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Low-Complexity \(l_0\)-Norm Penalized Shrinkage Linear and Widely Linear Affine Projection Algorithms

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Abstract

In this paper, we propose an \(l_0\)-norm penalized shrinkage linear affine projection (\(l_0\)-SL-AP) algorithm and an \(l_0\)-norm penalized shrinkage widely linear affine projection (\(l_0\)-SWL-AP) algorithm. The proposed algorithms provide variable step-size by minimizing the noise-free a posteriori error at each iteration and introduce an \(l_0\)-norm constraint to the cost function. The \(l_0\)-SWL-AP algorithm also exploits noncircular properties of the input signal. In contrast with conventional AP algorithms, the proposed algorithms increase the estimation accuracy for time-varying sparse system identification. A quantitative analysis of the convergence behavior for the \(l_0\)-SWL-AP algorithm verifies the capabilities of the proposed algorithms. To reduce the complexity, we also introduce dichotomous coordinate descent (DCD) iterations to the proposed algorithms (\(l_0\)-SL-DCD-AP and \(l_0\)-SWL-DCD-AP) in this paper. Simulations indicate that the \(l_0\)-SL-AP and \(l_0\)-SWL-AP algorithms provide faster convergence speed and lower steady-state misalignment than the previous APA-type algorithms. The \(l_0\)-SL-DCD-AP and \(l_0\)-SWL-DCD-AP algorithms perform similarly to their counterparts but with reduced complexity.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61471138, 50909029 and 61531012), Program of International S&T Cooperation (Grant No. 2013DFR20050), the Defense Industrial Technology Development Program (Grant No. B2420132004), the Acoustic Science and Technology Laboratory (2014).

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Authors and Affiliations

  1. Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin, 150001, China

    Youwen Zhang, Shuang Xiao, Dajun Sun & Lu Liu

  2. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin, 150001, China

    Youwen Zhang, Shuang Xiao, Dajun Sun & Lu Liu

Authors
  1. Youwen Zhang
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  2. Shuang Xiao
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  3. Dajun Sun
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  4. Lu Liu
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Correspondence to Shuang Xiao.

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Zhang, Y., Xiao, S., Sun, D. et al. Low-Complexity \(l_0\)-Norm Penalized Shrinkage Linear and Widely Linear Affine Projection Algorithms. Circuits Syst Signal Process 36, 3385–3408 (2017). https://doi.org/10.1007/s00034-016-0465-6

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  • DOI: https://doi.org/10.1007/s00034-016-0465-6

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