Gründinger Statistical Robust Beamforming for Broadcast Channels and Applications in Satellite Communication

1. Auflage 2019
ISBN: 978-3-030-29578-3
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 22, 261 Seiten

Reihe: Foundations in Signal Processing, Communications and Networking

This book investigates adaptive physical-layer beamforming and resource allocation that ensure reliable data transmission in the multi-antenna broadcast channel. The book provides an overview of robust optimization techniques and modelling approximations to deal with stochastic performance metrics. One key contribution of the book is a closed-form description of the achievable rates with unlimited transmit power for a rank-one channel error model. Additionally, the book provides a concise duality framework to transform mean square error (MSE) based beamformer designs, e.g., quality of service and balancing optimizations, into equivalent uplink filter designs. For the algorithmic solution, the book analyses the following paradigm: transmission to receivers with large MSE targets (low demands) is switched off if the transmit power is low. The book also studies chance constrained optimizations for limiting the outage probability. In this context, the book provides two novel conservative outage probability approximations, that result in convex beamformer optimizations. To compensate for the remaining inaccuracy, the book introduces a post-processing power allocation. Finally, the book applies the introduced beamformer designs for SatCom, where interference from neighboring spotbeams and channel fading are the main limitations.

Andreas Gründinger was born in Landshut (Germany) on October 13th, 1981. After secondary school, he started an apprenticeship as industrial electrician at BMW in Landshut, which he finished with high distinction in 2001. Three years later, he got the university acceptance, again with high distinction, from the local vocational high school. Andreas started his university studies in 2004 and received the B.Sc. degree in electrical engineering and M.Sc.(hons) in systems of information and multimedia technology, both from the Technische Universität München (TUM), Germany, in 2008 and 2010, respectively. From 2010 to 2015, he worked towards the doctoral degree in engineering at the Associate Institute for Signal Processing. He was recipient of the Qualcomm Innovation Fellowship Award in 2012 for his research proposal on coordinated communication in multi-satellite systems, authored and co-authored more than twenty conference papers and a journal paper and wrote two book chapters in 'Communications in Interference Limited Networks'. Since 2016, he is Development Engineer at the Center of Competence for Digital Signal Processing at Rohde & Schwarz, München, Germany. In 2018, he defended his dissertation on robust beamforming. His research interests include signal processing for wireless communications, with special emphasis on transceiver designs and resource allocation for MIMO systems, robust optimization, local and global optimization, and applications in satellite communication, massive MIMO, and relaying.

Autoren/Hrsg.

Gründinger, Andreas

Inhaltsverzeichnis

1;Preface;7
2;Acknowledgments;8
3;Introduction;9
4;Zusammenfassung;11
5;Contents;13
6;Acronyms;15
7;Nomenclature;17
8;List of Figures;20
9;List of Tables;22
10;1 Multi-User Downlink Communication;23
10.1;1.1 Gaussian Vector Broadcast Channel Model;27
10.2;1.2 Quality-of-Service Optimization and Rate Balancing;28
10.2.1;1.2.1 Quality-of-Service Optimization Problem;29
10.2.2;1.2.2 Rate Balancing Problem;30
10.2.3;1.2.3 Relation Between the Problems;31
10.3;1.3 Solutions for Perfect Transmitter Channel Knowledge;31
10.3.1;1.3.1 Uplink–Downlink Duality and Uplink Power Allocation;32
10.3.2;1.3.2 Convex Problem Reformulations;35
10.3.3;1.3.3 Quality-of-Service Feasibility;37
10.4;1.4 Beamformer Design with Multiple Power Constraints;39
10.4.1;1.4.1 QoS Optimization and Balancing with Multiple Power Constraints;40
10.5;1.5 Outline of the Chapters and the Contributions;42
10.5.1;1.5.1 Contributions for Ergodic Rates with Multiplicative Channel Errors;44
10.5.2;1.5.2 Contributions for Average MSEs with Additive Channel Errors;44
10.5.3;1.5.3 Contributions for Outage Rate Requirements;46
10.5.4;1.5.4 Applications to Satellite Communication;47
11;2 Models for Incomplete Channel Knowledge;50
11.1;2.1 Additive Error Models;51
11.1.1;2.1.1 Deterministic Channel Models;52
11.1.2;2.1.2 Stochastic Channel Models;53
11.1.3;2.1.3 Quantization Errors and Delays;54
11.2;2.2 Multiplicative Error Models;55
11.2.1;2.2.1 Deterministic Channel and Shadow Fading;55
11.2.2;2.2.2 Rank-One Channel Covariance Matrix;56
11.3;2.3 Multiplicative Approximations for Additive Fading;57
12;3 Precoder Design for Ergodic Rates with Multiplicative Fading;60
12.1;3.1 Closed-Form Rate Expressions;62
12.2;3.2 Lower and Upper Rate Bounds;63
12.2.1;3.2.1 Generalized Zero-Forcing Lower Bound;63
12.2.2;3.2.2 Bounds for Adaptive Beamforming;65
12.2.3;3.2.3 QoS and Balancing Optimization with Rate Bounds;67
12.2.3.1;3.2.3.1 Iterative Inner Rate Balancing Optimization;69
12.2.3.2;3.2.3.2 Outer Worst-Case Noise Optimization;71
12.2.3.3;3.2.3.3 Uplink–Downlink Transformation;73
12.3;3.3 Quality-of-Service Feasibility Region;73
12.4;3.4 Post-Processing Power Allocation;76
12.4.1;3.4.1 Post-Processing for QoS Optimization;77
12.4.2;3.4.2 Post-Processing for Ergodic Rate Balancing;78
12.5;3.5 Sequential Approximation Strategy;79
12.5.1;3.5.1 Sequential Quality-of-Service Optimization;81
12.5.2;3.5.2 Sequential Ergodic Rate Balancing;83
12.6;3.6 Branch and Bound Method;86
12.7;3.7 Numerical Optimization Results for Ergodic Rates;88
12.7.1;3.7.1 Power Minimization Results;89
12.7.2;3.7.2 Rate Balancing Results;91
12.7.3;3.7.3 Results for Sequential QoS Optimization and Balancing;93
13;4 Mean Square Error Transceiver Design for AdditiveFading;97
13.1;4.1 Mean Square Error Based Rate Bounds;99
13.2;4.2 Closed-Form Mean Square Error Expressions;100
13.3;4.3 Quality-of-Service Optimization;103
13.3.1;4.3.1 MSE Based Uplink–Downlink Dualities;106
13.3.2;4.3.2 Power Allocation and Worst-Case Noise Search;112
13.3.3;4.3.3 Primal Reconstruction of Beamformers;114
13.3.4;4.3.4 Expectation Evaluation for Alternating Convex Optimization;115
13.4;4.4 Quality-of-Service Feasibility Region;116
13.5;4.5 Average Mean Square Error Balancing;118
13.5.1;4.5.1 Alternating Convex Search for Balancing;121
13.5.2;4.5.2 Uplink–Downlink Dualities for Balancing;124
13.5.3;4.5.3 Iterative Minimum Mean Square Error Search;127
13.5.3.1;4.5.3.1 Uplink Weighted Sum-MSE Minimization;129
13.6;4.6 Ergodic Rate Balancing Approximations;130
13.7;4.7 Numerical Results for Mean Square Error Optimizations;132
13.7.1;4.7.1 Max–Min Mean Square Error Optimization Results;133
13.7.1.1;4.7.1.1 Per-User Mean Square Error Balancing Results;134
13.7.1.2;4.7.1.2 Per-user MSE Balancing Versus Weighted Sum-MSE Balancing;135
13.7.1.3;4.7.1.3 Complexity Comparison for MSE Balancing;137
13.7.2;4.7.2 Sum Mean Square Error Minimization Analysis;139
13.7.3;4.7.3 Approximate Rate Balancing Using MSE Optimizations;143
14;5 Outage Constrained Beamformer Design;146
14.1;5.1 Chance-Constrained Optimization;147
14.1.1;5.1.1 Basic Mathematical Background;147
14.1.2;5.1.2 Chance Constraints in Downlink Communication;150
14.2;5.2 Multiplicative Fading Example;152
14.3;5.3 Outage Probability Computation for Additive Fading;155
14.4;5.4 Power Allocation and Feasibility for Fixed Beamforming;156
14.4.1;5.4.1 Characteristic of the Chance Constraints;157
14.4.2;5.4.2 Fixed Point Framework for Power Allocation;159
14.4.3;5.4.3 Feasibility Detection for QoS Optimization;161
14.5;5.5 Robust Uncertainty Reformulations;162
14.5.1;5.5.1 Sphere Bounds for the Additive Channel Errors;162
14.5.2;5.5.2 Quadratic Bounds for the Orthogonal Channel Errors;164
14.5.3;5.5.3 QoS Optimization with Uncertainty Constraints;166
14.5.4;5.5.4 Balancing Optimization with Uncertainty Constraints;167
14.5.5;5.5.5 Beamformer Reconstruction and Direct Beamformer Optimization;168
14.6;5.6 Tractable Bounds with Concentration Inequalities;168
14.6.1;5.6.1 Markov's Inequality Based MSE Approximation;169
14.6.2;5.6.2 Bernstein-Type Inequality Bound for the SINR;169
14.6.3;5.6.3 Bernstein-Type Inequality Bound for the MSE;170
14.6.4;5.6.4 Related MSE Based Chance Constraint Approximation;173
14.7;5.7 Numerical Results for Chance-Constrained Optimization;174
14.7.1;5.7.1 Post-Processing Power Allocation for QoS Optimization;175
14.7.2;5.7.2 QoS Optimization with Channel Uncertainty Constraints;177
14.7.3;5.7.3 Rate Balancing with Approximated Chance Constraints;182
14.7.4;5.7.4 Comparison of the MSE Based Approximations;187
15;6 Applications in Satellite Communication;190
15.1;6.1 Satellite Channel Characteristic;191
15.1.1;6.1.1 Multi-Spotbeam Model;191
15.1.2;6.1.2 Fading Characteristics;194
15.1.3;6.1.3 Channel Error Model;195
15.2;6.2 Balancing Optimization for Satellite Communication;196
15.3;6.3 Ergodic Rate and Mean Square Error Optimization;197
15.4;6.4 Results for Rate and Mean Square Error Balancing;198
15.4.1;6.4.1 Results for Rain and Rank-One Additive Channel Fading;198
15.4.2;6.4.2 Results for Rain and Full-Rank Additive Channel Fading;200
15.4.3;6.4.3 Performance Limits with Per-Antenna Power Constraints;202
15.5;6.5 Outage Constrained Rate Optimization;205
15.5.1;6.5.1 Conservative Inner Optimization;206
15.5.2;6.5.2 Outer Optimization of Priors;208
15.6;6.6 Results for Outage Constrained Rate Balancing;209
15.6.1;6.6.1 Equal Fading Conditions for the Terminals;210
15.6.2;6.6.2 Effects for Distinct Fading Conditions;213
15.6.3;6.6.3 Outage Probabilities at the Terminals;214
16;7 Summary, Conclusions, and Open Research;217
16.1;7.1 Research Results for Robust Beamforming;217
16.1.1;7.1.1 Achievements and Open Problems for Multiplicative Channel Errors;217
16.1.2;7.1.2 Summary of Results for Average MSE Optimization;218
16.1.3;7.1.3 Contributions for Outage Rate Requirements;219
16.1.4;7.1.4 Summary and Conclusions for Satellite Communication;220
16.2;7.2 Other Research on Robust Beamforming;220
17;A Additional Information;222
17.1;A.1 Basic Properties of the Rate Based Optimizations;222
17.1.1;A.1.1 Positivity and Monotonicity for the Optimum of the QoS Problem;222
17.1.2;A.1.2 Positivity and Monotonicity for the Optimum of the Rate Balancing Problem;223
17.1.3;A.1.3 Relation Between the QoS Optimization and the Rate Balancing Problem;223
17.2;A.2 Interference Functions and Property Preserving Transforms;223
17.3;A.3 Ergodic Rate Bounds for Multiplicative Fading;227
17.3.1;A.3.1 Derivation of Lower and Upper Bounds on the Ergodic Rate;227
17.4;A.4 Feasible QoS Region with Ergodic Rate Bounds;229
17.5;A.5 On Uniqueness of the QoS Optimal Power Allocation;230
17.6;A.6 Duality for Second Order Cone Programs;231
17.6.1;A.6.1 Application to Uplink–Downlink Duality for MSE Based QoS Optimization;235
17.6.2;A.6.2 Reconstruction of the Primal Variables;236
17.7;A.7 Properties of the Dual Uplink MSE Optimizations;237
17.8;A.8 Some Distribution and Quantile Functions;239
18;References;243
19;Index;259