Sufficient condition for tap-length gradient adaption of LMS algorithm

Besides the traditional accesses to accelerate the convergence of LMS algorithm, such as step-size control and input signal decorrelation, tap-length control is an emerging technique and attracts more and more attentions. Many tap-length control schemes are proposed and most of them are based on gradient search method. In this paper, the sufficient condition for tap-length gradient adaption is obtained based on the assumption of white Gaussian input. The analysis reveals that two requirements should be satisfied when use gradient method to search for optimum tap-length. One is that the unknown impulse response has a decay envelope, while the other requires that the number of the tap difference should be selected carefully.