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

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