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New variable step-size fast NLMS algorithm for non-stationary systems

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Abstract

In the field of echo cancellation, the normalized least mean squares (NLMS) algorithm is the most popular adaptive algorithm due to its simplicity and ease of implementation. However, this category of algorithms presents a conflict between several performance criteria: the initial convergence speed, the tracking ability and the root mean square error of filtering (MSE) in the steady state. Variable-step algorithms (VSS) address the trade-off between convergence speed and low final MSE. Nevertheless, due to a fairly small adaptive step-size in the steady-state regime, they fail to adequately track variations of the unknown system and they are all implemented with the original NLMS algorithm. In this contribution, a new improved variable adaptation step algorithm capable to track time variations of the unknown system even after good convergence in the steady state is suggested. It is based on the use of the fast-normalized adaptive algorithm (FNLMS) for system identification and acoustic echo cancellation context. The purposes of using the FNLMS algorithm in the field of VSS are on the one hand to improve its final MSE and, on the other hand, to obtain a VSS algorithm with better convergence and tracking compared to the VSS NLMS algorithms. Simulation results show that the proposed VSS-Fast NLMS algorithm outperforms the original FNLMS algorithm in terms of steady-state error reduction and minimization after the initial transition phase while maintaining similar convergence speed and tracking capacity. Furthermore, it achieves visible improvements in terms of two objective criteria, i.e., a faster initial convergence rate and a better tracking ability than the ones of the non-parametric VSS-NLMS (NPVSS-NLMS) and traditional NLMS algorithms.

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Authors and Affiliations

  1. Detection Information and Communications Laboratory, University of Blida1, Route of Soumaa, B.P. 270, 09000, Blida, Algeria

    Imen Gueraini

  2. Signal Processing and Image Laboratory (LATSI), University of Blida1, Route of Soumaa, B.P. 270, 09000, Blida, Algeria

    Ahmed Benallal & Ayoub Tedjani

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  1. Imen Gueraini
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  2. Ahmed Benallal
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  3. Ayoub Tedjani
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Correspondence to Imen Gueraini.

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The authors declare that there is no conflict of interest.

Authors' contributions

IG is the major author who led all stages of the study. AB contributed to the theoretical aspect of adaptive filtering. AT contributed to the implementation part of the algorithms as well as to the writing part. All authors read and approved the final manuscript.

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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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The data used to support the findings of this study are available from the corresponding author upon request.

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Gueraini, I., Benallal, A. & Tedjani, A. New variable step-size fast NLMS algorithm for non-stationary systems. SIViP 17, 3099–3107 (2023). https://doi.org/10.1007/s11760-023-02531-0

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