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Table of contents
Contents
Page
List of Figures
List of Tables
I Motivation and Background
1 Introduction
1.1 Motivation and State of the Art
1.2 Organization of the thesis
1.3 Background Information
1.3.1 Background on Beamforming inMaMIMO
1.3.2 AlternatingMinorization
1.3.3 Background on Compressed Sensing
II Beamforming Techniques forMassive MIMO
2 Hybrid Beamforming
2.0.1 Summary of the Chapter
2.0.2 Phase Shifter Architecture
2.1 HBF Design using WSMSE forMulti-User MIMO
2.1.1 WSR Optimization in terms ofWSMSE
2.1.2 Design of the Analog Beamformer with Perfect CSIT
2.1.3 Mixed Time Scale Adaptation
2.2 Hybrid Beamforming for Globally Converging Phasor Design
2.2.1 AlternatingMinorization Approach
2.2.2 Digital BF Design
2.2.3 Design of Unconstrained Analog BF
2.2.4 Design of Phase Shifter Constrained Analog Beamformer
2.2.5 Simulation results
2.3 Hybrid Beamforming under Realistic Power Constraints
2.3.1 Digital BF Design
2.3.2 Optimization of Power Variables
2.3.3 Design of Unconstrained Analog BF
2.3.4 Hybrid Beamforming Design with Per-Antenna Power Constraints
2.3.5 AlgorithmConvergence
2.3.6 Conclusion
2.4 Hybrid Beamforming Design forMulti-User MIMO-OFDM Systems
2.4.1 MIMO OFDMChannelModel
2.4.2 WSRMaximization viaMinorization and Alternating Optimization
2.4.3 Digital BF Design
2.4.4 Design of Unconstrained Analog BF
2.4.5 AlgorithmConvergence
2.4.6 Analysis on the number of RF Chains and HBF Performance
2.4.7 Simulation Results
2.4.8 Conclusions and Perspectives
3 Hybrid Beamforming for Full-Duplex Systems
3.1 Introduction
3.1.1 Summary of the Chapter
3.2 Full-Duplex BidirectionalMIMO SystemModel
3.2.1 ChannelModel
3.3 WSR maximization through WSMSE
3.3.1 Two-stage transmit BF design
3.3.2 Hybrid Combiner/Two-Stage BF Capabilities for SI Power Reduction
3.3.3 Simulation Results
3.3.4 Conclusion
3.4 Robust Beamforming Design under Partial CSIT
3.4.1 EWSR maximization through alternating minorization
3.4.2 Two-stage transmit BF design
3.4.3 Optimization of streampowers
3.5 Simulation Results
3.6 Conclusion
4 NoncoherentMulti-UserMIMO Communications using Covariance CSIT
4.1 Introduction
4.2 Streamwise IBC SignalModel
4.3 Max WSR with Perfect CSIT
4.3.1 FromMax WSR toMin WSMSE
4.3.2 Minorization (DC Programming)
4.3.3 PathwiseWirelessMIMO ChannelModel
4.4 MIMO Interference Alignment (IA)
4.5 Expected WSR (EWSR)
4.5.1 Massive EWSR with pwCSIT
4.5.2 Interference management by Tx/Rx
4.5.3 Comparison of instantaneous CSIT and pathwise CSIT WSR at low SNR .
4.5.4 Comparison of instantaneous CSIT and pathwise CSIT WSR at high SNR .
4.6 Simulation Results
4.6.1 Conclusions and Perspectives
5 Rate Splitting for Pilot Contamination
5.1 Introduction
5.1.1 Summary of this Chapter
5.2 System model
5.2.1 Assumptions on the user channel
5.2.2 Channel estimation
5.2.3 Rate Splitting in Downlink transmissions
5.2.4 Spectral efficiency
5.3 Power optimization and precoding design
5.3.1 Power optimization
5.3.2 Precoding design for common message
5.4 Simulation Results
5.5 Concluding Remarks
III Stochastic Geometry based Large System Analysis
6 Asymptotic Analysis of Reduced Order Zero Forcing Beamforming
6.1 Introduction
6.1.1 Summary of this Chapter
6.2 Multi-UserMIMO SystemModel
6.3 Large System Analysis of Optimal BF-WSMSE
6.4 Large System Analysis of Optimal DPC
6.5 Reduced Order ZF
6.6 Large System Analysis for RO-ZF, Full Order ZF and ZF-DPC
6.6.1 Optimization of user powers pk
6.7 Optimization of the ZF Order
6.8 Simulation Results
6.9 Extension of RO-ZF BF to IBC under Partial CSIT
6.9.1 Channel and CSITModel
6.9.2 Partial CSIT BF based on Different Channel Estimates
6.9.3 BF with Partial CSIT
6.9.4 Max EWSR ZF BF in theMaMISO limit (ESEI-WSR)
6.9.5 Reduced Order ZF with Partial CSIT
6.9.6 Large System Analysis for RO-ZF and Full Order ZF
6.9.7 Optimization of the ZF Order
6.9.8 Simulation Results
6.9.9 Conclusions
7 Stochastic Geometry based Large SystemAnalysis
7.0.1 Summary of this Chapter
7.1 Massive MISO Stochastic Geometry based Large System Analysis
7.1.1 MISO IBC SignalModel
7.1.2 Channel and CSITModel
7.1.3 Various Channel Estimates for Partial CSIT
7.1.4 Beamforming with Partial CSIT
7.1.5 Further Considerations on EWSR Bounds
7.1.6 Asymptotic Analysis: Stochastic GeometryMaMISO Regime
7.1.7 Computation of eigenvalues ofWk,bi
7.1.8 EWSMSE BF in theMaMISO Stochastic Geometry Regime
7.1.9 Deterministic Equivalent of Auxiliary Quantities
7.1.10 Simplified SumRate Expressions with Different BF and Channel Estimators
7.1.11 Simulation Results
7.1.12 Channel Estimation Error/1/P
7.1.13 Constant Channel Estimation Error
7.1.14 Conclusion
IV Approximate Bayesian Inference for Sparse Bayesian Learning
8 Static and Dynamic Sparse Bayesian Learning usingMean Field Variational Bayes
8.1 Introduction
8.1.1 Summary of the Chapter
8.2 SignalModel-SBL
8.3 SBL using Type-IIML
8.3.1 Variational Interpretation of SBL
8.3.2 Overview of Fast SBL Algorithms
8.3.3 Variational Bayes
8.4 SAVE Sparse Bayesian Learning
8.4.1 Computational Complexity
8.4.2 Convergence Analysis of SAVE orMean Field Approximation
8.4.3 Sparsity Analysis with SAVE
8.4.4 Simulation results
8.4.5 Conclusion
8.4.6 Open Issues: Reduced Complexity Linear Tx/Rx Computation
8.5 Dynamic SBL-SystemModel
8.5.1 Gaussian PosteriorMinimizing the KL Divergence
8.6 SAVE SBL and Kalman Filtering
8.6.1 Diagonal AR(1) ( DAR(1) ) Prediction Stage
8.6.2 Measurement or Update Stage
8.6.3 Fixed Lag Smoothing
8.6.4 Estimation of Hyperparameters
8.7 VB-KF for Diagonal AR(1) (DAR(1))
8.7.1 DAR(1) Prediction Stage
8.7.2 Measurement or Update Stage
8.7.3 Fixed Lag Smoothing
8.7.4 Simulation Results
9 Sparse Bayesian Learning usingMessage Passing Algorithms
9.0.1 Summary of this Chapter
9.1 Approximate Inference Cost Functions: An Overview
9.1.1 Region Based Free Energy
9.1.2 Combined BP/MF Approximation
9.2 Dynamic SBL SystemModel
9.2.1 BP-MF based Static SBL
9.2.2 Dynamic BP-MF-EP based SBL
9.3 Optimal Partitioning of BP and MF nodes
9.3.1 Optimal Partitioning for Static SBL:
9.3.2 Optimal Partitioning for DAR-SBL:
9.4 Simulation Results
9.4.1 Conclusions
9.5 Posterior Variance Prediction: Large System Analysis for SBL using BP
9.5.1 Iterations inMatrix Form
9.5.2 Convergence Analysis of BP
9.5.3 Scalar Iterations
9.5.4 Original AMP Iterations and SBL-AMP
9.6 Bayesian SAGE (BSAGE)
9.7 Concluding Remarks on Combined BP-MF-EP DAR-SBL
9.8 Towards a Convergent AMP-SBL Solution
9.8.1 Fixed Points of Bethe Free Energy and GSwAMP-SBL
9.9 GSwAMP-SBL based Dynamic AR-SBL
9.10 GSwAMP-SBL for Nonlinear Kalman Filtering
9.10.1 Diagonal AR(1) ( DAR(1) ) Prediction Stage
9.10.2 Measurement Update (Filtering) Stage
9.10.3 Lag-1 Smoothing Stage
9.11 Simulation Results
9.11.1 ill-conditioned A case:
9.11.2 Non-zero mean A case:
9.11.3 Rank Deficient A case (Figure 9.8):
9.12 Conclusions
9.12.1 Conclusions and Perspectives
10 Sparse Bayesian Learning for Tensor Signal Processing
10.1 Summary of this Chapter
10.1.1 Tensor Notations
10.2 Hierarchical ProbabilisticModel
10.2.1 Application-MultipathWireless Channel Estimation
10.3 Variational Bayesian Inference for JointDictionary Learning and Sparse Signal Recovery
10.4 Kronecker Structured Dictionary Learning
10.4.1 SAVED-KS Sparse Bayesian Learning
10.4.2 Joint VB for KS Dictionary Learning
10.5 Identifiability of KS Dictionary Learning
10.5.1 Identifiability for mix of parametric and non-parametric KS factors
10.5.2 Simulation Results
10.5.3 Conclusions and Perspectives
10.6 Joint Dictionary Learning and Dynamic Sparse State Vector Estimation
10.6.1 Dynamic BP-MF-EP based SBL
10.6.2 Suboptimality of SAVED-KS DL and Joint VB
10.7 Optimal Partitioning of theMeasurement Stage and KS DL
10.8 Simulation Results
10.9 Conclusions and Perspectives
Bibliography
