Abstract

Abstract—In this letter, we show that worst-case robust beamforming, with uncertain weights subject to multiplicative variations, can be cast as a convex optimization problem. We interpret this problem as a weighted complex I-regularization of the nominal beamforming problem, and show that it can be solved with the same computational complexity as nominal beamforming, ignoring the variations. We derive a simple lower bound on how much worse the robust beamformer will be compared to the nominal beamformer solution with no weight uncertainty. We demonstrate the robust approach with a simple narrowband beamformer. Index Terms—Regularization, robust beamforming, robust optimization, robust sensor array signal processing. I. BEAMFORMING WE consider an array of sensor elements. Let be the array response to a wave of unit amplitude

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