Mean-square performance of the modified frequency-domain block LMS algorithm

The mean weight vector of the normalized frequency-domain block least-mean-square (NFBLMS)algorithm cannot converge to the optimal solution in the mean-square error sense for the non-causal and under-modeling cases. A modified frequency-domain block least-mean-square (MFBLMS)algorithm was proposed to resolve this problem, which was claimed to have optimal steady-state performance. In this paper, we present a comprehensive statistical analysis of the MFBLMS algorithm in both the full- and under-modeling conditions. We first present the equivalent time-domain expressions for the update equation and the error vector of the MFBLMS, which allows us to carry out the performance analysis completely in the time domain. The analytical model for both the mean and mean-square performance of the MFBLMS are provided without assuming a specific input distribution, and the closed-form solution of the step-size bound is given. It is found that the upper step-size bound of the MFBLMS algorithm is much smaller than that of the NFBLMS algorithm for the correlated inputs, and the MFBLMS algorithm does not always achieve a better steady-state performance than the NFBLMS algorithm. Simulation results agree with our theoretical analysis quite well.