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Sparse least mean p-power algorithms for channel estimation in the presence of impulsive noise

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Abstract

The least mean p-power (LMP) is one of the most popular adaptive filtering algorithms. With a proper p value, the LMP can outperform the traditional least mean square \((p=2)\), especially under the impulsive noise environments. In sparse channel estimation, the unknown channel may have a sparse impulsive (or frequency) response. In this paper, our goal is to develop new LMP algorithms that can adapt to the underlying sparsity and achieve better performance in impulsive noise environments. Particularly, the correntropy induced metric (CIM) as an excellent approximator of the \(l_0\)-norm can be used as a sparsity penalty term. The proposed sparsity-aware LMP algorithms include the \(l_1\)-norm, reweighted \(l_1\)-norm and CIM penalized LMP algorithms, which are denoted as ZALMP, RZALMP and CIMLMP respectively. The mean and mean square convergence of these algorithms are analysed. Simulation results show that the proposed new algorithms perform well in sparse channel estimation under impulsive noise environments. In particular, the CIMLMP with suitable kernel width will outperform other algorithms significantly due to the superiority of the CIM approximator for the \(l_0\)-norm.

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Acknowledgments

This work was supported by 973 Program (2015CB351703), National Natural Science Foundation of China (61371807, 61372152), and Key Project of major national science and technology on new generation of broadband wireless mobile communication network (2012ZX03001023-003, 2012ZX03001008-003, 2013ZX03002010-003).

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  1. School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Wentao Ma, Badong Chen, Hua Qu & Jihong Zhao

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  1. Wentao Ma
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  2. Badong Chen
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  3. Hua Qu
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  4. Jihong Zhao
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Correspondence to Wentao Ma.

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Ma, W., Chen, B., Qu, H. et al. Sparse least mean p-power algorithms for channel estimation in the presence of impulsive noise. SIViP 10, 503–510 (2016). https://doi.org/10.1007/s11760-015-0757-5

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