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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.

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Abstract-The robust Capon beamformer has been shown to alleviate the problem of signal cancellation resulting from steering vector errors, caused, e.g., by calibration and/or angleof-arrival errors, which would otherwise seriously deteriorate the performance of an adaptive beamformer. Here, we examine robust Capon beamforming of multi-dimensional arrays, where robustness to angle-of-arrival errors is needed in both azimuth and elevation. It is shown that the commonly used spherical uncertainty sets are unable to control robustness in each of these directions independently. Here, we instead propose the use of flat ellipsoidal sets to control the angle-of-arrival uncertainty. To also allow for other errors, such as calibration errors, we combine these flat ellipsoids with a higher-dimension error ellipsoid. Computationally efficient automatic techniques for estimating the necessary uncertainty sets are derived, and the proposed methods are evaluated using both simulated data and experimental underwater acoustics measurements, clearly showing the benefits of the technique.

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.