Dynamic Programming Training Period for an MSE Adaptive Equalizer

This paper concerns itself with the design of an algorithm that will shorten the training period and adaptation time of an adaptive equalizer. Time-invariant or slowly varying channels with white additive Gaussian noise are considered. An adaptive equalizer in the form of a nonrecursive transversal filter reduces the intersymbol interference. The training period consists of the transmission of isolated pulses between which the equalizer is adjusted. The algorithm uses a minimum mean-squared error criterion with a variable step size on each iteration. A fixed number of iterations is allowed for the error to be minimized. A constraint related to the average excess mean-squared error is included, and the set of step sizes is determined by invoking the principle of optimality in dynamic programming. The resulting algorithm is compared to the popular fixed step-size algorithm. Predicted and experimental results are given. A fairly well conditioned and a poorly conditioned channel are considered. Results show that the new algorithm has a faster adaptation time. It is more complex than the fixed step-size algorithm, but for long transversal filters requires little additional computation time.