Convergence analysis of sparse LMS algorithms with l 1-norm penalty based on white input signal

• Published in: Signal processing Vol. 90; no. 12; pp. 3289 - 3293
• Main Authors: Shi, Kun, Shi, Peng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 2010
• Subjects: l1 norm; Least mean square (LMS) algorithm; Mean square deviation (MSD); Sparsity; Zero attracting; Sparsity; l 1 norm; Zero attracting; Mean square deviation (MSD); Least mean square (LMS) algorithm
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2010.05.015

The zero-attracting LMS (ZA-LMS) algorithm is one of the recently published sparse LMS algorithms. It usesan l 1-norm penalty in the standard LMS cost function. In this paper, we perform convergence analysis of the ZA-LMS algorithm based on white input signals. The stability condition is examined and the steady-state mean square deviation (MSD) is derived in terms of the system sparsity, system response length, and filter parameters (step size and zero-attractor controller). In addition, we propose a criterion for parameter selection such that the ZA-LMS algorithm outperforms the standard LMS algorithm. The results are demonstrated through computer simulations.