  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
CG-algorithm diagonalizes the reduced-dimension covariance. Our simulations
show the benefits of the proposed approaches.
