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