Novel error variance estimation rule for nonparametric VSS-NLMS algorithm
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ORIGINAL PAPER
Novel error variance estimation rule for nonparametric VSS-NLMS algorithm Engin Cemal Mengüç1 Received: 3 October 2019 / Revised: 21 January 2020 / Accepted: 2 April 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract This paper presents a robust error variance estimation rule for the nonparametric variable step-size normalized least mean square (NPVSS-NLMS) algorithm. The proposed variance estimation rule accurately estimates the variance of the error signal. This is achieved by the variable exponential windowing parameter depending on the standard deviations of the sequential error signals. The accurate estimation of the error signal variance in the NPVSS-NLMS algorithm considerably improves the performance of the adaptive filter when compared to the classical NPVSS-NLMS algorithm. Moreover, the convergence and steady-state performances of the NPVSS-NLMS based on the proposed rule are analyzed in this study. The performance of the proposed algorithm is evaluated on system identification and acoustic echo canceling experiments and compared with that the classical NPVSS-NLMS algorithm. As a result, simulations show that the proposed algorithm with the help of the novel robust error variance estimation rule not only yields a dramatically reduced steady-state error but also achieves a faster convergence rate as compared with the classical counterparts. Furthermore, the theoretical results of the variable exponential windowing parameter used in the proposed rule are in very good agreement with its simulation results. Keywords Normalized least mean square (NLMS) · Adaptive filters · nonparametric variable step size · Error variance estimation
1 Introduction Adaptive filter algorithms play a significant role in various engineering applications [1–4]. One of the widely used adaptive filtering algorithms is the NLMS algorithm due to its robustness and easy implementation [1]. The stability of the NLMS algorithm depends on the choice of its step-size parameter [1]. As it is well known, if the step size is chosen by ensuring its stability bounds, it provides a balance between the convergence rate and steady-state error of the adaptive filter algorithm. If the step-size parameter is chosen as a large value, the algorithm quickly converges but produces a larger steady-state error. If this parameter is chosen as a small value, the algorithm exhibits a slow convergence but results in a lower steady-state error. In order to mitigate the mentioned issues, the step-size parameter needs to be adaptively controlled into the structure of the algorithm.
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Engin Cemal Mengüç [email protected] Electrical and Electronics Engineering Department, Nigde Ömer Halisdemir University, 51245 Nigde, Turkey
In the last two decades, a number of studies to adaptively update the step-size parameter have been proposed in the literature [5–15]. In [5], the individual step size is proposed for updating the weight coefficient of the adaptive filter. However, these step-size parameters are set to fixed values
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