Mean-square deviation analysis of the zero-attracting variable step-size LMS algorithm

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• 作者：Mohammad N. S. Jahromi ; Mohammad Shukri Salman…
• 关键词：Adaptive filters ; Sparsity ; Zero attracting ; System Identification
• 刊名：Signal, Image and Video Processing
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：11
• 期：3
• 页码：533-540
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Signal,Image and Speech Processing; Image Processing and Computer Vision; Computer Imaging, Vision, Pattern Recognition and Graphics; Multimedia Information Systems;
• 出版者：Springer London
• ISSN：1863-1711
• 卷排序：11

文摘

The well-known variable step-size least-mean-square (VSSLMS) algorithm provides faster convergence rate while maintaining lower mean-square error than the conventional LMS algorithm. The performance of the VSSLMS algorithm can be improved further in a channel estimation problem if the impulse response of the channel is sparse. Recently, a zero-attracting (ZA)-VSSLMS algorithm was proposed to exploit the sparsity of a channel. This was done by imposing an \(\ell _1\)-norm penalty to the original cost function of the VSSLMS algorithm which utilizes the sparsity in the filter taps during the adaptation process. In this paper, we present the mean-square deviation (MSD) analysis of the ZA-VSSLMS algorithm. A steady-state MSD expression for the ZA-VSSLMS algorithm is derived. An upper bound of the zero-attractor controller (\(\rho \)) that provides the minimum MSD is also provided. Moreover, the effect of the noise distribution on the MSD performance is shown theoretically. It is shown that the theoretical and simulation results of the algorithm are in good agreement with a wide range of parameters, different channel, input signal, and noise types.