Data-adaptive reduced-dimension robust Capon beamforming

Abstract

We present low complexity, quickly converging robust adaptive beamformers that combine robust Capon beamformer (RCB) methods and data-adaptive Krylov subspace dimensionality reduction techniques. We extend a recently proposed reduced-dimension RCB framework, which ensures proper combination of RCBs with any form of dimensionality reduction that can be expressed using a full-rank dimension reducing transform, providing new results for data-adaptive dimensionality reduction. We consider Krylov subspace methods computed with the Powers-of-R (PoR) and Conjugate Gradient (CG) techniques, illustrating how a fast CG-based algorithm can be formed by beneficially exploiting that the CGalgorithm diagonalizes the reduced-dimension covariance. Our simulations show the benefits of the proposed approaches.Index Terms-Robust adaptive beamforming, dimensionality reduction, Krylov subspace methods.

Reduced-dimension robust capon beamforming using Krylov-subspace techniques

“…Moreover, X ≥ 0 or X > 0 mean that the Hermitian symmetric matrix X is positive semidefinite or positive definite, respectively. We define X 1 2 such that X = X An operation is defined as one complex multiplication plus addition (and is approximately equivalent to four real multiplications and additions) such that, for X ∈ C M×N 1 Part of this work was presented at ICASSP 2013 [72]. and Y ∈ C N×P , XY requires MNP operations.…”

Robust Rank Reduction Algorithm with Iterative Parameter Optimization and Vector Perturbation

“…The proposed IOVP-RLS and IOVP-SG algorithms are implemented in both non-robust MVDR [2] and robust RCB [4] schemes, respectively. The competitors including two conventional full-rank beamformers, such as MVDR-RLS and RCB-RLS, as well as two reduced-rank beamformers, such as MVDR-Krylov and RCB-Krylov [14]. In this simulation, we select D = 2 for all reduced rank schemes, including MVDR-Krylov, RCB-Krylov, MVDR-IOVP-RLS/SG and RCB-IOVP-RLS/SG.…”

“…Despite the improved convergence and tracking performance achieved with Krylov methods [13,14], they are relatively complex and may suffer from numerical problems. On the other hand, the joint iterative optimization (JIO) technique reported in [16] outperforms the Krylov-based method with efficient adaptive implementations.…”

“…It offers a large reduction in the required number of training samples over full-rank methods [2], which may also addresses the problem of snapshot deficiency at low complexity. Several reduced-rank strategies for processing data collected from a large number of sensors have been reported in the last few years, which include beamspace methods [7], Krylov subspace techniques [13,14] and methods of joint and iterative optimization of parameters in [15][16][17].…”

“…Reduced-rank signal processing techniques [7][8][9][10][11][12][13][14][15][16][17] provide a way to address some of the problems mentioned above. Reduced dimension methods are often needed to speed up the convergence of beamforming algorithms and reduce their computational complexity.…”