Competitive Mean-Squared Error Beamforming

Abstract : We consider the problem of designing a linear beamformer to estimate a source signal s(t) from array observations. Conventional beamforming methods typically aim at maximizing the signal-to-interference-plus-noise ratio (SINR). However this does not guarantee a small mean-squared error (MSE), hence on average their resulting signal estimate ^s(t) can be far from s(t). To ensure that ^s(t) is close to s(t), we propose using the more appropriate design criterion of MSE. Since the MSE depends in general on s(t) which is unknown, it cannot be minimized directly. Therefore we develop a competitive beamforming approach, in which the beamformer is designed to minimize the worst-case regret over all s(t), where the regret is the difference between the MSE using a beamformer ignorant of s(t) and the smallest possible MSE attainable with a beamformer that knows s(t). Thus, we ensure that over a wide range of signal values, our beamformer will result in a relatively low MSE. We demonstrate through numerical examples that the proposed minimax regret beamformer (MMR) outperforms several existing standard and robust beamformers, for wide range of SNR values.