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On the convergence of LMS filters under periodic signals

Abstract:

The response of the Least Mean Square (LMS) algorithm to deterministic periodic inputs is considered. Under these conditions, initial values of the tap-weight vector can be identified that lead to periodic responses of LMS filters. The stability of these periodic responses determines the long-term convergence of the filter. This analysis presents some advantages over the classical studies based on the correlation matrix, because it leads to more accurate results and a better understanding of the filter operation. It is also shown that such an operation does not change essentially for more realistic inputs, as when the desired response is perturbed with a zero-mean random signal. Finally, to validate the obtained results, some simulations and experiments have been conducted for an adaptive noise canceller. © 2012 Elsevier Inc.