Improving parallel EKF-based nonlinear channel equalization using unscented transformation

The paper presents a new review of parallel Kalman filtering for nonlinear channel equalization. A Network of Extended Kalman Filters (nekf) has already been suggested for this purpose. This equalizer gives recursively a minimum mean squared error (mmse) estimation of a sequence of transmitted symbols according to a state formulation of a digital communication scheme. It is essentially based on two mechanisms: the approximation of the non Gaussiana posteriori probability density function (pdf) of the symbol sequence by a Weighted Gaussian Sum (wgs); and the local linearization of the nonlinear channel function for each branch of the network. Since the linearization, bearing on scattered symbol states, is one of the major limitations of thenekf, a new Kalman filtering approach, the Unscented Kalman Filter (ukf) suggested by Julier and Uhlman is considered in this paper for an interesting adaptation to the equalization context. Theukf algorithm is based on the equations of a Kalman filter, as the optimal linear minimum variance estimator, and on determining conditional expectations based on a kind of deterministic Monte-Carlo simulations. The new equalizer referred to as the Network ofukf (nukf), thus combines density approximation by awgs and the Unscented Transformation (ut) principle to circumvent the linearization brought within eachekf and is shown to perform better than thenekf based equalizer for severe nonlinear channels. Also, an adaptive version of thenukf is developed using the k-means clustering algorithm for noise-free channel output identification, since thenukf-based algorithm does not require the knowledge of the channel nonlinearity model.