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Novel Proportionate Adaptive Filters with Coefficient Vector Reusing

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Abstract

In this paper, a new family of adaptive filtering algorithms is presented, which aims to combine the small misalignment resulting from the reuse of past weight vectors with the fast convergence arising from the proportionate adaptation and logarithmic cost functions. This family of algorithms is obtained as a solution to a deterministic constrained optimization problem, by using the Lagrange multipliers technique, which differs from the traditionally employed stochastic gradient technique. Two special cases are proposed, namely the improved mu-law proportionate least mean logarithmic square with reuse of coefficients (IMPLMLS-RC) algorithm and the improved mu-law proportionate least logarithmic absolute difference with reuse of coefficients (IMPLLAD-RC) algorithm. An energy conservation relationship is established, which can be employed to perform stochastic transient analyses of the proposed algorithms. Simulations in system identification and active noise control applications show the advantages of the IMPLMLS-RC and IMPLLAD-RC algorithms over the traditional LMS and LAD, and the recently proposed LMLS and LLAD, with respect to both steady-state performance and robustness against impulsive noise.

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Notes

  1. Increasing L enhances the steady-state performance, which is important when the SNR is low [5], at the cost of reducing the convergence rate.

  2. Choosing a small \(\rho \) is equivalent to emphasizing the most recent adaptive coefficient vectors. In the case of \(\rho \rightarrow 1\), the last L estimated vectors assume similar importance.

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Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES) Finance Code 001 and CNPq—Brazil, Grants 431215/2016-2 and 309861/2017-9.

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Authors and Affiliations

  1. Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Maracanã, RJ, Brazil

    José V. G. de Souza

  2. Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Petrópolis, RJ, Brazil

    Diego B. Haddad & Felipe da R. Henriques

  3. Programa de Engenharia Elétrica, Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 21945-970, Brazil

    Mariane R. Petraglia

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  1. José V. G. de Souza
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  2. Diego B. Haddad
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  3. Felipe da R. Henriques
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  4. Mariane R. Petraglia
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Correspondence to Mariane R. Petraglia.

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This work was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico and in part by Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro.

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de Souza, J.V.G., Haddad, D.B., Henriques, F.d.R. et al. Novel Proportionate Adaptive Filters with Coefficient Vector Reusing. Circuits Syst Signal Process 39, 2473–2488 (2020). https://doi.org/10.1007/s00034-019-01266-z

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