A flexible sparse set-membership NLMS algorithm for multi-path and acoustic echo channel estimations

Abstract

A highly improved set-membership normalized least mean square (SM-NLMS) algorithm is carried out to further strengthen the estimation behavior of previously presented SM-NLMS algorithm for estimating sparse multi-path and acoustic echo channels. The newly developed sparse SM-NLMS algorithm utilizes an approximating l0 function (AL0) to modify the SM-NLMS’s cost function to devise a zero attractor. Then, a zero attractor is realized to provide a quick zero attraction for estimating the sparse signals. The proposed soft parameter functioned SM-NLMS (SPFSM-NLMS) algorithm is derived by means of the unconstrained stochastic gradient minimization method to form the finalized SPFSM-NLMS (FSPFSM-NLMS) algorithm. The FSPFSM-NLMS algorithm is derived mathematically, and whose estimation behavior is considered and analyzed on a multi-path sparse channel as well as an acoustic echo channel. Moreover, our presented FSPFSM-NLMS algorithm is also studied under various sparsity levels. The simulated results illustrate that the developed FSPFSM-NLMS algorithm provides a superior sparse channel estimation behavior compared to the zero-attracting SM-NLMS (ZASM-NLMS), reweighting ZASM-NLMS (RZASM-NLMS) and NLMS in terms of the steady-state performance and convergence speed.