We present low complexity, quickly converging robust adaptive beamformersthat combine robust Capon beamformer (RCB) methods and data-adaptive Krylovsubspace dimensionality reduction techniques. We extend a recently proposedreduced-dimension RCB framework, which ensures proper combination of RCBs withany form of dimensionality reduction that can be expressed using a full-rankdimension reducing transform, providing new results for data-adaptivedimensionality reduction. We consider Krylov subspace methods computed with thePowers-of-R (PoR) and Conjugate Gradient (CG) techniques, illustrating how afast CG-based algorithm can be formed by beneficially exploiting that theCG-algorithm diagonalizes the reduced-dimension covariance. Our simulationsshow the benefits of the proposed approaches.
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