New sequential partial update switch-mode noise-constrained NLMS adaptive filtering algorithms

The sequential partial update LMS (S-LMS)-based algorithms are efficient adaptive filtering algorithms for reducing the high arithmetic complexity in acoustic and related applications. A limitation of the algorithms is the degraded convergence speed. In this paper, a new family of sequential partial update switch-mode noise-constrained NLMS (S-SNC-NLMS) algorithms is proposed. These algorithms use a new variable step-size (VSS) method to increase the convergence speed of the traditional partial update algorithms while achieving the same steady-state excess mean square error (EMSE). It employs a maximum step-size to improve the initial convergence and exploits the prior knowledge of the additive noise variance as in the noise-constrained (NC) approach near convergence. The mean and mean square convergence behaviors of these new switch mode algorithms are studied to characterize its convergence condition and steady-state EMSE. Based on the theoretical results, an automatic threshold selection method for mode switching is also developed. Computer simulations are conducted to verify the theoretical results and effectiveness of the proposed algorithms.