Competitive Mean-Squared Error Beamforming
ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OFELECTRICAL ENGINEERING AND COMPUTER SCIENCE
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We consider the problem of designing a linear beamformer to estimate a source signal st 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 st can be far from st. To ensure that st is close to st, we propose using the more appropriate design criterion of MSE. Since the MSE depends in general on st 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 st, where the regret is the difference between the MSE using a beamformer ignorant of st and the smallest possible MSE attainable with a beamformer that knows st. 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.
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