On the Performance Analysis of Normalized Subband Adaptive Filtering Algorithm with Sparse Subfilters
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On the Performance Analysis of Normalized Subband Adaptive Filtering Algorithm with Sparse Subfilters Pedro P. S. Xavier1
· Diego B. Haddad2
· Mariane R. Petraglia3
Received: 16 July 2019 / Revised: 20 April 2020 / Accepted: 22 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Subband adaptive filtering algorithms can increase the convergence rate of system identification tasks when the input signal is colored. Recently, a new normalized subband adaptive filtering algorithm with sparse subfilters (NSAF-SF) has been proposed, whose main advantage is the lower computational complexity when compared to stateof-the-art subband approaches, while maintaining similar convergence performance. In this paper, the first- and second-order stochastic analyses of the NSAF-SF algorithm are presented in order to provide predictions about its transient and steady-state performances. A relationship between the adaptive subband coefficients and the ideal fullband transfer function is derived, and the algorithm is proven to produce an asymptotically unbiased solution. In addition, a closed-form expression is obtained for the steady-state mean square deviation (MSD) of the subfilter coefficients. Although the proposed analyses use conventional assumptions of statistical independence, they do not assume a specific stochastic characteristic for the input signal (e.g., Gaussianity or whiteness). Transient and steady-state theoretical predictions of the MSD are confirmed by simulations.
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, Brazil.
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Mariane R. Petraglia [email protected] Pedro P. S. Xavier [email protected] Diego B. Haddad [email protected]
1
Instituto Nacional da Propriedade Industrial, Rio de Janeiro, RJ, Brazil
2
Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Petrópolis, RJ, Brazil
3
Electrical Engineering Program, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, RJ 21945-970, Brazil
Circuits, Systems, and Signal Processing
Keywords Subband adaptive filtering · Sparsity-aware adaptive filtering · Multirate signal processing · Stochastic models
1 Introduction The acoustic echo canceling (AEC) task can be approached by system identification techniques, one of the most popular being the adaptive filtering (AF) [11,35]. AF algorithms consist of a dynamic subarea of signal processing theory. In general terms, they can be described as iterative and nonlinear estimators of an ideal vector w ∈ R N , which contains the taps of a transversal finite impulse response (FIR) structure [28]. It is a well-established fact that highly correlated input signals can cause deterioration of the adaptive filter convergence performance [11,19], which is a common issue in communications over broadband transmission lines, underwater acoustics, real-time traffic prediction, among others [32]. This problem can b
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