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The Extended Feature LMS Algorithm: Exploiting Hidden Sparsity for Systems with Unknown Spectrum

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Abstract

The feature least-mean-square (F-LMS) algorithm has already been introduced to exploit hidden sparsity in lowpass and highpass systems. In this paper, by proposing the extended F-LMS (EF-LMS) algorithm, we boosted the F-LMS algorithm to exploit hidden sparsity in more general systems, those which are neither lowpass nor highpass. To this end, by means of the so-called feature matrix, we reveal the hidden sparsity in coefficients and utilize the \(l_1\)-norm to exploit the exposed sparsity. As a result, the EF-LMS algorithm will improve the convergence rate and the steady-state mean-squared error (MSE) as compared to the traditional least-mean-square algorithm. Moreover, in this work, we analyze the convergence behavior of the coefficient vector and the steady-state MSE performance of the EF-LMS algorithm. Through synthetic and real-world experiments, it has been seen that the EF-LMS algorithm can improve the convergence rate and the steady-state MSE whenever the hidden sparsity is revealed.

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Notes

  1. This function was inspired by the discard function proposed in [36].

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Acknowledgements

The authors would like to thank the São Paulo Research Foundation (FAPESP) Grants #2015/22308-2, #2019/06280-1 and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Codes 23038.018065/2018-17 and 88881.371305/2019-01.

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Authors and Affiliations

  1. Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, SP, 05508-090, Brazil

    Hamed Yazdanpanah

  2. Programs of Defense and Electrical Engineering, Military Institute of Engineering (IME), Rio de Janeiro, RJ, 22290-270, Brazil

    José A. Apolinário Jr.

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  1. Hamed Yazdanpanah
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  2. José A. Apolinário Jr.
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Correspondence to Hamed Yazdanpanah.

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Yazdanpanah, H., Apolinário, J.A. The Extended Feature LMS Algorithm: Exploiting Hidden Sparsity for Systems with Unknown Spectrum. Circuits Syst Signal Process 40, 174–192 (2021). https://doi.org/10.1007/s00034-020-01461-3

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