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Complex-valued Gaussian signal processing: Optimality of MSE, incorporation of full statistics, and a unified view

In this paper, we study the performance of mean square error (MSE) and Gaussian entropy criteria for linear and widely linear complex filtering. The MSE criterion cannot exploit the full second-order statistics of the error signal. To this end, we propose a new Gaussian entropy criterion to exploit the full second-order statistics of the error signal, and compare the performance of the two criteria in linear and widely linear filters. We show that the minimum Gaussian entropy estimator is also the best linear unbiased estimator (BLUE).