Nearest Kronecker Product Decomposition Based Subband Adaptive Filter: Algorithms and Applications

TL;DR

This work proposes a type-I NKP-based normalized subband adaptive filter (NSAF) algorithm, namely NSAF-NKP-I, and develops two robust variants: the maximum correntropy criterion-based robust NSAF-NKP (RNSAF-NKP-MCC) and logarithmic criterion-based robust NSAF-NKP (RNSAF-NKP-LC) algorithms.

Abstract

Recently, the nearest Kronecker product (NKP) decomposition-based normalized least mean square (NLMS-NKP) algorithm has demonstrated superior convergence performance compared to the conventional NLMS algorithm. However, its convergence rate exhibits significant degradation when processing highly correlated input signals. To address this problem, we propose a type-I NKP-based normalized subband adaptive filter (NSAF) algorithm, namely NSAF-NKP-I. Nevertheless, this algorithm incurs substantially higher computational overhead than the NLMS-NKP algorithm. Remarkably, our enhanced type-II NKP-based NSAF (NSAF-NKP-II) algorithm achieves equivalent convergence performance while substantially reducing computational complexity. Furthermore, to enhance robustness against impulsive noise interference, we develop two robust variants: the maximum correntropy criterion-based robust NSAF-NKP (RNSAF-NKP-MCC) and logarithmic criterion-based robust NSAF-NKP (RNSAF-NKP-LC) algorithms. Additionally, detailed analyses of computational complexity, step-size range, and theoretical steady-state performance are provided for theproposed algorithms. To enhance the practicability of the NSAF-NKP-II algorithm in complex nonlinear environments, we further devise two nonlinear implementations: the trigonometric functional link network-based NKP-NSAF (TFLN-NSAF-NKP) and Volterra series expansion-based NKP-NSAF (Volterra-NKP-NSAF) algorithms. In active noise control (ANC) systems, we further propose the filtered-x NSAF-NKP-II (NKP-FxNSAF) algorithm. Simulation experiments in echo cancellation, sparse system identification, nonlinear processing, and ANC scenarios are conducted to validate the superiority of the proposed algorithms over existing state-of-the-art counterparts.

Figures (20)

• Figure 1: Structure of NSAF-NKP-I.
• Figure 2: Structure of NSAF-NKP-II.
• Figure 3: Scale function of the $i$th subband.
• Figure 4: The total multiplications per $k$ input samples of the NLMS, NSAF, NLMS-NKP, RLS-NKP, APA-NKP, NSAF-NKP-I, NSAF-NKP-II, RNSAF-NKP-MCC, and RNSAF-NKP-LC algorithms. (a) [$L=33$, $N=4$, $D=500$, $D_1=25$, $D_2=20$, and $k=4$] for the parameter setting; (b) [$L=17$, $N=2$, and $k=2$] for the parameter setting, and the other parameters of the algorithms are the same as those in Fig. 3(a).
• Figure 5: Structure of nonlinear subband NKP algorithms.