Robust NLMS algorithms with combined step-size against impulsive noises

In the presence of impulsive noises, the normalized least mean M-estimate (NLMM) algorithm has behaved better robustness and convergence than the normalized least mean square (NLMS) algorithm. In order to further solve the trade-off of the NLMM algorithm between convergence rate and steady-state misadjustment, we design a combined step-size (CSS) scheme that combines large and small step-sizes through an adaptive mixing factor, and the resulting CSS-NLMM algorithm obtains fast convergence and low steady-state misadjustment simultaneously. Importantly, the proposed CSS scheme can be straightforwardly extended to other robust NLMS algorithms. Moreover, the performance analysis of the CSS-NLMM algorithm is provided. Simulation results in impulsive noises have supported the effectiveness of the proposed CSS-NLMM algorithm and its performance analysis.