Blind Equalizers by Techniques of Optimal Non-linear Filtering Theory: Analysis and Derivation

Blind deconvolution, fundamental in signal processing applications, is a challenging problem. Although blind equalization is essentially a nonlinear filtering problem, it has not yet been treated by all the well known advanced techniques of optimal non-linear filtering theory. In this book we use the Edgeworth expansion, maximum entropy argumentations and the Laplace integral method in order to obtain two new groups of blind deconvolution methods which outperform the old and new algorithms. The proposed methods are based on new, closed formed approximated expressions for the conditional expectation suitable for the blind deconvolution problem. Since these expressions do not impose any restrictions (except that of even symmetric) on the probability distribution of the (unobserved) input sequence, they are suitable for a wider range of source pdf compared to Bellini's, Fiori's or Haykin's expression. The derivation of the above mentioned equalizers are accompanied by theoretical analysis of the performance in the mean square error (MSE) sense and are justified via simulation. These new methods are useful to professionals in Communications who seek for improved equalization methods.