In this paper, a new sparse adaptive filtering algorithm is proposed. The proposed algorithm introduces a log-sum penalty term into the cost function of a mixed norm leaky least-mean-square (NLLMS) algorithm. The cost function of the NLLMS algorithm is expressed in terms of sum of exponentials with a leakage factor. As a result of the log-sum penalty, the performance of the proposed algorithm is high in sparse system identification settings, especially, when the unknown system is highly sparse. The performance of the proposed algorithm is compared to those of the reweighted-zero-attracting LMS (RZA-LMS) and the p-norm variable step-size LMS (PNVSSLMS) algorithms in sparse system identification settings. The proposed algorithm shows superior performance compared to the aforementioned algorithms.
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