the Second Edition
List of Acronyms
List of Symbols
1 Introduction
1.1 The Evolution of Mobile Radio Systems
1.2 Basic Knowledge of Mobile Radio Channels
1.3 Structure of this Book
2 Random Variables, Stochastic Processes, and Deterministic Signals
2.1 Random Variables
2.1.1 Basic Definitions of Probability Theory
2.1.2 Important Probability Density Functions
2.1.3 Functions of Random Variables
2.2 Stochastic Processes
2.2.1 Stationary Processes
2.2.2 Ergodic Processes
2.2.3 Level-Crossing Rate and Average Duration of Fades
2.2.4 Linear Systems with Stochastic Inputs
2.3 Deterministic Signals
2.3.1 Deterministic Continuous-Time Signals
2.3.2 Deterministic Discrete-Time Signals
2.4 Further Reading
Appendix 2.A Derivation of Rice’s General Formula for the Level-Crossing Rate
3 Rayleigh and Rice Channels
3.1 System Theoretical Description of Multipath Channels
3.2 Formal Description of Rayleigh and Rice Channels
3.3 Elementary Properties of Rayleigh and Rice Channels
3.3.1 Autocorrelation Function and Spectrum of the Complex Envelope
3.3.2 Autocorrelation Function and Spectrum of the Envelope
3.3.3 Autocorrelation Function and Spectrum of the Squared Envelope
3.4 Statistical Properties of Rayleigh and Rice Channels
3.4.1 Probability Density Function of the Envelope and the Phase
3.4.2 Probability Density Function of the Squared Envelope
3.4.3 Level-Crossing Rate and Average Duration of Fades
3.4.4 The Statistics of the Fading Intervals of Rayleigh Channels
3.5 Further Reading
Appendix 3.A Derivation of the Jakes Power Spectral Density and the Corresponding Autocorrelation Function
Appendix 3.B Derivation of the Autocorrelation Function of the Envelope
Appendix 3.C Derivation of the Autocovariance Spectrum of the Envelope Under Isotropic Scattering Conditions
Appendix 3.D Derivation of the Level-Crossing Rate of Rice Processes with Different Spectral Shapes of the Underlying Gaussian Random Processes
4 Introduction to Sum-of-Sinusoids Channel Models
4.1 Principle of Deterministic Channel Modelling
4.2 Elementary Properties of Deterministic Sum-of-Sinusoids Processes
4.3 Statistical Properties of Deterministic Sum-of-Sinusoids Processes
4.3.1 Probability Density Function of the Envelope and the Phase
4.3.2 Level-Crossing Rate and Average Duration of Fades
4.3.3 Statistics of the Fading Intervals at Low Signal Levels
4.3.4 Stationarity and Ergodicity of Sum-of-Sinusoids Processes
4.4 Classes of Sum-of-Sinusoids Processes
4.5 Basics of Sum-of-Cisoids Channel Models
4.5.1 Elementary Properties of Stochastic Sum-of-Cisoids Processes
4.5.2 Probability Density Function of the Envelope and Phase
4.6 Criteria for the Performance Evaluation
4.7 Further Reading
Appendix 4.A Derivation of the Autocorrelation Function of the Squared Envelope of Complex Deterministic Gaussian Processes
Appendix 4.B Derivation of the Exact Solution of the Level-Crossing Rate and the Average Duration of Fades of Deterministic Rice Processes
5 Parametrization of Sum-of-Sinusoids Channel Models
5.1 Methods for Computing the Doppler Frequencies and Gains
5.1.1 Method of Equal Distances (MED)
5.1.2 Mean-Square-Error Method (MSEM)
5.1.3 Method of Equal Areas (MEA)
5.1.4 Monte Carlo Method (MCM)
5.1.5 Jakes Method (JM)
5.1.6 Lp-Norm Method (LPNM)
5.1.7 Method of Exact Doppler Spread (MEDS)
5.1.8 Randomized Method of Exact Doppler Spread (RMEDS)
5.1.9 Method of Exact Doppler Spread with Set Partitioning (MEDS-SP)
5.2 Methods for Computing the Phases
5.3 Fading Intervals of Deterministic Rayleigh Processes
5.4 Parametrization of Sum-of-Cisoids Channel Models
5.4.1 Problem Description
5.4.2 Extended Method of Exact Doppler Spread (EMEDS)
5.4.3 Lp-Norm Method (LPNM)
5.4.4 Generalized Method of Equal Areas (GMEA)
5.4.5 Performance Analysis
5.5 Concluding Remarks and Further Reading
Appendix 5.A Analysis of the Relative Model Error by Using the Monte Carlo Method
Appendix 5.B Proof of the Convergence of the Sample Mean Autocorrelation Function by Using the MEDS-SP
Appendix 5.C Proof of the Condition for Uncorrelated Inphase and Quadrature Components of SOC Processes
6 Frequency-Nonselective Channel Models
6.1 The Extended Suzuki Process of Type I
6.1.1 Modelling and Analysis of Short-Term Fading
6.1.2 Modelling and Analysis of Long-Term Fading
6.1.3 The Stochastic Extended Suzuki Process of Type I
6.1.4 The Deterministic Extended Suzuki Process of Type I
6.1.5 Applications and Simulation Results
6.2 The Extended Suzuki Process of Type II
6.2.1 Modelling and Analysis of Short-Term Fading
6.2.2 The Stochastic Extended Suzuki Process of Type II
6.2.3 The Deterministic Extended Suzuki Process of Type II
6.2.4 Applications and Simulation Results
6.3 The Generalized Rice Process
6.3.1 The Stochastic Generalized Rice Process
6.3.2 The Deterministic Generalized Rice Process
6.3.3 Applications and Simulation Results
6.4 The Modified Loo Model
6.4.1 The Stochastic Modified Loo Model
6.4.2 The Deterministic Modified Loo Model
6.4.3 Applications and Simulation Results
6.5 Modelling of Nonstationary Land Mobile Satellite Channels
6.5.1 Lutz’s Two-State Channel Model
6.5.2 M-State Channel Models
6.5.3 Modelling of Nonstationary Real-World LMS Channels
7 Frequency-Selective Channel Models
7.1 The Ellipse Model of Parsons and Bajwa
7.2 System Theoretical Description of Frequency-Selective Channels
7.3 Frequency-Selective Stochastic Channel Models
7.3.1 Correlation Functions
7.3.2 The WSSUS Model According to Bello
7.3.3 The COST 207 Channel Models
7.3.4 The HIPERLAN/2 Channel Models
7.4 Frequency-Selective Sum-of-Sinusoids Channel Models
7.4.1 System Functions of Sum-of-Sinusoids Uncorrelated Scattering (SOSUS) Models
7.4.2 Correlation Functions and Power Spectral Densities of SOSUS Models
7.4.3 Delay Power Spectral Density, Doppler Power Spectral Density, and Characteristic Quantities of SOSUS Models
7.4.4 Determination of the Model Parameters of SOSUS Models
7.4.5 Simulation Models for the COST 207 Channel Models
7.5 Methods for Modelling of Given Power Delay Profiles
7.5.1 Problem Description
7.5.2 Methods for the Computation of the Discrete Propagation Delays and the Path Gains
7.5.3 Comparison of the Parameter Computation Methods
7.5.4 Applications to Measured Power Delay Profiles
7.6 Perfect Modelling and Simulation of Measured Wideband Mobile Radio Channels
7.6.1 The Sum-of-Cisoids Uncorrelated Scattering (SOCUS) Model
7.6.2 The Principle of Perfect Channel Modelling
7.6.3 Application to a Measured Wideband Indoor Channel
7.7 Further Reading
Appendix 7.A Specification of the L-Path COST 207 Channel Models
Appendix 7.B Specification of the L-Path HIPERLAN/2 Channel Models
8 MIMO Channel Models
8.1 The Generalized Principle of Deterministic Channel Modelling
8.2 The One-Ring MIMO Channel Model
8.2.1 The Geometrical One-Ring Scattering Model
8.2.2 The Reference Model for the One-Ring MIMO Channel Model
8.2.3 Simulation Models for the One-Ring MIMO Channel Model
8.2.4 Parameter Computation Methods
8.2.5 Performance Evaluation
8.2.6 Simulation Results
8.3 The Two-Ring MIMO Channel Model
8.3.1 The Geometrical Two-Ring Scattering Model
8.3.2 The Reference Model for the Two-Ring MIMO Channel Model
8.3.3 Simulation Models for the Two-Ring MIMO Channel Model
8.3.4 Isotropic and Non-Isotropic Scattering Scenarios
8.3.5 Parameter Computation Methods
8.4 The Elliptical MIMO Channel Model
8.4.1 The Geometrical Elliptical Scattering Model
8.4.2 The Reference Model for the Elliptical MIMO Channel Model
8.4.3 Simulation Models for the Elliptical MIMO Channel Model
8.4.4 Model Extensions
8.5 Further Reading
Appendix 8.A Proof of Ergodicity
9 High-Speed Channel Simulators
9.1 Discrete-Time Deterministic Processes
9.2 Realization of Discrete-Time Deterministic Processes
9.2.1 Look-Up Table System
9.2.2 Matrix System
9.2.3 Shift Register System
9.3 Properties of Discrete-Time Deterministic Processes
9.3.1 Elementary Properties of Discrete-Time Deterministic Processes
9.3.2 Statistical Properties of Discrete-Time Deterministic Processes
9.4 Realization Complexity and Simulation Speed
9.5 Comparison of the Sum-of-Sinusoids Method with the Filter Method
9.6 Further Reading
10 Selected Topics in Mobile Radio Channel Modelling
10.1 Design of Multiple Uncorrelated Rayleigh Fading Waveforms
10.1.1 Problem Description
10.1.2 Generalized Method of Exact Doppler Spread (GMEDSq)
10.1.3 Related Parameter Computation Methods
10.1.4 The Effect of Finite Simulation Time on the Cross-Correlation Properties
10.1.5 Further Reading
10.2 Spatial Channel Models for Shadow Fading
10.2.1 The Reference Model for Shadow Fading
10.2.2 The Simulation Model for Shadow Fading
10.2.3 Correlation Models for Shadow Fading
10.2.4 Further Reading
10.3 Frequency Hopping Mobile Radio Channels
10.3.1 The Reference Model for Frequency Hopping Channels
10.3.2 The Simulation Model for Frequency Hopping Channels
10.3.3 Performance Analysis
10.3.4 Simulation Results
10.3.5 Further Reading
Appendix 10.A Derivation of the Spatial Autocorrelation Function of Lognormal Processes
Appendix 10.B Derivation of the Level-Crossing Rate of Spatial Lognormal Processes
Appendix 10.C Derivation of the Level-Crossing Rate of Sum-of-Sinusoids Shadowing Simulators
Appendix 10.D Application of the Method of Equal Areas (MEA) on the Gudmundson Correlation Model
Appendix 10.E Derivation of the Time-Frequency Cross-Correlation Function of Frequency Hopping Channels
Appendix 10.F Parametrization of Frequency Hopping Channel Simulators
References
Index
RED BOX RULES ARE FOR PROOF STAGE ONLY. DELETE BEFORE FINAL PRINTING. Mobile Radio Channels Second Edition Matthias Pätzold, University of Agder, Norway Providing a comprehensive overview of the modelling, analysis, and simulation of mobile radio channels, this book gives a detailed understanding of fundamental issues and examines state-of-the-art techniques in mobile radio channel modelling. It presents several mobile fading channels, including terrestrial and satellite fl at-fading channels, various types of wideband channels, and advanced MIMO channels, providing a fundamental understanding of the issues currently being investigated in the fi eld. Important classes of narrowband, wideband, and space-time wireless channels are explored in detail with descriptions of effi cient simulation methods for mobile radio channels being central. Strong emphasis is placed on the detailed origin of the presented channel models and a high degree of mathematical unity is conveyed. Using the described channel models, the reader can evaluate the performance of wireless communication systems under propagation conditions which are typical for multipath channels in various environments. • Introduces the fundamentals of stochastic and deterministic channel models • Explores the modelling and simulation of both wideband and narrowband mobile radio channels as well as several classes of MIMO channels • Describes general concepts including geometrical, reference, and simulation models • Discusses several methods for the modelling of given Doppler, delay, and angular profi les • Elaborates on methods for the design, analysis, and realization of effi cient channel simulators • Examines techniques for the development of fast channel simulators • Provides links for downloading MATLAB® programs, enabling the simulation and analysis of the mobile radio channel models presented, on the companion website (www.wiley.com/go/paetzold) Cover Design: Jim Wilkie Mobile Radio Channels Second Edition Pätzold M o b i i l e R a d o C h a n n e l s Second Edition Matthias Pätzold
P1: TIX/XYZ JWST087-FM P2: ABC JWST087-Patzold August 19, 2011 21:35 Printer Name: Yet to Come
P1: TIX/XYZ JWST087-FM P2: ABC JWST087-Patzold August 19, 2011 21:35 Printer Name: Yet to Come MOBILE RADIO CHANNELS
P1: TIX/XYZ JWST087-FM P2: ABC JWST087-Patzold August 19, 2011 21:35 Printer Name: Yet to Come
P1: TIX/XYZ JWST087-FM P2: ABC JWST087-Patzold August 19, 2011 21:35 Printer Name: Yet to Come MOBILE RADIO CHANNELS Second Edition Matthias P¨atzold University of Agder, Norway A John Wiley & Sons, Ltd., Publication
P1: TIX/XYZ JWST087-FM P2: ABC JWST087-Patzold August 19, 2011 21:35 Printer Name: Yet to Come This edition first published 2012 © 2012 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. Library of Congress Cataloging-in-Publication Data P¨atzold, Matthias, professor of mobile communications. Mobile radio channels / Matthias P¨atzold. – 2nd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-470-51747-5 (cloth) 1. Mobile communication systems. (Wireless communications). I. Title. 2. Radio wave propagation. 3. Radio resource management TK5103.2.P385 2012 621.3845–dc23 A catalogue record for this book is available from the British Library. Print ISBN: 978-0-470-51747-5 ePDF ISBN: 978-1-119-97412-3 oBook ISBN: 978-1-119-97411-6 ePub ISBN: 978-1-119-97525-0 Mobi ISBN: 978-1-119-97526-7 Typeset in 10/12pt Times by Aptara Inc., New Delhi, India 2011015882
P1: TIX/XYZ JWST087-FM P2: ABC JWST087-Patzold August 19, 2011 21:35 Printer Name: Yet to Come Contents Preface to the Second Edition List of Acronyms List of Symbols 1 Introduction 1.1 The Evolution of Mobile Radio Systems 1.2 Basic Knowledge of Mobile Radio Channels 1.3 Structure of this Book 2 Random Variables, Stochastic Processes, and Deterministic Signals 2.1 Random Variables 2.1.1 Basic Definitions of Probability Theory 2.1.2 Important Probability Density Functions 2.1.3 Functions of Random Variables 2.2 Stochastic Processes 2.2.1 Stationary Processes 2.2.2 Ergodic Processes 2.2.3 Level-Crossing Rate and Average Duration of Fades 2.2.4 Linear Systems with Stochastic Inputs 2.3 Deterministic Signals 2.3.1 Deterministic Continuous-Time Signals 2.3.2 Deterministic Discrete-Time Signals 2.4 Further Reading Appendix 2.A Derivation of Rice’s General Formula for the Level-Crossing Rate 3 Rayleigh and Rice Channels 3.1 System Theoretical Description of Multipath Channels 3.2 Formal Description of Rayleigh and Rice Channels 3.3 Elementary Properties of Rayleigh and Rice Channels 3.3.1 Autocorrelation Function and Spectrum of the Complex Envelope 3.3.2 Autocorrelation Function and Spectrum of the Envelope 3.3.3 Autocorrelation Function and Spectrum of the Squared Envelope xi xv xix 1 1 8 12 17 17 17 24 35 37 40 42 43 45 48 48 50 52 52 55 56 61 62 62 65 67
P1: TIX/XYZ JWST087-FM P2: ABC JWST087-Patzold August 19, 2011 21:35 Printer Name: Yet to Come vi Contents 3.4 Statistical Properties of Rayleigh and Rice Channels 3.4.1 Probability Density Function of the Envelope and the Phase 3.4.2 Probability Density Function of the Squared Envelope 3.4.3 Level-Crossing Rate and Average Duration of Fades 3.4.4 The Statistics of the Fading Intervals of Rayleigh Channels 3.5 Further Reading Appendix 3.A Derivation of the Jakes Power Spectral Density and the Corresponding Autocorrelation Function Appendix 3.B Derivation of the Autocorrelation Function of the Envelope Appendix 3.C Derivation of the Autocovariance Spectrum of the Envelope Under Isotropic Scattering Conditions Appendix 3.D Derivation of the Level-Crossing Rate of Rice Processes with Different Spectral Shapes of the Underlying Gaussian Random Processes 4 Introduction to Sum-of-Sinusoids Channel Models 4.1 Principle of Deterministic Channel Modelling 4.2 Elementary Properties of Deterministic Sum-of-Sinusoids Processes 4.3 Statistical Properties of Deterministic Sum-of-Sinusoids Processes 4.3.1 Probability Density Function of the Envelope and the Phase 4.3.2 Level-Crossing Rate and Average Duration of Fades 4.3.3 4.3.4 Statistics of the Fading Intervals at Low Signal Levels Stationarity and Ergodicity of Sum-of-Sinusoids Processes 4.4 Classes of Sum-of-Sinusoids Processes 4.5 Basics of Sum-of-Cisoids Channel Models 4.5.1 Elementary Properties of Stochastic Sum-of-Cisoids Processes 4.5.2 Probability Density Function of the Envelope and Phase 4.6 Criteria for the Performance Evaluation 4.7 Further Reading Appendix 4.A Derivation of the Autocorrelation Function of the Squared Envelope of Complex Deterministic Gaussian Processes Appendix 4.B Derivation of the Exact Solution of the Level-Crossing Rate and the Average Duration of Fades of Deterministic Rice Processes 5 Parametrization of Sum-of-Sinusoids Channel Models 5.1 Methods for Computing the Doppler Frequencies and Gains 5.1.1 Method of Equal Distances (MED) 5.1.2 Mean-Square-Error Method (MSEM) 5.1.3 Method of Equal Areas (MEA) 5.1.4 Monte Carlo Method (MCM) 5.1.5 5.1.6 Lp-Norm Method (LPNM) 5.1.7 Method of Exact Doppler Spread (MEDS) 5.1.8 Randomized Method of Exact Doppler Spread (RMEDS) 5.1.9 Method of Exact Doppler Spread with Set Partitioning (MEDS-SP) Jakes Method (JM) 69 70 72 73 77 84 84 88 90 91 95 96 102 107 108 115 120 122 123 126 127 129 135 135 136 137 149 151 151 157 162 170 178 189 201 205 207
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