Parallel Kalman filtering for optimal symbol-by-symbol estimation in an equalization context

In this paper, the equalization is placed in an estimation framework where the unknown state to be estimated is a finite sequence of transmitted symbols. A Network of Kalman Filters (NKF) has been suggested for this purpose which is based on modeling the a posteriori symbol state probability density function (pdf) by a Weighted Gaussian Sum (WGS). As the theoretical number of Gaussian terms is increasing dramatically through iterations, several variations on the NKF are presented here while seeking a compromise between complexity and optimal equalization in terms of bit error rate (BER) performance. The suggested trade-off solution consists in merging and pruning the NKF at the beginning of each symbol sequence prediction step. To deal with nonstationary channel equalization, blind hybrid channel/symbol estimation algorithms based on a Kalman (or RLS) channel identification are shown to have a better BER performance and a more stable convergence behavior, compared to the Augmented Network of Kalman Filters (ANKF) and to the Blind Bayesian Equalizer (BBE) developed in (IEEE Trans. Commun. 42 (1994) 1019). Finally, the structure of the NKF is shown to be a kind of Recurrent Radial Basis Function Network (RRBFN) of a reduced size and its performance is compared to that of RBF-based equalizers (IEEE Trans. Neural Networks 4 (1993) 570).