Reduced-dimension robust capon beamforming using Krylov-subspace techniques

Abstract

We present low-complexity, quickly converging robust adaptive beamformers, for beamforming large arrays in snapshot deficient scenarios. The proposed algorithms are derived by combining data-dependent Krylov-subspace-based dimensionality reduction, using the Powers-of-R or conjugate gradient (CG) techniques, with ellipsoidal uncertainty set based robust Capon beamformer methods. Further, we provide a detailed computational complexity analysis and consider the efficient implementation of automatic, online dimension-selection rules. We illustrate the benefits of the proposed approaches using simulated data.

Low-Complexity Uncertainty-Set-Based Robust Adaptive Beamforming for Passive Sonar

“…Since we have chosen σ 2 1,KF to be equal to the DAS estimate, it means that the spatial spectrum would be similar to the DAS spectrum. We apply the ad hoc rescaling of the weights (29) noting that this will not affect the output SNR. In the following, we term this implementation the Kalman Filtering Implementation of WC-RAB (WC-KF).…”

“…THE KRYLOV-RDRCB In [29], a family of Krylov-subspace reduced-dimension robust Capon beamformers (Krylov-RDRCBs) was derived, which project the data onto a reduced-rank Krylov subspace and solve an RCB problem in the reduced-dimension space. Here, we describe the Conjugate Gradient RDRCB, which uses the conjugate algorithm [42], [43] to expand a rank-N Krylov-subspace basis…”

“…Since covariance matrix estimation error can be viewed as a type of array steering vector error [21], many of the robust adaptive techniques that are used to deal with array steering vector errors, including robust Capon beamforming, can also, up to a point, alleviate the effects of snapshot deficiency. Other notable approaches, which can be combined with robust Capon beamforming, when needed, include using reduced-dimension techniques, such as beamspace [22] or sub-array [23]- [26] preprocessing, eigenvalue [27] and Krylov methods [28], [29], dominant mode rejection [27], [30], [31], null broadening [32], and wideband integration techniques [19]. For instance in [18], [33], a framework for combining any reduced-dimension technique with robust Capon beamforming was derived for producing reduced-dimension RCBs (RDRCBs), whereas in [19], the wideband nature of sonar signals was exploited to speed-up algorithm convergence and reduce computational complexity, by using the steered covariance matrix method with the RCB to form wideband RCBs (WBRCBs).…”

“…Two of these use steepest descent methods, with one exploiting variable diagonal loading [38], which we term RCB-VDL-SD, and the other exploiting scaled projections [39], which we term RCB-SP-SD. The third, which we term the Krylov-RDRCB, solves the RCB problem by first projecting the data onto a reduced-rank Krylov-subspace and then solving a reduced-dimension RCB problem [29]. For quick reference, we refer the reader to Table II, which summarizes the complexity of the five efficient algorithms and the eigenvalue decomposition based 1 In [34], it was suggested that a recursive eigenvalue decomposition (EVD) approach could be used to implement the RCB.…”

Application of an Improved GSC in Tte Communication With Antenna Array

“…However, because the microphone spacing is generally greater than the voice signal wavelength, with the classic adaptive beamformer based on GSC, like the Griffiths-Jim beamformer [9] and some others, slight direction estimation error will cancel part of the desired signal [10]. Many signal processing techniques, which are called robust adaptive beamforming, have been proposed to avoid the cancellation of the desired signal [11][12][13][14][15], because their performance is robust against errors. However, the problems of using GSC algorithm are not so serious while processing SLF signals.…”