Wireless Communications (eBook)

Keith Q.T. Zhang, electronics engineer, educator. Achievements include research in wireless communications. Member of Institute of Electrical and Electronics Engineers (associate editor letters 2000-2008). B. England, Tsinghua University, Beijing, 1970. Doctor of Philosophy, McMaster University, Hamilton, Ontario, Canada, 1985. Senior member technical staff Spar Aerospace Ltd, Satellite Communications Division, Montreal, 1991--1993. Professor Ryerson, Toronto, Canada, 1993--2002, City University, Hong Kong, since 2000.

Preface xvii

Acknowledgments xix

1 Introduction 1

1.1 Resources for wireless communications 3

1.2 Shannon's theory 3

1.3 Three challenges 4

1.4 Digital modulation versus coding 5

1.5 Philosophy to combat interference 6

1.6 Evolution of processing strategy 7

1.7 Philosophy to exploit two-dimensional random fields 7

1.8 Cellular: Concept, Evolution, and 5G 8

1.9 The structure of this book 10

1.10 Repeatedly used abbreviations and math symbols 10

Problems 12

References 12

2 Mathematical Background 14

2.1 Introduction 14

2.2 Congruence mapping and signal spaces 14

2.3 Estimation methods 19

2.3.1 Maximum likelihood estimation (MLE) 20

2.3.2 Maximum a posteriori estimation 21

2.4 Commonly used distributions in wireless 21

2.4.1 Chi-square distributions 21

2.4.2 Gamma distribution 25

2.4.3 Nakagami distribution 26

2.4.4 Wishart distribution 26

2.5 The calculus of variations 28

2.6 Two inequalities for optimization 29

2.6.1 Inequality for Rayleigh quotient 29

2.6.2 Hadamard inequality 29

2.7 Q-function 30

2.8 The CHF method and its skilful applications 32

2.8.1 Gil-Pelaez's lemma 32

2.8.2 Random variables in denominators 32

2.8.3 Parseval's theorem 33

2.9 Matrix operations and differentiation 33

2.9.1 Decomposition of a special determinant 33

2.9.2 Higher order derivations 33

2.9.3 Kronecker product 34

2.10 Additional reading 34

Problems 34

References 35

3 Channel Characterization 37

3.1 Introduction 37

3.2 Large-scale propagation loss 38

3.2.1 Free-space propagation 39

3.2.2 Average large-scale path loss in mobile 40

3.2.3 Okumura's model 40

3.2.4 Hata's model 42

3.2.5 JTC air model 42

3.3 Lognormal shadowing 43

3.4 Multipath characterization for local behavior 44

3.4.1 An equivalent bandwidth 44

3.4.2 Temporal evolution of path coefficients 49

3.4.3 Statistical description of local fluctuation 50

3.4.4 Complex Gaussian distribution 50

3.4.5 Nakagami fading 51

3.4.6 Clarke-Jakes model 52

3.5 Composite model to incorporate multipath and shadowing 53

3.6 Example to illustrate the use of various models 54

3.6.1 Static design 54

3.6.2 Dynamic design 55

3.6.3 Large-scale design 56

3.7 Generation of correlated fading channels 56

3.7.1 Rayleigh fading with given covariance structure 56

3.7.2 Correlated Nakagami fading 57

3.7.3 Complex correlated Nakagami channels 62

3.7.4 Correlated lognormal shadowing 62

3.7.5 Fitting a lognormal sum 64

3.8 Summary 65

3.9 Additional reading 66

Problems 66

References 68

4 Digital Modulation 70

4.1 Introduction 70

4.2 Signals and signal space 71

4.3 Optimal MAP and ML receivers 72

4.4 Detection of two arbitrary waveforms 74

4.5 MPSK 77

4.5.1 BPSK 77

4.5.2 QPSK 79

4.5.3 MPSK 81

4.6 M-ary QAM 85

4.7 Noncoherent scheme-differential MPSK 88

4.7.1 Differential BPSK 88

4.7.2 Differential MPSK 89

4.7.3 Connection to MPSK 89

4.8 MFSK 90

4.8.1 BFSK with coherent detection 90

4.9 Noncoherent MFSK 92

4.10 Bit error probability versus symbol error probability 93

4.10.1 Orthogonal MFSK 93

4.10.2 Square M-QAM 93

4.10.3 Gray-mapped MPSK 94

4.11 Spectral efficiency 96

4.12 Summary of symbol error probability for various schemes 97

4.13 Additional reading 98

Problems 98

References 102

5 Minimum Shift Keying 103

5.1 Introduction 103

5.2 MSK 104

5.3 de Buda's approach 105

5.3.1 The basic idea and key equations 105

5.4 Properties of MSK signals 106

5.5 Understanding MSK 108

5.5.1 MSK as FSK 108

5.5.2 MSK as offset PSK 109

5.6 Signal space 109

5.7 MSK power spectrum 110

5.8 Alternative scheme-differential encoder 113

5.9 Transceivers for MSK signals 115

5.10 Gaussian-shaped MSK 116

5.11 Massey's approach to MSK 117

5.11.1 Modulation 117

5.11.2 Receiver structures and error performance 117

5.12 Summary 119

Problems 119

References 120

6 Channel Coding 121

6.1 Introduction and philosophical discussion 121

6.2 Preliminary of Galois fields 123

6.2.1 Fields 123

6.2.2 Galois fields 124

6.2.3 The primitive element of GF(q) 124

6.2.4 Construction of GF(q) 124

6.3 Linear block codes 126

6.3.1 Syndrome test 129

6.3.2 Error-correcting capability 132

6.4 Cyclic codes 134

6.4.1 The order of elements: a concept in GF(q) 134

6.4.2 Cyclic codes 136

6.4.3 Generator, parity check, and syndrome polynomial 137

6.4.4 Systematic form 138

6.4.5 Syndrome and decoding 140

6.5 Golay code 141

6.6 BCH codes 141

6.6.1 Generating BCH codes 142

6.6.2 Decoding BCH codes 143

6.7 Convolutional codes 146

6.7.1 Exampl