In this paper, a novel weighted zero-attracting leaky-LMS (WZA-LLMS) adaptive algorithm for sparse systems is proposed. In the proposed algorithm, a log-sum penalty is incorporated into the cost function of the leaky-LMS algorithm, which results in a shrinkage in the update equation. This shrinkage gives the algorithm the ability of attracting zeros, i.e., when the system is sparse, and hence improves its performance. The performance of the proposed WZA-LLMS algorithm is compared to those of the standard leaky-LMS and ZA-LMS algorithms in sparse system identification settings. The WZA-LLMS algorithm shows superior performance compared to the algorithms.
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