A Variable Step-Size Matrix Normalized Subband Adaptive Filter

The normalized subband adaptive filter (NSAF) presented by Lee and Gan can obtain faster convergence rate than the normalized least-mean-square (NLMS) algorithm with colored input signals. However, similar to other fixed step-size adaptive filtering algorithms, the NSAF requires a tradeoff between fast convergence rate and low misadjustment. Recently, a set-membership NSAF (SM-NSAF) has been developed to address this problem. Nevertheless, in order to determine the error bound of the SM-NSAF, the power of the system noise should be known. In this paper, we propose a variable step-size matrix NSAF (VSSM-NSAF) from another point of view, i.e., recovering the powers of the subband system noises from those of the subband error signals of the adaptive filter, to further improve the performance of the NSAF. The VSSM-NSAF uses an effective system noise power estimate method, which can also be applied to the under-modeling scenario, and therefore need not know the powers of the subband system noises in advance. Besides, the steady-state mean-square behavior of the proposed algorithm is analyzed, which theoretically proves that the VSSM-NSAF can obtain a low misadjustment. Simulation results show good performance of the new algorithm as compared to other members of the NSAF family.