A simplified network of LMS filters for Bayesian equalization based on a state model

The network of Kalman filter (NKF) structure was proposed to perform optimal Bayesian symbol-by-symbol estimation in a SISO equalization context [(P. Grohan et al., September 1997)(R. Amara et al., 2002)]. By approximating the error filtering covariance matrix of each branch of the network by a diagonal one, we show in this paper that the NKF can be simplified into a particular network of normalized LMS filters (NLMSF) minimizing the error on the predicted channel output, so that reducing the corresponding complexity. We also propose an adjusting procedure of the approximating matrix which is still related to the second order statistics of the symbol state estimation error. Simulations show the good performance of the NLMSF based equalizer compared to the NKF version for both short and long memory linear channels.