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 Abstract—The leaky least-mean-square (LLMS) algorithm was first proposed to mitigate the drifting problem of the least- mean-square (LMS) algorithm. Though the LLMS algorithm solves this problem, its performance is similar to that of the LMS algorithm. In this paper, we propose an improved version of the LLMS algorithm that brings better performance to the LLMS algorithm and similarly solves the problem of drifting in the LMS algorithm. This better performance is achieved at a negligible increase in the computational complexity. The performance of the proposed algorithm is compared to that of the conventional LLMS algorithm in a system identification and a noise cancellation settings in additive white and correlated, Gaussian and impulsive, noise environments. Index Terms—Leaky least-mean-square, system identification, noise cancellation.

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.