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

2026-01-15

IEEE Transactions on Audio, Speech, and Language Processing

AI Summary

This work proposes a novel subband adaptive filtering framework based on the recent Kronecker product decomposition to address the slow convergence under highly correlated inputs, high computational complexity, and poor robustness against impulsive noise exhibited by the conventional NKP-NLMS algorithm. By integrating Type-I and an improved Type-II structure, the proposed approach significantly enhances convergence speed while reducing computational cost. Furthermore, robustness and nonlinear modeling capability are strengthened through the incorporation of the maximum correntropy criterion, logarithmic cost functions, and nonlinear extensions such as trigonometric link networks and Volterra series, with the framework extended to active noise control scenarios. Experimental results demonstrate that the proposed NSAF-NKP-II and its robust variants consistently outperform state-of-the-art methods in tasks including echo cancellation, sparse system identification, and nonlinear signal processing, offering superior efficiency, robustness, and practical applicability.

Technology Category

• Machine Learning: Kernel Methods
• Natural Language Processing: Safety and Robustness
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 the proposed 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.

Problem

• Kronecker product decomposition
• subband adaptive filtering
• convergence degradation
• impulsive noise robustness
• computational complexity

Innovation

• Nearest Kronecker Product
• Subband Adaptive Filter
• Computational Complexity Reduction
• Robust Adaptive Filtering
• Nonlinear System Identification