Abstract: The present invention uses a feedback equalizer architecture with feedback samples comprised of weighted contributions of scaled soft and inversely-scaled hard decision samples, and adapts forward and feedback filters using weighted contributions of update error terms, such as Constant Modulus Algorithm (CMA) and Least Mean Squares (LMS) error terms. Combining weights are selected on a symbol-by-symbol basis by a novel measure of current sample quality. Adaptation methods of the sample quality measure are discussed. Furthermore, the present invention contains an automatic gain control circuit whose gain is adjusted at every symbol instance by a stochastic gradient descent update rule, minimizing novel cost criteria, to provide scaling factors for the hard and soft decisions.