Sparse LMS/F algorithms with application to adaptive system identification

Abstract

Standard least mean square/fourth (LMS/F) is a classical adaptive algorithm that combined the advantages of both least mean square (LMS) and least mean fourth (LMF). The advantage of LMS is fast convergence speed while its shortcoming is suboptimal solution in low signal-to-noise ratio (SNR) environment. On the contrary, the advantage of LMF algorithm is robust in low SNR while its drawback is slow convergence speed in high SNR case. Many finite impulse response systems are modeled as sparse rather than traditionally dense. To take advantage of system sparsity, different sparse LMS algorithms with l p -LMS and l 0 -LMS have been proposed to improve adaptive identification performance. However, sparse LMS algorithms have the same drawback as standard LMS. Different from LMS filter, standard LMS/F filter can achieve better performance. Hence, the aim of this paper is to introduce sparse penalties to the LMS/F algorithm so that it can further improve identification performance. We propose two sparse LMS/F algorithms using two sparse constraints to improve adaptive identification performance. Two experiments are performed to show the effectiveness of the proposed algorithms by computer simulation. In the first experiment, the number of nonzero coefficients is changing, and the proposed algorithms can achieve better mean square deviation performance than sparse LMS algorithms. In the second experiment, the number of nonzero coefficient is fixed, and mean square deviation performance of sparse LMS/F algorithms is still better than that of sparse LMS algorithms.

Group-Constrained Maximum Correntropy Criterion Algorithms for Estimating Sparse Mix-Noised Channels

“…Moreover, adaptive filters algorithms have been further developed for sparse channel estimations. Similar to the previous investigations [2,6,7,[10][11][12][13][14][15][16][21][22][23][24]26,27], the proposed GC-MCC and RGC-MCC algorithms are investigated and their performance is compared with the SPF-MCC algorithm. In the following experiment, the proposed GC-MCC and RGC-MCC algorithms are investigated in different SNR environments.…”

“…To better exert the p i to the channel coefficients, the channel coefficients are classified according to their magnitudes. From the measurement and the previous investigations of the sparse channels [2,6,7,[10][11][12][13][14][15][16][21][22][23][24]26,27], we found that few channel coefficients are active non-zero ones, while most of the channel coefficients are inactive zero or near-zero ones. Thus, we propose a threshold to categorize the channel coefficients into two groups.…”

Improved adaptive sparse channel estimation using mixed square/fourth error criterion

“…To exploit the channel sparsity, SFEC-based ℓ p -norm-penalized sparse LMS/F filtering algorithm (LP-LMS/F) was proposed in [12]. In [12], we conduct the performance confirmation of LP-LMS/F by means of computer simulations.…”

“…In [12], we conduct the performance confirmation of LP-LMS/F by means of computer simulations. However, mathematical analysis for LP-LMS/F algorithm is very challenging due to the fact that ℓ p -norm is nonconvex function [13].…”

“…Specifically, initial work in [16] is extended and sparse LMS/F filtering algorithms are studied comprehensively from computer simulations and theoretical analysis. Different to the work in [12], a profound mathematical analysis for sparse LMS/F algorithms is given by adopting ℓ 1 -norm based convex sparse constraint functions, ZA and RZA. Throughout this paper, two sparse LMS-type algorithms (i.e., ZA-LMS and RZA-LMS) denote SEC based ASCE algorithms; the proposed two sparse LMS/F-type algorithms (i.e., ZA-LMS/F and RZA-LMS/F) stand for SFEC based ASCE algorithms.…”