A Robust Zero-point Attraction LMS Algorithm on Near Sparse System Identification

TL;DR

This paper introduces a modified ZA-LMS algorithm with dynamic zero-point attraction and partial l1 norm penalty, improving near sparse system identification performance and robustness.

Contribution

It proposes the DWZA-LMS algorithm with dynamic weighting and partial l1 norm, enhancing robustness for near sparse systems compared to existing methods.

Findings

DWZA-LMS outperforms standard ZA-LMS in near sparse system identification.

The algorithm maintains computational efficiency while improving robustness.

Theoretical analysis and simulations confirm the effectiveness of DWZA-LMS.

Abstract

The newly proposed $l_1$ norm constraint zero-point attraction Least Mean Square algorithm (ZA-LMS) demonstrates excellent performance on exact sparse system identification. However, ZA-LMS has less advantage against standard LMS when the system is near sparse. Thus, in this paper, firstly the near sparse system modeling by Generalized Gaussian Distribution is recommended, where the sparsity is defined accordingly. Secondly, two modifications to the ZA-LMS algorithm have been made. The $l_1$ norm penalty is replaced by a partial $l_1$ norm in the cost function, enhancing robustness without increasing the computational complexity. Moreover, the zero-point attraction item is weighted by the magnitude of estimation error which adjusts the zero-point attraction force dynamically. By combining the two improvements, Dynamic Windowing ZA-LMS (DWZA-LMS) algorithm is further proposed, which shows better performance on near sparse system identification. In addition, the mean square performance of DWZA-LMS algorithm is analyzed. Finally, computer simulations demonstrate the effectiveness of the proposed algorithm and verify the result of theoretical analysis.