Blind Equalization with Arbitrarily Fixed Time Delay

抄録

A method of blind equalization which outputs the estimate of a_k-S under arbitrarily fixed delay S is proposed. The conventional blind cost function has the form like f(z_k), where z_k is equalizer's output. Such form, however, has never an exceptional force so that the estimate of a_k-S is uniquely drawn out from the received sequence, yk,y_k－1,y_k－2,.... A strong force to maximize the mutual information between z_k and a_k－S is needed in our problem. An idea of this paper comes from the fact that if input of the equalizer is white, the equalizer should be the matched filter, and its truncation at time S gives the optimum solution in sense that E[(z_k － a_k－S)²] is minimized. The proposed blind system consists of two parts as follows. At first, in order to whiten the received signal, we preset the linear prediction system which outputs the prediction error before the blind equalization. Note that the prediction system is causal and can be updated in blind way simply by the power minimization. The second part is the conventional long (theoretically both side infinite) FIR blind equalizer whose input is the prediction error. This FIR blind equalizer yields the matched filter for the prediction error. The true blind equalizer is given by truncating the matched filter at time S, and to which we input the prediction error in parallel way. It can be shown that such connection of the causal linear prediction system and the truncated matched filter gives the direct solution derived by minimizing E[(z_k － a_k－S)²].