Nonlinear channel equalizer using Gaussian sum approximations

The aim of this paper is to revisit the problem of nonlinear channel equalization. The equalization is here viewed as the estimation, from the observation of the channel output, of the state vector of the channel consisting of the last transmitted symbols. If the probability density function of the state vector given all the available observations (the a posteriori density function) were known, an estimate of the state vector for any performance criterion could be determined. Alspach and Sorenson (1972) proposed an approximation, by a weighted sum of Gaussian probability density functions, that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations. The application of these results to the minimum mean square error solution of the nonlinear channel equalization problem provides a new scheme which consists of the convex combination of the output of several extended Kalman filters operating in parallel