A Soft Decision-Directed LMS Algorithm for Blind Equalization

We propose a new adaptation algorithm for equalizers operating on very distorted channels. The algorithm is based on the idea of adjusting the equalizer tap gains to maximize the likelihood that the equalizer outputs would be generated by a mixture of two gaussians with known means. The familiar decision-directed least mean square (LMS) algorithm is shown to be an approximation to maximizing the likelihood that the equalizer outputs come from such an i.i.d. source. The algorithm is developed in the context of a binary PAM channel and simulations demonstrate that the new algorithm converges in channels for which the decision-directed LMS algorithm does not converge.