An affine approximation to the robust beamforming problem

The standard robust beamforming approach tries to optimize the worst case performance over a continuum of signal steering vector distortions with a bounded norm. This approach can be too conservative when the norm bound on distortions is large and if an estimated distortion vector is available. In this paper, we propose a new robust formulation which approximates the robust solution by an affine mapping incorporating the side information of an estimated distortion vector (when available). Within this formulation, the conventional robust beamformer can be viewed as a constant approximation of the robust solution for the case when the side information of distortion vector is unavailable. We present two reformulations of the robust affine beamforming problem as a semi-definite program (SDP) which can be efficiently solved using the interior point methods. Once computed, the affine mapping can be used repeatedly to generate low-complexity robust approximations to the optimum beamforming solution whenever new information on distortion vector is available.