Design of decision device for the adaptation of decision directed equalizers

Adaptation of the coefficients of an equalizer usually takes place in the decision directed mode. The decision used for adaptation has a profound influence on the performance of the equalizer. In this work, we consider the influence of the probabilistic model used by a soft information decision device on the performance of the equalizer. It is shown that the equalizer output is distributed as a Gaussian Mixture, and these statistics are used to form a soft-decision device. We show that this is very near optimal in the sense of the Recursive Expected Least Squares algorithm introduced in prior work. Sub-optimal decision devices that are often more practical are also introduced and the loss of performance as a result of using these is considered.