An investigation on the step-size bound of the partitioned frequency-domain block LMS (PFBLMS) algorithm

In this paper, we present an analysis on the step-size bound that guarantees the stability of the partitioned frequency-domain block LMS (PFBLMS). Frequency domain adaptive filters are attractive in applications requiring a large number of coefficients such as acoustic echo cancellation (AEC). However, the very restrictive convergence bound for BLMS has limited its usefulness. Since PFBLMS belongs to the BLMS family, it may suffer the very restrictive step-size bound too. Derivations on step-size bounds for the PFBLMS have been reported recently, but are not consistent with each other. In this paper, we analyse the step-size bound of PFBLMS, and derive a bound which is N times larger than that of the BLMS. This finding makes PFBLMS much more practical in the application of AEC. Extensive simulation results are provided to support our analysis.