Pseudo Random Signal Processing: Theory and Application

438 Pages·2005·15.67 MB·English

by  Hans-Jurgen Zepernick

Pseudo Random Signal Processing

Pseudo Random
Signal Processing
Theory and Application
Hans-Jiirgen Zepernick
Blekinge Institute of Technology, Sweden
Adolf Finger
Dresden University of Technology, Germany
John Wiley &. Sons, Ltd
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ISBN-1O 0-470-86657-8 (HB)
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Contents
Preface ix
List of abbreviations xi
List of common symbols xvii
1 Introduction 1
1.1 Prologue 1
1.2 Elements of pseudo random signal processing 2
1.3 Outline of the book 5
2 Characterization of signals and sequences 7
2.1 Classification of signals and sequences 7
2.1.1 Morphological classification 8
2.1.2 Phenomenological classification 9
2.1.3 Energy classification 12
2.1.4 Spectral classification 12
2.2 Transformations of signals and sequences 13
2.2.1 Basic transformations 13
2.3 Correlation measures 16
2.3.1 Autocorrelation and crosscorrelation functions 17
2.3.2 Discrete periodic correlation functions 19
2.3.3 Aperiodic correlation functions 23
2.3.4 Other properties and relationships 26
2.3.5 Correlation of binary sequences 34
2.3.6 Orthogonality 37
2.4 Power spectral density 39
2.4.1 Power spectral density of analog signals 39
2.4.2 Power spectral density of periodic signals 41
2.4.3 Power spectral density of periodic pulse trains 44
2.5 Pseudo random signals and sequences 45
2.5.1 Pseudo randomness criteria 45
2.5.2 Pseudo randomness and power spectral density 48
2.5.3 Pseudo randomness and polyphase sequences 49
vi CONTENTS
3 Mathematical foundations 51
3.1 Algebraic structures 51
3.1.1 Binary algebra, semigroup, and monoid 51
3.1.2 Groups, rings, and fields 53
3.2 Polynomials over finite fields 61
3.2.1 Polynomials and polynomial rings 61
3.2.2 Euclidean algorithm for polynomials 62
3.2.3 Irreducible polynomials 67
3.2.4 Cyclotomic cosets and minimal polynomials 73
3.2.5 Primitive polynomials 78
4 Binary pseudo random sequences 87
4.1 Classification 87
4.2 Maximal-length sequences 89
4.2.1 Linear recurring sequences 90
4.2.2 Maximal-length sequences 92
4.2.3 Properties of maximal-length sequences 95
4.2.4 Autocorrelation functions of maximal-length sequences 102
4.3 Binary sequences with good autocorrelation 106
4.3.1 Difference sets 106
4.3.2 De Bruijn sequences 108
4.3.3 Quadratic residue sequences 109
4.3.4 Other difference set sequences 110
4.3.5 Barker sequences and Williard sequences 112
4.4 Binary sequences with special crosscorrelation 114
4.4.1 Transorthogonal and orthogonal sequences 114
4.4.2 Gold sequences 118
4.4.3 Gold-like sequences 122
4.4.4 Kasarni sequences 123
5 Nonbinary pseudo random sequences 127
5.1 Classification 127
5.2 Interference-free window sequences 131
5.2.1 Large-area synchronous codes 131
5.3 Complex-valued sequences 147
5.3.1 Complex maximal-length sequences 147
5.3.2 Polyphase sequences 149
5.3.3 Quadriphase sequences 154
5.4 Polyphase sequences with special correlations 159
5.4.1 Equivalent odd and even correlation sequences 159
5.4.2 Oppermann sequences 163
6 Generating pseudo random signals 173
6.1 Linear autonomous automata 173
6.1.1 Mathematical description 173
6.1.2 Canonical forms 175
6.1.3 State cycles 179
CONTENTS vii
6.2 Generating maximal-length sequences 182
6.2.1 Standard circuits for binary maximal-length sequences 182
6.2.2 Special cases of modulo 2 arithmetic 184
6.2.3 High-speed sequence generation 189
6.2.4 Nonbinary sequence generation with binary encoding 193
6.3 Transformations of maximal-length sequences 195
6.3.1 Transversal filtering 195
6.3.2 Histogram transformation through mapping 201
6.3.3 Generation of phase-shifted maximal-length sequences 204
6.4 Combinations of maximal-length sequences 209
6.4.1 Modifications of binary maximal-length sequences 209
6.4.2 Product sequences 210
6.4.3 Combination sequences 210
6.4.4 Concatenated sequences 211
6.5 Pseudo random signal processing with microprocessors and memory circuits 212
6.5.1 Realizations with microprocessors 212
6.5.2 Realizations with memory circuits 213
6.5.3 Realizations with programmable logic devices 215
6.5.4 WIND-FLEX 218
6.5.5 Pseudo random signal generators 220
7 Applications of pseudo random signal processing 225
7.1 Spread spectrum communications 226
7.1.1 Basic concepts 227
7.1.2 Basic spread spectrum systems 228
7.1.3 Spread spectrum communication systems 236
7.1.4 Universal mobile telecommunications system 242
7.1.5 Bluetooth 263
7.2 Ranging and navigation systems 269
7.2.1 Ranging principles 269
7.2.2 Correlation receivers 272
7.2.3 Synchronization 275
7.2.4 Global positioning system 288
7.2.5 Galileo 301
7.2.6 Other ranging and navigation systems 310
7.3 Scrambling 314
7.3.1 Scrambling functions 315
7.3.2 Scrambling techniques 316
7.3.3 Scramblers for wireline systems 325
7.3.4 Scramblers for wireless systems 331
7.4 Automatic testing and system verification 340
7.4.1 Signature analysis 341
7.4.2 Built-in self-test schemes 349
7.4.3 Bit error analysis 352
7.5 Cryptology 359
7.5.1 Cryptosystems 360
7.5.2 Generators for stream ciphers 361
7.5.3 Feedback carry shift registers 366
viii CONTENTS
7.5.4 Content scrambling system for digital versatile discs 372
7.5.5 Encryption in radio and television systems 373
7.5.6 Security encryption algorithm AS of the global system for mobile communication 376
7.6 Other applications 379
7.6.1 Correlation analysis of linear systems 379
7.6.2 Optical fiber systems 381
7.6.3 Angular sensor systems 384
7.6.4 Add-on data transmission in analog television 386
Bibliography 391
Index 403