This work presents cost-effective low-rank techniques for designing robustadaptive beamforming (RAB) algorithms. The proposed algorithms are based on theexploitation of the cross-correlation between the array observation data andthe output of the beamformer. Firstly, we construct a general linear equationconsidered in large dimensions whose solution yields the steering vectormismatch. Then, we employ the idea of the full orthogonalization method (FOM),an orthogonal Krylov subspace based method, to iteratively estimate thesteering vector mismatch in a reduced-dimensional subspace, resulting in theproposed orthogonal Krylov subspace projection mismatch estimation (OKSPME)method. We also devise adaptive algorithms based on stochastic gradient (SG)and conjugate gradient (CG) techniques to update the beamforming weights withlow complexity and avoid any costly matrix inversion. The main advantages ofthe proposed low-rank and mismatch estimation techniques are theircost-effectiveness when dealing with high dimension subspaces or large sensorarrays. Simulations results show excellent performance in terms of the outputsignal-to-interference-plus-noise ratio (SINR) of the beamformer among all thecompared RAB methods.
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