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Diffusion Sparse Sign Algorithm with Variable Step-Size

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Abstract

In this paper, we propose the diffusion sparse sign algorithm with variable step-size for distributed estimation in sparse and impulsive interference environments. Firstly, we address the problem of in-network distributed estimation for sparse vectors under the impulsive noise environment. In order to exploit the sparsity of the vector of interest, we incorporate the sparse norms (\({l_1}\)-norm and \(RW{l_1}\)-norm) into the cost function of the standard diffusion sign algorithm, which accelerates the convergence speed of zero or near-zero components. In addition, we propose the adaptive variable step-size to further improve the convergence rate of the proposed algorithm. The variable step-size is derived by the correlation entropy, which contains a modified Gaussian kernel function and is robust to impulsive noise. In this paper, every node combines its correlation entropy function with the information of its neighborhood to drive the variable step-size at each iteration. Simulation results show that the proposed algorithm outperforms the standard diffusion SA in the sparse and impulsive system and the convergence rate of the proposed algorithm is faster than constant step-size algorithms.

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Authors and Affiliations

  1. College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Feng Chen, Xiaoxia Liu, Shukai Duan, Lidan Wang & Jiagui Wu

  2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Feng Chen

  3. Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Chongqing, 400715, China

    Feng Chen, Xiaoxia Liu & Jiagui Wu

  4. Chongqing Collaborative Innovation Center for Brain Science, Chongqing, 400715, China

    Feng Chen

Authors
  1. Feng Chen
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  2. Xiaoxia Liu
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  3. Shukai Duan
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  4. Lidan Wang
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  5. Jiagui Wu
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Corresponding author

Correspondence to Shukai Duan.

Additional information

This work was supported in part by the Doctoral Fund of Southwest University (No. SWU113067), the Fundamental Research Funds for the Central Universities (Grant Nos. XDJK2017B053, XDJK2017D176, XDJK2017D180, XDJK2017D181) and Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2017jcyjAX2065).

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Chen, F., Liu, X., Duan, S. et al. Diffusion Sparse Sign Algorithm with Variable Step-Size. Circuits Syst Signal Process 38, 1736–1750 (2019). https://doi.org/10.1007/s00034-018-0935-0

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  • DOI: https://doi.org/10.1007/s00034-018-0935-0

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