Complex-Valued Linear and Widely Linear Filtering Using MSE and Gaussian Entropy

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 has been extensively studied, and with a widely linear filter form, it can take into account the full second-order statistics of the input signal. However, it cannot exploit the full second-order statistics of the error, and doubles the dimension of the parameter vector to be estimated. In this paper, we introduce the use of Gaussian entropy criterion such that full second-order statistics of the error can be taken into account, and compare the performance of the Gaussian entropy and MSE criteria for a linear and widely linear filter implementation in batch and adaptive implementations. Detailed performance analysis with numerical examples is presented to investigate the relationship and performance differences of the two criteria in diverse scenarios.