Abstract Though the Leaky Least-Mean-Square (LLMS) algorithm mitigates the drifting problem of the LMS algorithm, its performance is similar to that of the LMS algorithm in terms of convergence rate. In this paper, we propose a new LLMS algorithm that has a better performance than the LLMS algorithm in terms of the convergence rate and at the same time solves the drifting problem in the LMS algorithm. This better performance is achieved by expressing the cost function in terms of a sum of exponentials at a negligible increase in the computational complexity. The convergence analysis of the proposed algorithm is presented. Also, a normalized version of the proposed algorithm is presented. The performance of the proposed algorithm is compared to those of the conventional LLMS algorithm and a Modified version of the Leaky Least-Mean-Square (MLLMS) algorithm in channel estimation and channel equalization settings in additive white Gaussian and white and correlated impulsive noise environments.

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