Minimax Robust A Priori Information Aware Channel Equalization

An a priori information aware channel equalizer accepts some prior information about the unknown transmit symbols, in addition to the knowledge of channel coefficients and noise covariance, and therefore offers a superior performance as compared to an equalizer that lacks this additional information. Such an equalizer is employed, for instance, in turbo equalization systems, where it is placed in conjunction with a channel decoder that provides the necessary a priori information. In this paper, we consider the design of such an a priori information aware equalizer, under an imperfect knowledge of channel parameters. Precisely speaking, we pursue a minimax optimization procedure to robustify the design of the equalizer in presence of an uncertainty about the channel coefficients as well as the interference plus noise covariance. To this end, we employ a Kullback-Leibler divergence based, and a norm based uncertainty class, obtain closed form expressions for the worst-case uncertainties, and finally arrive at the optimal mean-square error (MSE) equalizers that offer the best worst-case performance under uncertainty. Finally, we show that the proposed minimax robust equalizer achieves significant performance gains in comparison to the conventional (nonrobust) equalizer, both as a standalone entity and also as part of an iterative detection system.