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Cyclic Division Algebras: A Tool for Space–Time Coding
Contents
1 Introduction 1
1.1 Division Algebra Based Codes 2
1.2 Organization 3
2 The MIMO System Model 5
2.1 Introduction 5
2.2 Design Criteria for Space–Time Codes 7
2.3 Modulations and Full-Rate Codes 10
2.4 Decoding 13
2.5 Constellation Shaping 14
3 An Information Theoretic Perspective 21
3.1 Mutual Information of a Gaussian MIMO Channel 22
3.2 The Outage Probability 23
3.3 Diversity-Multiplexing Gain Trade-off
of MIMO Channels 27
3.4 Trade-off Achieving Codes 32
3.5 Non-Vanishing Determinant Codes 37
3.6 Information Preserving Codes 39
4 Cyclic Division Algebras 41
4.1 Fields and Algebras 42
4.2 Algebras on Number Fields 45
4.3 Norm and Ring of Integers 55
4.4 Shaping, Lattices and Discriminant 61
5 Perfect Space–Time Block Codes 69
5.1 Definition of Perfect Space–Time Codes 69
5.2 The Golden Code 72
5.3 A Perfect STBC for 3 Antennas 75
5.4 A Perfect STBC for 4 Antennas 77
5.5 A Perfect STBC for 5 Antennas 79
5.6 A Perfect STBC for 6 Antennas 81
5.7 Optimality of Perfect STBCs 83
6 New Applications and Conclusion 85
6.1 Coding for Wireless Networks 85
6.2 Trellis/Block Coded Modulations 87
6.3 Other Issues 88
6.4 Conclusion 89
Acknowledgments 91
References 93
2010-06-21
OFDM Simulation Using Matlab
CONTENTS
Abstract .............................................................................................. 1
1 Introduction .................................................................................. 1
2 OFDM Transmission .................................................................... 2
2.1 DVB-T Example................................................................... 2
2.2 FFT Implementation............................................................ 4
3 OFDM Reception .......................................................................... 9
4 Conclusion.................................................................................. 11
5 Appendix..................................................................................... 11
5.1 OFDM Transmission......................................................... 11
5.2 OFDM Reception............................................................... 13
5.3 Eq. (2.1.4) vs. IFFT ............................................................ 16
6 References.................................................................................. 17
2010-06-21
Majorization and Matrix-Monotone Functions in Wireless Communications
Contents
1 Introduction 1
1.1 Majorization Theory 1
1.2 Matrix-Monotone Functions 3
1.3 Classification and Organization 4
1.4 Notation 7
2 Majorization Theory 9
2.1 Definition and Examples 10
2.2 Basic Results 18
2.3 Majorization and Optimization 30
3 Matrix-Monotone Functions 33
3.1 Definition and Examples 33
3.2 Basic Characterizations 43
3.3 Matrix Norms 47
3.4 Further Properties 52
4 Application of Majorization in Wireless
Communications 59
4.1 Spatial Correlation in Multiple Antenna Systems 59
4.2 User Distribution in Cellular Communication Systems 86
ix
5 Application of Matrix-Monotone Functions
in Wireless Communications 103
5.1 Generalized Multiple Antenna Performance Measures 103
5.2 Optimization of Matrix-Monotone Functions 114
6 Appendix 133
6.1 Linear Algebra 133
6.2 Convex Optimization 134
7 Acknowledgments 141
References
2010-06-21
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