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In this paper, we introduce a new algorithm to deal with the stalling effectin the LMS algorithm used in adaptive filters. We modify the update rule of thetap weight vectors by adding noise, generated by a noise generator. Theproperties of the proposed method are investigated by two novel theorems. As itis shown, the resulting algorithm, called Added Noise LMS (AN-LMS), improvesthe resistance capability of the conventional LMS algorithm against thestalling effect. The probability of update with additive white Gaussian noiseis calculated in the paper. Convergence of the proposed method is investigatedand it is proved that the rate of convergence of the introduced method is equalto that of LMS algorithm in the expected value sense, provided that thedistribution of the added noise is uniform. Finally, it is shown that the orderof complexity of the proposed algorithm is linear as the conventional LMSalgorithm.

A New Noise-Assistant LMS Algorithm for Preventing the Stalling Effect