Open Accessl 0 ‐norm penalised shrinkage linear and widely linear LMS algorithms for sparse system identification
Author(s) -
Zhang Youwen,
Xiao Shuang,
Huang Defeng David,
Sun Dajun,
Liu Lu,
Cui Hongyu
Publication year - 2017
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2015.0218
Subject(s) - algorithm , a priori and a posteriori , norm (philosophy) , least mean squares filter , rate of convergence , adaptive filter , computer science , least squares function approximation , system identification , convergence (economics) , recursive least squares filter , mathematics , channel (broadcasting) , statistics , database , political science , computer network , philosophy , epistemology , estimator , economic growth , law , economics , measure (data warehouse)
In this study, the authors propose an l 0 ‐norm penalised shrinkage linear least mean squares ( l 0 ‐SH‐LMS) algorithm and an l 0 ‐norm penalised shrinkage widely linear least mean squares ( l 0 ‐SH‐WL‐LMS) algorithm for sparse system identification. The proposed algorithms exploit the priori and the posteriori errors to calculate the varying step‐size, thus they can adapt to the time‐varying channel. Meanwhile, in the cost function they introduce a penalty term that favours sparsity to enable the applicability for sparse condition. Moreover, the l 0 ‐SH‐WL‐LMS algorithm also makes full use of the non‐circular properties of the signals of interest to improve the tracking capability and estimation performance. Quantitative analysis of the convergence behaviour for the l 0 ‐SH‐WL‐LMS algorithm verifies the capabilities of the proposed algorithms. Simulation results show that compared with the existing least mean squares‐type algorithms, the proposed algorithms perform better in the sparse channels with a faster convergence rate and a lower steady‐state error. When channel changes suddenly, a filter with the proposed algorithms can adapt to the variation of the channel quickly.