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To overcome the tradeoff of the conventional normalized least mean square(NLMS) algorithm between fast convergence rate and low steady-statemisalignment, this paper proposes a variable step size (VSS) NLMS algorithm bydevising a new strategy to update the step size. In this strategy, the inputsignal power and the cross-correlation between the input signal and the errorsignal are used to estimate the true tracking error power, reducing the effectof the system noise on the algorithm performance. Moreover, the steady-stateperformances of the algorithm are provided for Gaussian white input signal andare verified by simulations. Finally, simulation results in the context of thesystem identification and acoustic echo cancellation (AEC) have demonstratedthat the proposed algorithm has lower steady-state misalignment than other VSSalgorithms.

A Novel Variable Step Size NLMS Algorithm Based on the Power Estimate of the System Noise