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access icon free l 0-norm penalised shrinkage linear and widely linear LMS algorithms for sparse system identification

  • Author(s): Youwen Zhang 1, 2 ; Shuang Xiao 1, 2 ; Defeng (David) Huang 3 ; Dajun Sun 1, 2 ; Lu Liu 1, 2 ; Hongyu Cui 1, 2
    • View affiliations
    • Affiliations: 1: College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, People's Republic of China ;
      2: Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, People's Republic of China ;
      3: School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Australia
  • Source: Volume 11, Issue 1, February 2017, p. 86 – 94
    DOI:  10.1049/iet-spr.2015.0218 , Print ISSN 1751-9675, Online ISSN 1751-9683
© The Institution of Engineering and Technology
Received 27/05/2015, Accepted 06/08/2016, Revised 18/12/2015, Published 11/08/2016

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.

Inspec keywords: estimation theory; identification; time-varying channels; least squares approximations; adaptive filters

Other keywords: priori errors; steady-state error; cost function; convergence rate; estimation performance improvement; least mean squares algorithm; tracking capability improvement; time-varying channel; l0-norm penalised shrinkage widely linear LMS algorithms; noncircular signal properties; varying step-size calculation; l0-SH-WL-LMS algorithm; adaptive filter; l0-norm penalised shrinkage linear LMS algorithm; l0-SH-LMS algorithm; channel variation; posteriori errors; sparse system identification

Subjects: Filtering methods in signal processing; Signal processing theory; Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Other topics in statistics; Other topics in statistics; Simulation, modelling and identification

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