A new and effective nonparametric variable step-size normalized least-mean-square algorithm and its performance analysis

This paper presents a new and effective nonparametric variable step-size normalized least-mean-square (VSS-NLMS) algorithm which provides excellent performance in various signal-to-noise ratio (SNR) scenarios. The step-size update expressions are based on steady-state step-size which derives from the filter weight update equations. Specifically, the step-size adjustment rules employ the square root of the estimated error power and the system noise power to enhance the effectiveness of the proposed algorithm. Detailed transient-state and steady-state analyses are presented for the Gaussian white input signal and suggest that the steady-state performance of the proposed algorithm is independent of the smoothing parameter (used in the step-size update expressions). In addition, performance comparisons between the proposed algorithm and other well-known VSS-NLMS algorithms show the improvements of the proposed algorithm. Furthermore, theoretical analyses and simulated behaviors of the proposed algorithm are in good agreement for both transient-state and steady-state. Through simulation results, the irrelevance between the steady-state performance and the smoothing parameter is verified.