##
###
An Improved Sparsity-aware NSAF-SF Adaptive Algorithm

Mariane Petraglia, Pedro Paulo Xavier, Diego Haddad, Fernanda de Oliveira

2020
*
Electronics Letters
*

Normalised subband adaptive filtering algorithms have attracted attention due to their ability to present faster convergence in the case of coloured excitation data. The NSAF-SF scheme is an example of a state-of-the-art subband adaptive algorithm that demands a low computational burden. This Letter proposes a deterministic local optimisation approach with affine constraints whose result leads to an enhanced NSAF-SF updating mechanism. One of these constraints consists of a projection into a
## more »

... erplane derived from a relaxed ℓ 1 -norm restriction, which provides a sparsity-promoting scheme. Such a constraint incorporates prior information into the (originally sparsity-agnostic) NSAF-SF. Such prior information concerns the energy concentration of the ideal transfer function that the adaptive filter intends to identify. Furthermore, the advanced optimisation problem is modified in order to make the advanced adaptive filter robust against impulsive noise. The simulations present a performance improvement for both transient and steady-state regions. Introduction: Adaptive filtering have been widely used in many fields such as communications, control, biomedical and financial engineering, among others [1]. In such applications, the environment is constantly changing, thereby requiring a system that adapts itself in order to maintain an adequate performance. In adaptive filtering, an optimisation algorithm is used to approximate the best filter coefficients for every instant the system is operating. The least mean square (LMS) adaptive algorithm is very popular due to its simplicity and robustness [1] . Nevertheless, its convergence rate becomes small when the input signal is correlated, making the LMS unsuitable for many applications, as well as its normalised counterpart (i.e. the NLMS algorithm) [2] . Subband adaptive filtering (SAF) came as an alternative to improve the convergence rate, besides reducing the filter complexity [3]. SAF schemes typically employ a filterbank that decomposes the input signal in multiple subbands. Ideally, each subband contains a set of exclusive frequencies from the original frequency range [1]. The advantage of such decomposition is two-fold: it allows for exploiting the characteristics of each subband signal and improves the convergence rate because the subband signals have a smaller dynamic range than that of the original signal [1]. The problem with the regular SAF is that the convergence rate is still limited by band edge effects [3] . To further improve the convergence rate, the normalised SAF (NSAF) was proposed in [3] . In the NSAF design, the principle of minimum disturbance is also applied, and the update design is thus considered a solution of a multiple constraints optimisation problem. The goal of the NSAF using sparse filters (NSAF-SF) is to preserve the convergence rate while reducing the computational complexity [4] . This goal is achieved by using the same premises of the NSAF algorithm (i.e. minimum disturbance principle and multiple-constraint optimisation) in a modified structure that takes advantage from the fact that non-adjacent subbands have no significant spectral superposition. The computational complexity of the NSAF-SF is significantly smaller than that of the NSAF when one considers the number of multiplications per input sample (NMPIS) performed by each algorithm [4] . Reductions over 70% in NMPIS can be observed, for example when the employed filterbank has 16 subbands [4] . The approach proposed in this Letter enhances the convergence rate of the NSAF-SF by incorporating a sparsity-aware algorithm that does not require additional user-defined parameters. Further, a modification of the proposed algorithm is also advanced in order to guarantee robustness against impulsive noise. Such modification considers the maximum correntropy criterion [5] .

doi:10.1049/el.2020.0661
fatcat:6456g7sujffjfnyjjvochjlss4