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A New Affine Projection Algorithm with Adaptive \(l_{0}\)-norm Constraint for Block-Sparse System Identification

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Abstract

To improve the performance of identifying the block-sparse systems, firstly, a new sparsity aware block-sparse proportionate affine projection algorithm (BS-PAPA) with a fixed zero attractor is proposed in this paper. The proposed algorithm is obtained by integrating a weighted \(l_{0}\)-norm penalty into the cost function of the BS-PAPA. Adding the penalty results in zero attraction terms in the weight update recursive equation of the BS-PAPA, which helps in the shrinkage of inactive coefficients. The proposed algorithm is named \(l_{0}\)-block-sparse proportionate affine projection algorithm (\(l_{0}\)-BS-PAPA). The convergence analysis in the mean is derived for the \(l_{0}\)-BS-PAPA. Secondly, for applications having time varying measurement noise, an adaptive zero attractor \(l_{0}\)-BS-PAPA is also developed by adaptive optimisation of the zero attractor. This one is more robust to the varying degree of measurement noise than the former. A variable step-size \(l_{0}\)-BS-PAPA is also introduced to further enhance the performance of the \(l_{0}\)-BS-PAPA. Computer simulation experiments reveal that the \(l_{0}\)-BS-PAPA outperforms the existing algorithms in block-sparse systems in terms of convergence rate, normalised misalignment, and tracking ability.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Thanthai Periyar Government Institute of Technology, Vellore, Tamil Nadu, India

    Senthil Murugan Boopalan

  2. Department of Electronics and Communication Engineering, St. Joseph’s College of Engineering, Chennai, Tamil Nadu, India

    Swarnalatha Alagala

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  1. Senthil Murugan Boopalan
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  2. Swarnalatha Alagala
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Correspondence to Senthil Murugan Boopalan.

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Boopalan, S.M., Alagala, S. A New Affine Projection Algorithm with Adaptive \(l_{0}\)-norm Constraint for Block-Sparse System Identification. Circuits Syst Signal Process 42, 1792–1807 (2023). https://doi.org/10.1007/s00034-022-02197-y

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