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A mixed norm constraint IPNLMS algorithm for sparse channel estimation

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Abstract

This paper presents a novel approach for structure extraction of the cluster sparse system identification. Different from adopting \(\ell _1\)-norm constraint to regularize the sparsity in the improved proportionate normalized least mean square (IPNLMS) algorithm, we directly work with the block sparse structure via \(\ell _{1,0}\)-norm constraint. In particular, we develop a cluster sparse IPNLMS by the block \(\ell _0\) norm regularization, named IPNLMS-BL0 method. The cluster sparse constraint is regarded as an extended version for the sparse constraint term. On the other hand, the iterations of IPNLMS-BL0 are derived by the steepest descent strategy. Then, we provide the analysis of block size choices of the cluster sparse constraint, computational complexity, and steady-state error of the proposed method. Various simulations are designed to test the performance of the IPNLMS-BL0 algorithm and its counterparts to identify and track the unknown sparse systems. The results are provided and analyzed to confirm the effectiveness and superiority of the proposed IPNLMS-BL0 algorithm.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Project No. 61701405), in part by the Fundamental Research Funds for the Central Universities (Project No. 3102019HHZY030022), in part by Natural Science Basic Research Plan in Shaanxi Province of China (Project No. 2019JQ463), in part by Stable Supporting Fund of Acoustic Science and Technology Laboratory, Harbin Engineering University (Project No. JCKYS2019604SSJS014), and in part by China Postdoctoral Science Foundation (Project No. 2019T120957).

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Authors and Affiliations

  1. School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, Shaanxi, China

    Fei-Yun Wu, Yan-Chong Song, Tian Tian, Kunde Yang & Rui Duan

  2. Key Laboratory of Ocean Acoustics and Sensing (Northwestern Polytechnical University), Ministry of Industry and Information Technology, Xi’an, Shaanxi, China

    Fei-Yun Wu, Yan-Chong Song, Tian Tian, Kunde Yang & Rui Duan

  3. Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin, China

    Xueli Sheng

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  1. Fei-Yun Wu
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  2. Yan-Chong Song
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  3. Tian Tian
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  4. Kunde Yang
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Correspondence to Fei-Yun Wu or Kunde Yang.

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Wu, FY., Song, YC., Tian, T. et al. A mixed norm constraint IPNLMS algorithm for sparse channel estimation. SIViP 16, 457–464 (2022). https://doi.org/10.1007/s11760-021-01975-6

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  • DOI: https://doi.org/10.1007/s11760-021-01975-6

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