1 Introduction 1
1.1 MIMO Channels 1
1.2 MIMO Communication Systems 7
1.3 A First Glimpse at Linear Transceivers: Beamforming 9
1.4 Historical Perspective on MIMO Transceivers 16
1.5 Outline 20
2 Majorization Theory 23
2.1 Basic Definitions 23
2.2 Basic Results 27
2.3 Multiplicative Majorization 33
3 Linear MIMO Transceivers 37
3.1 System Model 40
3.2 Problem Formulation 44
3.3 Optimum Linear Receiver 47
3.4 Optimum Linear Transmitter with
Schur-Convex/Concave Cost Functions 55
3.5 Optimum Linear Transmitter with Individual QoS
Constraints 76
3.6 Optimum Linear Transmitter with Arbitrary Cost
Functions 86
3.7 Extension to Multicarrier Systems 98
ix3.8 Summary 100
3.A Appendix: Characterization of BER Function
for QAM Constellations 101
3.B Appendix: Optimum Left Singular Vectors of P 103
3.C Appendix: Optimum Ordering of Eigenvalues 106
3.D Appendix: Proofs of Schur-Concavity/Convexity Lemmas 106
3.E Appendix: Waterfilling Algorithms 109
4 Nonlinear Decision Feedback MIMO Transceivers 113
4.1 System Model 114
4.2 Problem Formulation 118
4.3 Optimum Decision Feedback Receiver 120
4.4 Optimum Transmitter with Global Measure
of Performance 124
4.5 Optimum Transmitter with Individual QoS Constraints 140
4.6 A Dual Form Based on Dirty Paper Coding 149
4.7 A Particular Case: CDMA Sequence Design 155
4.8 Summary 159
4.A Appendix: Mutual Information and Wiener Filter 160
4.B Appendix: Proof of Lemma 4.1 162
4.C Appendix: Proof of Theorem 4.3 163
4.D Appendix: Proof of Procedure in Table 4.1 167
4.E Appendix: Proof of Power Allocation for QoS 168
5 Extensions and Future Lines of Research 175
5.1 Multiuser Systems 175
5.2 Robust Designs for Imperfect CSI 179
5.3 ML Decoding 182
5.4 Information-Theoretic Approach 184
A Convex Optimization Theory 185
A.1 Convex Problems 186
A.2 Classes of Convex Problems 187
A.3 Reformulating a Problem in Convex Form 189A.4 Lagrange Duality Theory and KKT Optimality
Conditions 190
A.5 Sensitivity Analysis 192
A.6 Efficient Numerical Algorithms to Solve
Convex Problems 194
A.7 Primal and Dual Decompositions 194
B Matrix Results 201
B.1 Generalized Triangular Decompositions 201
B.2 Miscellaneous Matrix Results 208
Acknowledgements 211
References