Gradient adaptive step-size LMS algorithms: past results and new developments

This paper presents a thorough study of a number of variable stepsize LMS (VSLMS) algorithms from the present literature along with a few new extensions of them. One class of these algorithms where the gradient estimate is smoothed, achieves better tracking performance than the other class which uses the instantaneous gradient. We give some reasons explaining this observation. Most of the previous publications on the VSLMS algorithm focus on a common step-size parameter for all the filter taps. Here, we emphasize the use of multiple stepsize parameters for different taps resulting in better tracking behavior. The adaptation of the LMS algorithm step-size parameters according to multiplicative update recursions (i.e., geometrical progressions), leads to better tracking performance. Simulation results showing the differences among the behaviors of various algorithms are presented