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

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

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