Variable-step-size LMS algorithm: new developments and experiments

The variable-step-size least-mean-square (VSLMS) algorithm is explored and adopted for tracking of time-varying environments. Two implementations of the VSLMS algorithm are proposed. The emphasis is on implementations sizes with different step sizes at various taps of the adaptive filter. General analysis of the VSLMS algorithm appears to be somewhat involved. However, for one implementation a limited analysis of the algorithm is found possible. For this implementation it is shown that, when the input samples to the adaptive filter are zero-mean, Gaussian and uncorrelated with one another, the VSLMS algorithm can adapt itself to select the optimum set of step sizes which results in the best-tracking performance. Simulation experiments with the VSLMS algorithm show that, under fairly mild conditions, both of the proposed implementations adapt toward the optimum step sizes