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An Improved Proportional Normalization Least Mean p-Power Algorithm for Adaptive Filtering

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Abstract

Under α stable distribution impulse noise environment, the least mean p-power algorithm (LMP) cannot handle the instability of the algorithm well, due to the large amplitude of the input signal and the large number of useless small weight coefficients in the sparse channel, which delay the convergence speed of the algorithm. In this paper, we develop a new adaptive filtering algorithm, named the proportional normalization least mean p-power (PNLMP) adaptive filtering algorithm. We first introduce a step size control matrix to improve the overall convergence speed and convergence accuracy of the algorithm. Next, to reduce the influence of a large impulse response on the LMP algorithm, a high-order tongue-line function about error is introduced in the normalization processing. Finally, we extend the tongue-line function to ensure that the cost function can also switch freely between V-shaped and M-shaped. This new algorithm overcomes the problem that the traditional LMP algorithm is only applicable to a specific environment and solves the problem of slow convergence speed and low convergence accuracy. Under α stable distribution impulse noise environment, the simulations show that the PNLMP algorithm can improve the convergence speed and stronger system tracking capability compared with existing algorithms, overcoming the problems of slow overall convergence and low convergence accuracy in the traditional algorithm.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 52071164 and in part by the Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant KYCX22_3844.

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Authors and Affiliations

  1. Ocean College, Jiangsu University of Science and Technology, Changshan Road, Zhenjiang, 212100, Jiangsu Province, China

    Banggui Cai, Biao Wang, Boyu Zhu & Yunan Zhu

  2. Sichuan Vocational College of Health and Rehabilitation, Deming Road, Zigong, 643000, Sichuan Province, China

    Banggui Cai

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  1. Banggui Cai
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  2. Biao Wang
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  4. Yunan Zhu
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Correspondence to Biao Wang.

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Cai, B., Wang, B., Zhu, B. et al. An Improved Proportional Normalization Least Mean p-Power Algorithm for Adaptive Filtering. Circuits Syst Signal Process 42, 6951–6965 (2023). https://doi.org/10.1007/s00034-023-02441-z

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