A Competitive Mean-Squared Error Approach to Beamforming

We treat the problem of beamforming for signal estimation where the goal is to estimate a signal amplitude from a set of 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), so that on average the resulting signal estimate can be far from the true signal. Here, we consider strategies that attempt to minimize the MSE between the estimated and unknown signal waveforms. The methods we suggest all maximize the SINR but at the same time are designed to have good MSE performance. Since the MSE depends on the signal power, which is unknown, we develop competitive beamforming approaches that minimize a robust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret. We demonstrate through numerical examples that the suggested minimax beamformers can outperform several existing standard and robust methods, over a wide range of signal-to-noise ratio (SNR) values. Finally, we apply our techniques to subband beamforming and illustrate their advantage in estimating a wideband signal.