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Variable Step-Size Sparsity-Induced Augmented Complex-Valued NLMS Algorithm

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Abstract

The widely linear model has attracted much attention due to its good features for non-circular adaptive signal processing in recent years. In this paper, a sparsity-induced augmented complex-valued NLMS algorithm is proposed to promote the performance of the adaptive filter for estimating sparse systems, which is established by incorporating the \(l_0\)-norm regularization into the squared error normalized by the input vector. To address the problem of trade-off between fast convergence rate and low steady-state misalignment, we minimize the variance of the a posteriori error to derive an optimal step-size and then some practical problems are considered. Simulation results are provided to verify the superior performance of the proposed algorithm.

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Data Availability Statement

The data that support the findings of this study are available from the first author on reasonable request.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 61471251 and in part by the Natural Science Foundation of Jiangsu Province under Grant BK20191419 and BK20181431.

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  1. School of Electronic and Information Engineering, Soochow University, Suzhou, 215006, China

    Yulian Zong & Jingen Ni

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  1. Yulian Zong
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  2. Jingen Ni
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Correspondence to Jingen Ni.

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Zong, Y., Ni, J. Variable Step-Size Sparsity-Induced Augmented Complex-Valued NLMS Algorithm. Circuits Syst Signal Process 40, 4686–4695 (2021). https://doi.org/10.1007/s00034-021-01679-9

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  • DOI: https://doi.org/10.1007/s00034-021-01679-9

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