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Novel Affine Projection Sign SAF Against Impulsive Interference and Noisy Input: Algorithm Derivation and Convergence Analysis

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Abstract

To enhance the convergence performance of the affine projection sign subband adaptive filter (AP-SSAF) algorithm under highly correlated inputs, the novel AP-SSAF (NAP-SSAF) algorithm was proposed through fully utilizing the decorrelation characteristic of SAF, which obtains quicker convergence behavior than the AP-SSAF algorithm. However, under unknown system identification, the estimation accuracy of the NAP-SSAF algorithm may unavoidably decrease when the input of the adaptive filter is contaminated by noise. To alleviate this issue, in this paper, we propose the bias-compensated NAP-SSAF (BC-NAP-SSAF) algorithm to alleviate the estimated bias through employing unbiasedness criterion. Benefiting from the unbiased criterion, the proposed BC-NAP-SSAF algorithm achieves an asymptotically unbiased estimation. Moreover, the convergence bounds of the proposed BC-NAP-SSAF algorithm in the mean and mean-square senses are provided to ensure stability, which are obtained by resorting to Price’s theorem along with some reasonable assumptions. The effectiveness of the derived theoretical convergence bounds is also corroborated. Finally, numerical simulations under system identification and acoustic echo cancellation applications demonstrate that the proposed BC-NAP-SSAF algorithm outperforms other algorithms in terms of estimation accuracy and tracking capability for noisy input under impulsive noise environment.

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The data that support the findings of this study are available from the corresponding author on request.

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Acknowledgements

This work was in part by National Natural Science Foundation of China (grant: 62171388, 61871461, 61571374) and in part by the Fundamental Research Funds for the Central Universities (Grant: 2682021ZTPY091).

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  1. Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Dongxu Liu & Haiquan Zhao

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  1. Dongxu Liu
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Correspondence to Haiquan Zhao.

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Liu, D., Zhao, H. Novel Affine Projection Sign SAF Against Impulsive Interference and Noisy Input: Algorithm Derivation and Convergence Analysis. Circuits Syst Signal Process 42, 6182–6209 (2023). https://doi.org/10.1007/s00034-023-02395-2

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