MIMO wireless communications over generalized fading channels

290 Pages·2017·13.311 MB·English

by  Brijesh Kumbhani, Rakhesh Singh Kshetrimayum

MIMO
Wireless
Communications
over Generalized
Fading Channels

MIMO
Wireless
Communications
over Generalized
Fading Channels
Brijesh Kumbhani
Rakhesh Singh Kshetrimayum
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Brijesh Kumbhani would like to dedicate this book
to his elder brother
Late Chaturbhai Kumbhani.
Rakhesh Singh Kshetrimayum would like to dedicate
this book
to his mom for her indomitable courage.

Contents
List of Figures xiii
List of Tables xvii
Preface xix
Acknowledgments xxi
1 Introduction to MIMO Systems 1
1.1 Evolution of MIMO systems . . . . . . . . . . . . . . . . . . 2
1.1.1 Higher order modulation schemes . . . . . . . . . . . . 3
1.1.2 Diversity techniques . . . . . . . . . . . . . . . . . . . 5
1.1.2.1 Selection diversity . . . . . . . . . . . . . . . 6
1.1.2.2 Equal gain combining . . . . . . . . . . . . . 6
1.1.2.3 Maximal ratio combining . . . . . . . . . . . 7
1.2 MIMO system and channel models . . . . . . . . . . . . . . . 8
1.3 Open loop MIMO systems . . . . . . . . . . . . . . . . . . . 10
1.3.1 Spatial multiplexing . . . . . . . . . . . . . . . . . . . 11
1.3.2 Space time block codes . . . . . . . . . . . . . . . . . 13
1.3.3 Spatial modulation . . . . . . . . . . . . . . . . . . . . 16
1.4 Closed loop MIMO systems . . . . . . . . . . . . . . . . . . . 20
1.4.1 Power allocation . . . . . . . . . . . . . . . . . . . . . 20
1.4.2 Transmit antenna selection . . . . . . . . . . . . . . . 23
1.4.2.1 Selection combining at the receiver. . . . . . 26
1.4.2.2 MRC at the receiver . . . . . . . . . . . . . . 26
1.4.3 Transmit antenna selection based spatial modulation . 27
2 Generalized Fading Channels 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Introduction to fading channels . . . . . . . . . . . . . . . . 31
2.2.1 Fast and slow fading . . . . . . . . . . . . . . . . . . . 31
2.2.2 Frequency flat and frequency selective fading . . . . . 31
2.3 Commonly used fading distributions . . . . . . . . . . . . . . 32
2.3.1 Rayleigh fading . . . . . . . . . . . . . . . . . . . . . . 33
2.3.2 Hoyt fading . . . . . . . . . . . . . . . . . . . . . . . . 33
vii
viii Contents
2.3.3 Rician fading . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 Generalized fading distributions . . . . . . . . . . . . . . . . 34
2.4.1 Nakagami-m fading. . . . . . . . . . . . . . . . . . . . 35
2.4.1.1 Physical model . . . . . . . . . . . . . . . . . 35
2.4.1.2 CDF and MGF of Nakagami-m fading . . . . 36
2.4.1.3 Special cases . . . . . . . . . . . . . . . . . . 37
2.4.2 η µ fading . . . . . . . . . . . . . . . . . . . . . . . . 38
−
2.4.2.1 Physical model . . . . . . . . . . . . . . . . . 39
2.4.2.2 η µ fading: PDF of SNR . . . . . . . . . . 41
−
2.4.2.3 CDF and MGF of η µ fading . . . . . . . . 41
−
2.4.2.4 Special cases . . . . . . . . . . . . . . . . . . 42
2.4.3 κ µ fading. . . . . . . . . . . . . . . . . . . . . . . . 44
−
2.4.3.1 Physical model . . . . . . . . . . . . . . . . . 44
2.4.3.2 CDF and MGF of κ µ fading . . . . . . . . 46
−
2.4.3.3 Special cases . . . . . . . . . . . . . . . . . . 46
2.4.4 α µ fading . . . . . . . . . . . . . . . . . . . . . . . 48
−
2.4.4.1 Physical model . . . . . . . . . . . . . . . . . 48
2.4.4.2 CDF and MGF of α µ fading . . . . . . . . 50
−
2.4.4.3 Special cases . . . . . . . . . . . . . . . . . . 51
2.5 Generation of channel coefficients . . . . . . . . . . . . . . . 54
2.5.1 Channel coefficients for commonly used fading
distributions . . . . . . . . . . . . . . . . . . . . . . . 54
2.5.2 Channel coefficients for generalized fading distributions 56
2.5.2.1 Generating Nakagami-m faded channel
coefficients . . . . . . . . . . . . . . . . . . . 56
2.5.2.2 Generating η µ faded channel coefficients . 58
−
2.5.2.3 Generating κ µ faded channel coefficients . 59
−
2.5.2.4 Generating α µ faded channel coefficients . 60
−
3 Spatial Multiplexing 63
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2 Diversity multiplexing trade-off and the capacity of MIMO
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3 Spatial multiplexing . . . . . . . . . . . . . . . . . . . . . . 66
3.3.1 Detection complexity of spatially multiplexed systems 69
3.4 Nakagami-m fading channel model for spatially multiplexed
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5 Spatial multiplexing over η µ fading channels . . . . . . . . 75
−
3.6 Spatial multiplexing over κ µ fading channels . . . . . . . 78
−
3.7 Spatial multiplexing over α µ fading channels . . . . . . . 81
−
Contents ix
4 Spatial Modulation 87
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 SM transmission reception schemes . . . . . . . . . . . . . . 88
4.3 Performance analysis of SM MIMO systems . . . . . . . . . . 90
4.3.1 Outage probability . . . . . . . . . . . . . . . . . . . . 91
4.3.2 Symbol error rate. . . . . . . . . . . . . . . . . . . . . 91
4.3.3 Channel capacity . . . . . . . . . . . . . . . . . . . . . 93
4.4 Performance of SM systems over Nakagami-m fading channels 94
4.4.1 Outage probability . . . . . . . . . . . . . . . . . . . . 94
4.4.2 Symbol error rate. . . . . . . . . . . . . . . . . . . . . 95
4.5 Error performance of SM systems over κ µ fading channels 99
−
4.6 Error performance of SM systems over η µ fading channels 103
−
4.7 Error performance of SM systems over α µ fading channels 105
−
4.8 Generalized spatial modulation . . . . . . . . . . . . . . . . . 107
5 Transmit Antenna Selection 111
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2 Antenna selection criteria . . . . . . . . . . . . . . . . . . . . 113
5.2.1 Received power based antenna selection . . . . . . . . 113
5.2.1.1 Norm based transmit antenna selection . . . 114
5.2.2 Capacity based antenna selection . . . . . . . . . . . . 115
5.3 TAS system model . . . . . . . . . . . . . . . . . . . . . . . . 116
5.4 TAS over Nakagami-m fading channels . . . . . . . . . . . . 119
5.4.1 PDF of received SNR after antenna selection . . . . . 119
5.4.2 Outage probability . . . . . . . . . . . . . . . . . . . . 121
5.4.3 Error performance analysis . . . . . . . . . . . . . . . 124
5.4.3.1 BPSK and MPSK modulation schemes . . . 125
5.4.3.2 MQAM and QPSK modulation schemes . . . 127
5.5 TAS over κ µ fading channels . . . . . . . . . . . . . . . . 129
−
5.5.1 PDF of received SNR after antenna selection . . . . . 130
5.5.2 Outage probability . . . . . . . . . . . . . . . . . . . . 131
5.5.3 Error performance . . . . . . . . . . . . . . . . . . . . 132
5.5.4 BPSK and MPSK modulation schemes. . . . . . . . . 134
5.5.5 MQAM and QPSK modulation schemes . . . . . . . . 136
5.5.6 Channel capacity . . . . . . . . . . . . . . . . . . . . . 136
5.6 TAS over η µ fading channels . . . . . . . . . . . . . . . . 139
−
5.6.1 PDF and MGF of received SNR after antenna selection 140
5.6.2 Probability of error. . . . . . . . . . . . . . . . . . . . 142
5.6.2.1 Approximate probability of error . . . . . . . 142
5.6.2.2 Exact probability of error . . . . . . . . . . . 143
5.6.2.3 Asymptotic probability of error. . . . . . . . 145
5.6.3 Channel capacity . . . . . . . . . . . . . . . . . . . . . 146
5.7 TAS over α µ fading channels . . . . . . . . . . . . . . . . 149
−