Dynamic adjustment of the least-mean-square step-size based on variances of weight fluctuations

We present in this paper a new method that adjusts the step-size of the LMS algorithm dynamically according to the uniformity among the variances of the fluctuations in the filter weights. This new method of LMS step-size adjustment is based on the optimality condition of the LMS algorithm proved by Ungerboeck (1972), which states that when the LMS algorithm operates in its optimum state (i.e., all the filter weights converges to their optimum), every filter weight fluctuates with the same variance around its optimum setting. Using the above criterion, the proposed method increases the step-size to a relatively large magnitude when the fluctuations of various filter weights are different, and decreases the step-size to a small magnitude when such fluctuations are more equal.