Wideband Beamforming
Contents
About the Series Editors
Preface
1 Introduction
1.1 Array Signal Processing
1.2 Narrowband Beamforming
1.3 Wideband Beamforming
1.4 Wideband Beam Steering
1.4.1 Beam Steering for Narrowband Arrays
1.4.2 Beam Steering for Wideband Arrays
1.4.3 A Unified Interpretation
1.5 Summary
2 Adaptive Wideband Beamforming
2.1 Reference Signal-Based Beamformer
2.1.1 Least Mean Square Algorithm
2.1.2 Normalized Least Mean Square Algorithm
2.1.3 Recursive Least Squares Algorithm
2.1.4 Comparison of Computational Complexities
2.1.5 Frequency-Domain and Subband Adaptive Algorithms
2.1.6 Simulations
2.2 Linearly Constrained Minimum Variance Beamforming
2.2.1 A Simple Formulation of Constraints
2.2.2 Optimum Solution to the LCMV Problem
2.2.3 Frost’s Algorithm for LCMV Beamforming
2.2.4 Simulations
2.3 Constraints Design for LCMV Beamforming
2.3.1 Eigenvector Constraint Design
2.3.2 Design Example
2.3.3 Application to Wideband DOA Estimation
2.4 Generalized Sidelobe Canceller
2.4.1 GSC Structure
2.4.2 GSC with Tapped Delay-Lines
2.4.3 Blocking Matrix Design
2.4.4 Simulations
2.5 Other Minimum Variance Beamformers
2.5.1 Soft Constrained Minimum Variance Beamformer
2.5.2 Correlation Constrained Minimum Variance Beamformer
2.6 Robust Adaptive Beamforming
2.6.1 Spatially Extended Constraints
2.6.2 Norm-Restrained Approaches
2.7 Summary
3 Subband Adaptive Beamforming
3.1 Fundamentals of Filter Banks
3.1.1 Basic Multirate Operations
3.1.2 Perfect Reconstruction Condition for Filter Banks
3.1.3 Oversampled Modulated Filter Banks
3.2 Subband Adaptive Filtering
3.3 General Subband Adaptive Beamforming
3.3.1 Reference Signal Based Beamformer
3.3.2 Generalized Sidelobe Canceller
3.3.3 Reconstruction of the Fullband Beamformer
3.3.4 Simulations
3.4 Subband Adaptive GSC
3.4.1 Structure
3.4.2 Analysis of the Computational Complexity
3.4.3 Reconstruction of the Fullband Beamformer
3.4.4 Simulations
3.5 Temporally/Spatially Subband-Selective Beamforming
3.5.1 Partially Adaptive GSC
3.5.2 Temporally/Spatially Subband-Selective Blocking Matrix
3.5.3 Temporally/Spatially Subband-Selective Transformation Matrix
3.5.4 Application to Subband Adaptive GSC
3.5.5 Extension to the General Subband Adaptive Beamforming Structure
3.5.6 Simulations
3.6 Frequency-Domain Adaptive Beamforming
3.6.1 Frequency-Domain Formulation
3.6.2 Constrained Frequency-Domain Adaptive Algorithm
3.6.3 Frequency-Domain GSC
3.6.4 Simulations
3.7 Transform-Domain Adaptive Beamforming
3.7.1 Transform-Domain GSC
3.7.2 Subband-Selective Transform-Domain GSC
3.7.3 Simulations
3.8 Summary
4 Design of Fixed Wideband Beamformers
4.1 Iterative Optimization
4.1.1 Traditional Methods
4.1.2 Convex Optimization
4.2 The Least Squares Approach
4.2.1 Standard Formulation
4.2.2 Constrained Least Squares
4.3 The Eigenfilter Approach
4.3.1 Standard Approach
4.3.2 Maximum Energy
4.3.3 Total Least Squares
4.4 Summary
5 Frequency Invariant Beamforming
5.1 Introduction
5.2 Design Based on Multi-Dimensional Inverse Fourier Transform
5.2.1 Continuous Sensor and Signals
5.2.2 Discrete Sensors and Signals
5.2.3 Design Examples
5.2.4 Further Generalization to the FIB Design
5.3 Subband Design of Frequency Invariant Beamformers
5.3.1 First Implementation
5.3.2 Second Implementation–Scaled Aperture
5.3.3 Design Examples
5.4 Frequency Invariant Beamforming for Circular Arrays
5.4.1 Phase Mode Processing
5.4.2 FIB Design
5.4.3 Design Example
5.5 Direct Optimization for Frequency Invariant Beamforming
5.5.1 Convex Optimization
5.5.2 Least Squares
5.5.3 Eigenfilter
5.6 Beamspace Adaptive Wideband Beamforming
5.6.1 Structure
5.6.2 Analysis of the Beamspace Adaptive Method
5.6.3 Design of Independent FIBs
5.6.4 Simulations
5.7 Summary
6 Blind Wideband Beamforming
6.1 Blind Source Separation
6.1.1 Introduction
6.1.2 A Blind Source Extraction Example
6.2 Blind Wideband Beamforming
6.3 Blind Beamforming Based on Frequency Invariant Transformation
6.3.1 Structure
6.3.2 The Algorithm
6.3.3 Simulations
6.4 Summary
7 Wideband Beamforming with Sensor Delay-Lines
7.1 Sensor Delay-Line Based Structures
7.1.1 Introduction
7.1.2 Wideband Response of the SDL-Based Structure
7.2 Frequency Invariant Beamforming
7.2.1 2-D Arrays
7.2.2 3-D Arrays
7.3 Adaptive Beamforming
7.3.1 Reference Signal Based Beamformer
7.3.2 Linearly Constrained Minimum Variance Beamformer
7.3.3 Discussions
7.3.4 Simulations
7.4 Beamspace Adaptive Beamforming
7.4.1 Structure
7.4.2 Simulations
7.5 Summary
8 Wideband Beamforming for Multipath Signals
8.1 The Wideband Multipath Problem
8.2 Approach Based on a Narrowband Beamformer
8.2.1 Structure
8.2.2 Simulations
8.3 Approach Based on Blind Source Separation
8.3.1 Structure
8.3.2 Simulations
8.4 MIMO System
8.4.1 Evolution to a MIMO System
8.4.2 MIMO Beamforming and Equalization
8.5 Summary
Appendix A: Matrix Approximation
Appendix B: Differentiation with Respect to a Vector
Appendix C: Genetic Algorithm
C.1 The Principle
C.1.1 Chromosome Representation
C.1.2 Parent Selection
C.1.3 Genetic Operation
C.1.4 Fitness Evaluation
C.1.5 Initialization
C.1.6 Termination
C.2 Design Example in Section 3.5.2
Bibliography
Index