Fractional-Order Subband p-Norm Adaptive Filter via Transformation Nearest Kronecker Product Decomposition for Active Noise Control

TL;DR

This paper introduces a novel fractional-order subband p-norm adaptive filter using transformation nearest Kronecker product decomposition, improving robustness and computational efficiency for active noise control in non-Gaussian and sparse environments.

Contribution

It proposes a new NKP-FoNSPN algorithm with a TNKP decomposition technique, providing lower complexity and better noise reduction performance than existing methods.

Findings

The proposed algorithms outperform traditional NSPN in various noise scenarios.

TNKP-FoNSPN achieves lower steady-state misadjustment and computational cost.

Simulations and real-world tests confirm superior noise reduction performance.

Abstract

The conventional normalized subband p-norm (NSPN) algorithm achieves robustness in $\alpha$-stable noise ($1<\alpha \leq 2$) by utilizing low-order error moments. However, its performance degrades significantly under three scenarios: (1) non-Gaussian inputs, (2) $\alpha$-stable noise with $0<\alpha \leq 1$, and (3) sparse system identification. To address these limitations, this paper proposes a fractional-order NSPN algorithm based on the nearest Kronecker product (NKP) decomposition and fractional-order stochastic gradient descent, termed NKP-FoNSPN. Theoretical bounds for the fractional-order parameter $\beta$ are also derived. Notably, when $\beta=1$, the NKP-FoNSPN reduces to a new NKP-NSPN algorithm, while its non-NKP decomposition variant becomes the fractional-order NSPN (FoNSPN) algorithm. Furthermore, a novel transformation-based NKP (TNKP) decomposition technique is designed, which exhibits lower computational complexity than conventional NKP for specific filter structures. The resulting TNKP-based FoNSPN (TNKP-FoNSPN) achieves lower steady-state misadjustment and multiplication cost compared with the NKP-FoNSPN algorithm. Additionally, complete computational complexity analyses are provided. For active noise control (ANC) scenarios, we develop filtered-x variants: NKP-FxFoNSPN and TNKP-FxFoNSPN. From the former, two additional variants are derived: NKP-FxNSPN and FxFoNSPN. Simulations using diverse noise sources (pink, helicopter, gunshot, pile driver, and traction substation noise) demonstrate the superiority of the proposed algorithms. Finally, we validate their noise reduction performance in a real constructed single-channel duct ANC and a simulated multi-channel ANC systems.