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Mobile Fading Channels 移动衰落信道.pdf
Front Matter.pdf
Chapter 1.pdf
Chapter 2.pdf
chapter 3.pdf
chapter 4.pdf
Chapter 5.pdf
chapter 6.pdf
chapter 7.pdf
chapter 8.pdf
Appendix A.pdf
Appendix B.pdf
Appendix C.pdf
Appendix D.pdf
Appendix E.pdf
MATLAB-Programs.pdf
Abbreviations .pdf
Symbols.pdf
Bibliography.pdf
Index .pdf
Mobile Fading Channels. Matthias P¨atzold
Copyright 2002 John Wiley & Sons, Ltd.
ISBN: 0-471-49549-2
MOBILE
FADING
CHANNELS
MOBILE
FADING
CHANNELS
Matthias Pätzold
Professor of Mobile Communications
Agder University College, Grimstad, Norway
Originally published in the German language by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, D-65189
Wiesbaden, Germany, under the title “Matthias Pätzold: Mobilfunkkanäle. 1. Auflage (1st Edition)”. Copyright ©
Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, 1999.
Copyright © 2002 by John Wiley & Sons, Ltd
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V
Preface
This book results from my teaching and research activities at the Technical Uni-
versity of Hamburg-Harburg (TUHH), Germany. It is based on my German book
“Mobilfunkkan¨ale — Modellierung, Analyse und Simulation” published by Vieweg &
Sohn, Braunschweig/Wiesbaden, Germany, in 1999. The German version served as a
text for the lecture Modern Methods for Modelling of Networks, which I gave at the
TUHH from 1996 to 2000 for students in electrical engineering at masters level.
The book mainly is addressed to engineers, computer scientists, and physicists, who
work in the industry or in research institutes in the wireless communications field and
therefore have a professional interest in subjects dealing with mobile fading channels.
In addition to that, it is also suitable for scientists working on present problems of
stochastic and deterministic channel modelling. Last, but not least, this book also is
addressed to master students of electrical engineering who are specialising in mobile
radio communications.
In order to be able to study this book, basic knowledge of probability theory and
system theory is required, with which students at masters level are in general
familiar. In order to simplify comprehension, the fundamental mathematical tools,
which are relevant for the objectives of this book, are recapitulated at the beginning.
Starting from this basic knowledge, nearly all statements made in this book are
derived in detail, so that a high grade of mathematical unity is achieved. Thanks
to sufficient advice and help, it is guaranteed that the interested reader can verify
the results with reasonable effort. Longer derivations interrupting the flow of the
content are found in the Appendices. There, the reader can also find a selection
of MATLAB-programs, which should give practical help in the application of the
methods described in the book. To illustrate the results, a large number of figures
have been included, whose meanings are explained in the text. Use of abbreviations
has generally been avoided, which in my experience simplifies the readability consid-
erably. Furthermore, a large number of references is provided, so that the reader is led
to further sources of the almost inexhaustible topic of mobile fading channel modelling.
My aim was to introduce the reader to the fundamentals of modelling, analysis,
and simulation of mobile fading channels. One of the main focuses of this book is
the treatment of deterministic processes. They form the basis for the development
of efficient channel simulators. For the design of deterministic processes with given
correlation properties, nearly all the methods known in the literature up to now
are introduced, analysed, and assessed on their performance in this book. Further
focus is put on the derivation and analysis of stochastic channel models as well
as on the development of highly precise channel simulators for various classes of
frequency-selective and frequency-nonselective mobile radio channels. Moreover, a
primary topic is the fitting of the statistical properties of the designed channel models
VI
to the statistics of real-world channels.
At this point, I would like to thank those people, without whose help this book
would never have been published in its present form. First, I would like to express
my warmest thanks to Stephan Kraus and Can Karadogan, who assisted me with
the English translation considerably. I would especially like to thank Frank Laue for
performing the computer experiments in the book and for making the graphical plots,
which decisively improved the vividness and simplified the comprehension of the text.
Sincerely, I would like to thank Alberto D´ıaz Guerrero and Qi Yao for reviewing most
parts of the manuscript and for giving me numerous suggestions that have helped me
to shape the book into its present form. Finally, I am also grateful to Mark Hammond
and Sarah Hinton my editors at John Wiley & Sons, Ltd.
Matthias P¨atzold
Grimstad
January 2002
Contents
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 THE EVOLUTION OF MOBILE RADIO SYSTEMS . . . . . . . . .
1.2 BASIC KNOWLEDGE OF MOBILE RADIO CHANNELS . . . . . .
1.3 STRUCTURE OF THIS BOOK . . . . . . . . . . . . . . . . . . . . .
Important Probability Density Functions
2 RANDOM VARIABLES, STOCHASTIC PROCESSES, AND
DETERMINISTIC SIGNALS . . . . . . . . . . . . . . . . . . . . . . .
2.1 RANDOM VARIABLES . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1
. . . . . . . . . . . .
2.1.2 Functions of Random Variables . . . . . . . . . . . . . . . . . .
2.2 STOCHASTIC PROCESSES . . . . . . . . . . . . . . . . . . . . . . .
Stationary Processes . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . .
2.3 DETERMINISTIC CONTINUOUS-TIME SIGNALS . . . . . . . . . .
2.4 DETERMINISTIC DISCRETE-TIME SIGNALS . . . . . . . . . . . .
2.2.1
2.2.2 Ergodic Processes
2.2.3 Level-Crossing Rate and Average Duration of Fades
VII
1
1
3
7
11
11
15
19
20
22
25
25
27
29
3 RAYLEIGH AND RICE PROCESSES AS REFERENCE MODELS 33
3.1 GENERAL DESCRIPTION OF RICE AND RAYLEIGH PROCESSES 34
3.2 ELEMENTARY PROPERTIES OF RICE AND RAYLEIGH PRO-
CESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 STATISTICAL PROPERTIES OF RICE AND RAYLEIGH PRO-
CESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Probability Density Function of the Amplitude and the Phase .
3.3.2 Level-Crossing Rate and Average Duration of Fades
. . . . . .
3.3.3 The Statistics of the Fading Intervals of Rayleigh Processes . .
39
39
41
46
35
4 INTRODUCTION TO THE THEORY OF DETERMINISTIC
PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 PRINCIPLE OF DETERMINISTIC CHANNEL MODELLING . . . .
4.2 ELEMENTARY PROPERTIES OF DETERMINISTIC PROCESSES
4.3 STATISTICAL PROPERTIES OF DETERMINISTIC PROCESSES .
4.3.1 Probability Density Function of the Amplitude and the Phase .
4.3.2 Level-Crossing Rate and Average Duration of Fades
. . . . . .
Statistics of the Fading Intervals at Low Levels . . . . . . . . .
4.3.3
55
56
59
63
64
72
77
VIII
Contents
4.3.4 Ergodicity and Criteria for the Performance Evaluation . . . .
78
81
5 METHODS FOR THE COMPUTATION OF THE MODEL
PARAMETERS OF DETERMINISTIC PROCESSES . . . . . . . .
5.1 METHODS FOR THE COMPUTATION OF THE DISCRETE
83
DOPPLER FREQUENCIES AND DOPPLER COEFFICIENTS . . .
83
5.1.1 Method of Equal Distances (MED) . . . . . . . . . . . . . . . .
90
5.1.2 Mean-Square-Error Method (MSEM) . . . . . . . . . . . . . . .
5.1.3 Method of Equal Areas (MEA) . . . . . . . . . . . . . . . . . .
95
5.1.4 Monte Carlo Method (MCM) . . . . . . . . . . . . . . . . . . . 104
5.1.5 Lp-Norm Method (LPNM)
. . . . . . . . . . . . . . . . . . . . 113
5.1.6 Method of Exact Doppler Spread (MEDS) . . . . . . . . . . . . 128
. . . . . . . . . . . . . . . . . . . . . . . . 133
5.1.7
5.2 METHODS FOR THE COMPUTATION OF THE DOPPLER PHASES143
5.3 FADING INTERVALS OF DETERMINISTIC RAYLEIGH PROCESSES145
Jakes Method (JM)
6 FREQUENCY-NONSELECTIVE STOCHASTIC AND DETER-
MINISTIC CHANNEL MODELS . . . . . . . . . . . . . . . . . . . . . 155
6.1 THE EXTENDED SUZUKI PROCESS OF TYPE I . . . . . . . . . . 157
6.1.1 Modelling and Analysis of the Short-Term Fading . . . . . . . 157
6.1.1.1 Probability Density Function of the Amplitude and the
6.1.1.2
Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Level-Crossing Rate and Average Duration of Fades . 166
6.1.2 Modelling and Analysis of the Long-Term Fading . . . . . . . . 169
6.1.3 The Stochastic Extended Suzuki Process of Type I . . . . . . . 172
6.1.4 The Deterministic Extended Suzuki Process of Type I . . . . . 176
6.1.5 Applications and Simulation Results . . . . . . . . . . . . . . . 181
. . . . . . . . . 185
6.2.1 Modelling and Analysis of the Short-Term Fading . . . . . . . 186
6.2 THE EXTENDED SUZUKI PROCESS OF TYPE II
6.2.1.1 Probability Density Function of the Amplitude and the
6.2.1.2
Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Level-Crossing Rate and Average Duration of Fades . 193
. . . . . . 196
6.2.2 The Stochastic Extended Suzuki Process of Type II
6.2.3 The Deterministic Extended Suzuki Process of Type II . . . . . 200
6.2.4 Applications and Simulation Results . . . . . . . . . . . . . . . 205
6.3 THE GENERALIZED RICE PROCESS . . . . . . . . . . . . . . . . . 208
6.3.1 The Stochastic Generalized Rice Process . . . . . . . . . . . . . 209
6.3.2 The Deterministic Generalized Rice Process . . . . . . . . . . . 213
6.3.3 Applications and Simulation Results . . . . . . . . . . . . . . . 217
6.4 THE MODIFIED LOO MODEL . . . . . . . . . . . . . . . . . . . . . 218
. . . . . . . . . . . . . . . 218
6.4.1 The Stochastic Modified Loo Model
6.4.1.1 Autocorrelation Function and Doppler Power Spectral
Density . . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.4.1.2 Probability Density Function of the Amplitude and the
6.4.2 The Deterministic Modified Loo Model
Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Level-Crossing Rate and Average Duration of Fades . 228
. . . . . . . . . . . . . 230
6.4.1.3
Contents
IX
6.4.3 Applications and Simulation Results . . . . . . . . . . . . . . . 236
7 FREQUENCY-SELECTIVE STOCHASTIC AND DETERMIN-
ISTIC CHANNEL MODELS . . . . . . . . . . . . . . . . . . . . . . . . 241
7.1 THE ELLIPSES MODEL OF PARSONS AND BAJWA . . . . . . . . 244
7.2 SYSTEM THEORETICAL DESCRIPTION OF FREQUENCY-
SELECTIVE CHANNELS . . . . . . . . . . . . . . . . . . . . . . . . . 245
7.3 FREQUENCY-SELECTIVE STOCHASTIC CHANNEL MODELS . . 250
7.3.1 Correlation Functions
. . . . . . . . . . . . . . . . . . . . . . . 250
7.3.2 The WSSUS Model According to Bello . . . . . . . . . . . . . . 251
7.3.2.1 WSS Models . . . . . . . . . . . . . . . . . . . . . . . 251
7.3.2.2 US Models . . . . . . . . . . . . . . . . . . . . . . . . 253
7.3.2.3 WSSUS Models
. . . . . . . . . . . . . . . . . . . . . 253
7.3.3 The Channel Models According to COST 207 . . . . . . . . . . 259
7.4 FREQUENCY-SELECTIVE DETERMINISTIC CHANNEL MODELS 267
7.4.1
System Functions of Frequency-Selective Deterministic Channel
Models
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
7.4.2 Correlation Functions and Power Spectral Densities of DGUS
Models
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
7.4.3 Delay Power Spectral Density, Doppler Power Spectral Density,
and Characteristic Quantities of DGUS Models . . . . . . . . . 276
7.4.4 Determination of the Model Parameters of DGUS Models . . . 281
7.4.4.1 Determination of the discrete propagation delays and
delay coefficients . . . . . . . . . . . . . . . . . . . . . 281
7.4.4.2 Determination of the discrete Doppler frequencies and
7.4.4.3 Determination of the Doppler phases
. . . . . . . . . . . . . . . . . . . 283
. . . . . . . . . 284
Doppler coefficients
7.4.5 Deterministic Simulation Models for the Channel Models
According to COST 207 . . . . . . . . . . . . . . . . . . . . . . 284
8 FAST CHANNEL SIMULATORS . . . . . . . . . . . . . . . . . . . . . 289
8.1 DISCRETE DETERMINISTIC PROCESSES . . . . . . . . . . . . . . 290
8.2 REALIZATION OF DISCRETE DETERMINISTIC PROCESSES . . 292
8.2.1 Tables System . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
8.2.2 Matrix System . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
8.2.3
Shift Register System . . . . . . . . . . . . . . . . . . . . . . . 297
8.3 PROPERTIES OF DISCRETE DETERMINISTIC PROCESSES . . . 297
8.3.1 Elementary Properties of Discrete Deterministic Processes . . . 298
. . . 305
8.3.2
Statistical Properties of Discrete Deterministic Processes
8.3.2.1 Probability Density Function and Cumulative Distri-
bution Function of the Amplitude and the Phase . . . 306
Level-Crossing Rate and Average Duration of Fades . 313
8.4 REALIZATION EXPENDITURE AND SIMULATION SPEED . . . . 315
8.5 COMPARISON WITH THE FILTER METHOD . . . . . . . . . . . . 317
8.3.2.2
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