Two Improved Wavelet Transform Domain LMS Sign Adaptive Filter Algorithms Against Impulsive Interferences

Abstract

In this paper, the improved wavelet transform domain least mean squares (IWTDLMS) adaptive algorithm is established. The IWTDLMS algorithm has a faster convergence speed than the conventional WTDLMS for colored input signals. Since the performances of WTDLMS and IWTDLMS are degraded in impulsive noise interference, the IWTDLMS sign algorithm (IWTDLMS-SA) is proposed. In comparison with IWTDLMS, the IWTDLMS-SA has lower computational complexity. In order to improve the performance of IWTDLMS-SA, the variable step-size IWTDLMS-SA (VSS-IWTDLMS-SA) is introduced. The VSS-IWTDLMS-SA is derived by minimizing the \(\ell _1\)-norm of the a posteriori error vector. To increase the tracking ability of the VSS-IWTDLMS-SA, the modified VSS-IWTDLMS-SA (MVSS-IWTDLMS-SA)is presented. The simulation results demonstrate that the proposed algorithms have a faster convergence rate and lower misadjustment than the conventional WTDLMS. The robustness feature of the IWTDLMS-SA, VSS-IWTDLMS-SA, and MVSS-IWTDLMS-SA against impulsive noises is also verified through several experiments in a system identification setup.

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Correspondence to Seyed Mahmoud Khademiyan.

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Abadi, M.S.E., Mesgarani, H. & Khademiyan, S.M. Two Improved Wavelet Transform Domain LMS Sign Adaptive Filter Algorithms Against Impulsive Interferences. Circuits Syst Signal Process 40, 958–979 (2021). https://doi.org/10.1007/s00034-020-01508-5

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Keywords

  • Adaptive filters
  • Sign algorithm
  • Variable step size
  • Wavelet transform
  • Impulsive noise interference