Adaptive equalization using normalized stochastic approximation methods

An optimal procedure for incrementing the tap gains of an adaptive tapped-delay-line data channel equalizer is presented. The equalizer algorithm is a normalized Robbins-Monro stochastic approximation procedure which converges to tap gain values bounded by those which minimize mean-square error (MSE) and those which minimize median-square error (MDSE). A truncated version of the algorithm with minimum and maximum allowable values of tap gains will also converge. The problem addressed here is selection of an optimal scalar stepping sequence for the multi-dimensional stochastic search scheme; the objective is accelerated convergence. The optimal sequence derived is minimax in that maximum MSE in tap gain settings is minimized at each iteration. Generally speaking, the optimal approach is to hold step size constant initially, and to then reduce step size at each iteration.