Fast computation of a discrete-time whitened matched filter based on Kalman filtering

In this paper, fast techniques for computing the coefficients of a Kalman-based prefilter originally developed by Mulgrew are proposed. This prefilter approximates a minimum-phase overall impulse response. In conjunction with a reduced-complexity equalizer, near optimum performance compared to maximum-likelihood sequence estimation is demonstrated for wireless channels. We suggest an exact recursive solution as well as a new iterative solution. In both solutions, the computational complexity of calculating the prefilter coefficients is O(L_WMF) with respect to L_WMF, where L_WMF is the number of prefilter coefficients. For comparison, the complexity of the original algorithm is O(L_WMF³).