Mixed-gradients Distributed Filtered Reference Least Mean Square Algorithm -- A Robust Distributed Multichannel Active Noise Control Algorithm

TL;DR

This work tackles robust distributed multichannel active noise control (DMCANC) under cross-talk and network delays byIntroducing compensation filters $c_{mk}(n)$ to align cross-path differences and exchanging local gradients $oldsymbol{ abla}_k(n)$ rather than control filters. The Mixed-Gradients Distributed FxLMS (MGDFxLMS) integrates local and neighboring gradients to update global filters $oldsymbol{w}_k(n)$, while an auto-shrink step size $eta(n)=eta_0 e^{-2oldsymbol{ riangle}/f}$ enhances stability under delays. The paper derives the optimal global solution, provides convergence bounds with and without delays, and demonstrates through simulations and real-noise experiments that MGDFxLMS achieves centralized-like performance with improved resilience to communication latency. An additional ASSS extension (ASSS-MGDFxLMS) shows robust performance under varying network conditions, making the approach practical for real-world DMCANC deployments.

Abstract

Distributed multichannel active noise control (DMCANC), which utilizes multiple individual processors to achieve a global noise reduction performance comparable to conventional centralized multichannel active noise control (MCANC), has become increasingly attractive due to its high computational efficiency. However, the majority of current DMCANC algorithms disregard the impact of crosstalk across nodes and impose the assumption of an ideal network devoid of communication limitations, which is an unrealistic assumption. Therefore, this work presents a robust DMCANC algorithm that employs the compensating filter to mitigate the impact of crosstalk. The proposed solution enhances the DMCANC system's flexibility and security by utilizing local gradients instead of local control filters to convey enhanced information, resulting in a mixed-gradients distributed filtered reference least mean square (MGDFxLMS) algorithm. The performance investigation demonstrates that the proposed approach performs well with the centralized method. Furthermore, to address the issue of communication delay in the distributed network, a practical strategy that auto-shrinks the step size value in response to the delayed samples is implemented to improve the system's resilience. The numerical simulation results demonstrate the efficacy of the proposed auto-shrink step size MGDFxLMS (ASSS-MGDFxLMS) algorithm across various communication delays, highlighting its practical value.

Figures (15)

• Figure 1: The schematic diagram of conventional multichannel ANC, where $S_{mk}$ represents the secondary path from the $k$th secondary source to the $m$th error sensor.
• Figure 2: A DMCANC network, where each ANC node consists of a secondary source, an error sensor, and an ANC controller.
• Figure 3: The schematic diagram of DMCANC, where each ANC controller exchanges information through a distributed network. The anti-noise wave generated by each ANC controller is transmitted to all error microphones, leading to inter-node cross-talk effects.
• Figure 4: Block diagram of obtaining compensation filters using the FxLMS algorithm, where $S_{mk}(z)$ and $S_{mm}(z)$ are the cross and self secondary path respectively. $\hat{S}_{mm}(z)$ denotes the estimated self secondary path and $C_{mk}(z)$ represents the compensation filter.
• Figure 5: The block diagram of mixed-gradient distributed FxLMS (MGDFxLMS) algorithm for the $k$th node, where $P_k(z)$ represents the primary path and $\gamma_k(n)$ denotes the interference generated by other nodes.