Improving convergence of the NLMS algorithm using constrained subband updates

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Abstract
We propose a new design criterion for subband adaptive filters (SAFs). The proposed multiple-constraint optimization criterion is based on the principle of minimal disturbance, where the multiple constraints are imposed on the updated subband filter outputs. Compared to the classical fullband least-mean-square (LMS) algorithm, the subband adaptive filtering algorithm derived from the proposed criterion exhibits faster convergence under colored excitation. Furthermore, the recursive tap-weight adaptation can be expressed in a simple form comparable to that of the normalized LMS (NLMS) algorithm. We also show that the proposed multiple-constraint optimization criterion is related to another known weighted criterion. The efficacy of the proposed criterion and algorithm are examined and validated via mathematical analysis and simulation.