On the convergence analysis of the transform domain normalized LMS and related M-estimate algorithms

In this paper, we study the convergence performance of the transform domain normalized least mean square (TDNLMS) algorithm and its robust version, the TD normalized least mean M-estimate (TDNLMM) algorithm, which is derived from robust M-estimation and has the improved performance over their conventional TDNLMS counterpart in impulsive noise environment. Using the Pricepsilas theorem and its extension, and by introducing new special integral functions, related expectations can be evaluated so as to obtain decoupled difference equations describing the mean and mean square behaviors of these algorithms. The analytical results are in good agreement with computer simulation results.