A novel automatic step-size adjustment approach in the LMS algorithm

A variable step-size is necessary in the least-mean-square (LMS) algorithm to achieve both fast convergence and a small final excess mean-square estimation error. As a well-studied area, many variations of the LMS algorithm with variable step-sizes have been proposed in the literature. A common point in these algorithms is that the step-size is computed according to some pre-specified formulas with preset control parameters, and therefore the generated step-size is a predetermined constant at each single time point. In this paper, we propose a novel parameter-free step-size adjustment approach, in which the step-size is viewed as a variable, and rechosen at each new time point to minimize a least-squares cost function. Experiments for the linear prediction of random processes show the effectiveness of the proposed approach in rapidly driving the mean-square estimation error to a small final steady-state value. The most significant feature of the new approach is that no control parameters need to be set in advance.