Variations of LMS algorithms
This chapter considers the most popular modified least mean square (LMS)-type algorithms proposed by researchers, as well as some ones proposed by the authors. Most of these algorithms were designed on an ad hoc basis to improve convergence behavior, reduce computational requirements, and decrease the steady-state mean-square error. The Variable step-size LMS algorithm was introduced in 1986 to facilitate the conflicting requirements, whereas a large step-size parameter is needed for fast convergence and a small step-size parameter is needed to reduce the misadjustment factor. The implementation of the LMS filter in the frequency domain can be accomplished simply by taking the Discrete Fourier Transform of both the input data and the desired signal. The advantage of doing this is due to the fast processing of the signal using the Fast Fourier Transform algorithm. The performance of the Error-Data Normalized Step-Size algorithm is compared with the Normalized LMS algorithm in an adaptive noise canceller.