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A novel approach to geometric algebra-based variable step-size LMS adaptive filtering algorithm

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Abstract

The study of signal processing has recently devoted significantly more attention to adaptive filtering techniques. By addressing the shortcoming of the conventional geometric algebra-based fixed step-size least mean square algorithm that is unable to satisfy in terms of both reducing steady-state error and a faster convergence speed, simultaneously, this study presents an improved logarithmic function-based variable step-size least mean square geometric algebra adaptive filtering algorithm by establishing the step-size factor \(\mu \) and error signal e(n) nonlinear function relationship. The instantaneous values of a current error estimate e(n) and the previous error estimate \(e(n-1)\) are used to determine the step size of the defined algorithm. Besides, an extensive discussion is given on the performance of algorithm under influence of parameters \(\varvec{\gamma }\) and \(\varvec{T}\) as well as comparative analysis with other existing geometric algebra-based adaptive filters. Computer simulation reveals that the proposed approach not only has a low steady-state error, robustness against impulsive noise, and fast convergence speed, but it also overcomes some existing algorithm’s instability under steady-state phase.

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Data availability statement

The data analyzed in this study are available upon reasonable request.

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Funding

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 61771299.

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Authors and Affiliations

  1. School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, Shanghai, People’s Republic of China

    Khurram Shahzad, Rui Wang & Junaid Jamshid

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  1. Khurram Shahzad
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  2. Rui Wang
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  3. Junaid Jamshid
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Contributions

KS involved in conceptualization, methodology, simulation, and writing original draft of manuscript. WR took part in supervision, validation, project administration, review & editing the manuscript, and funding acquisition. JJ involved in formal analysis, review, and editing.

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Correspondence to Khurram Shahzad or Rui Wang.

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Shahzad, K., Wang, R. & Jamshid, J. A novel approach to geometric algebra-based variable step-size LMS adaptive filtering algorithm. SIViP (2024). https://doi.org/10.1007/s11760-024-03196-z

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