Array processing: Kronecker product beamforming

Intro; Abstract; Contents; Acronyms; 1 Introduction; 1.1 Beamforming; 1.2 Organization of the Work; References; 2 Problem Formulation with Uniform Linear Arrays; 2.1 Signal Model; 2.2 Beamforming with Kronecker Product Filters; 2.3 Performance Measures; References; 3 Beamforming with Uniform Linear Arrays; 3.1 Fixed Beamformers; 3.1.1 Delay and Sum; 3.1.2 Partial Maximum DF; 3.1.3 Maximum DF; 3.1.4 Null Steering; 3.2 Adaptive Beamformers; 3.2.1 Other Measures; 3.2.2 Wiener; 3.2.3 Tradeoff; 3.2.4 MVDR; 3.2.5 LCMV; 3.2.6 Maximum SNR; 3.3 Combined Fixed/Adaptive Beamformers.
3.4 Differential Beamformers3.4.1 Preliminaries and Other Measures; 3.4.2 Cardioid; 3.4.3 Dipole; 3.4.4 Hypercardioid; 3.4.5 Supercardioid; References; 4 Generalization with Uniform Linear Arrays; 4.1 Signal Model and Problem Formulation; 4.2 Beamforming with Kronecker Product Filters; 4.3 Performance Measures; 4.4 Differential Beamformers; 4.4.1 Principle; 4.4.2 Dipole; 4.4.3 Cardioid; 4.4.4 Hypercardioid; 4.4.5 Supercardioid; References; 5 Approach with Nonuniform Linear Arrays; 5.1 Signal Model and Problem Formulation; 5.2 Kronecker Product Beamforming; 5.3 Illustrative Example.
5.4 Performance Measures5.5 Examples of Beamformers; 5.5.1 Delay and Sum; 5.5.2 Partial Superdirective; 5.5.3 Superdirective; 5.5.4 Dipole; 5.5.5 Supercardioid; 5.5.6 Wiener; References; 6 Approach with Rectangular Arrays; 6.1 Signal Model and Problem Formulation; 6.2 2-D Beamforming; 6.3 Performance Measures; 6.4 Fixed Beamformers; 6.4.1 Delay and Sum; 6.4.2 Combined Superdirective/Delay and Sum; 6.4.3 Maximum DF; 6.4.4 Null Steering; References; 7 Spatiotemporal Signal Enhancement; 7.1 Signal Model and Problem Formulation; 7.2 Signal Enhancement with Kronecker Product Filters.
7.3 Performance Measures7.4 Optimal Signal Enhancement Kronecker Product Filters; 7.4.1 Wiener; 7.4.2 Tradeoff; 7.4.3 MVDR; References; Index.

The focus of this book is on array processing and beamforming with Kronecker products. It considers a large family of sensor arrays that allow the steering vector to be decomposed as a Kronecker product of two steering vectors of smaller virtual arrays. Instead of directly designing a global beamformer for the original array, once the steering vector has been decomposed, smaller virtual beamformers are designed and separately optimized for each virtual array. This means the matrices that need to be inverted are smaller, which increases the robustness of the beamformers, and reduces the size of the observations. The book explains how to perform beamforming with Kronecker product filters using an unconventional approach. It shows how the Kronecker product formulation can be used to derive fixed, adaptive, and differential beamformers with remarkable flexibility. Furthermore, it demonstrates how fixed and adaptive beamformers can be intelligently combined, optimally exploiting the advantages of both. The problem of spatiotemporal signal enhancement is also addressed, and readers will learn how to perform Kronecker product filtering in this context.