[Paper Review] Active Noise Control based on the Momentum Multichannel Normalized Filtered-x Least Mean Square Algorithm

Dongyuan Shi, Woon‐Seng Gan+3 more|arXiv (Cornell University)|Aug 7, 2023

Advanced Adaptive Filtering Techniques9 citations

TL;DR

The paper proposes a momentum-enhanced multichannel normalized filtered-x LMS (MNFxLMS) algorithm for active noise control, showing faster convergence and robustness to varying noise power, validated on a 4-channel ANC setup with real piling and fMRI noises.

ABSTRACT

Multichannel active noise control (MCANC) is widely utilized to achieve significant noise cancellation area in the complicated acoustic field. Meanwhile, the filter-x least mean square (FxLMS) algorithm gradually becomes the benchmark solution for the implementation of MCANC due to its low computational complexity. However, its slow convergence speed more or less undermines the performance of dealing with quickly varying disturbances, such as piling noise. Furthermore, the noise power variation also deteriorates the robustness of the algorithm when it adopts the fixed step size. To solve these issues, we integrated the normalized multichannel FxLMS with the momentum method, which hence, effectively avoids the interference of the primary noise power and accelerates the convergence of the algorithm. To validate its effectiveness, we deployed this algorithm in a multichannel noise control window to control the real machine noise.

Motivation & Objective

• Motivate multichannel active noise control (MCANC) for larger noise-reduction areas with manageable computation.
• Address slow convergence and sensitivity to noise power in FxLMS-based MCANC.
• Develop a momentum-enabled MNFxLMS to accelerate convergence while maintaining input-power robustness.
• Validate the proposed method on measured primary/secondary paths with real-world noises.

Proposed method

• Review the multichannel normalized FxLMS (MNFxLMS) algorithm and its normalization to mitigate input-power variation.
• Introduce a momentum term that accumulates past gradient information to accelerate convergence (momentum MNFxLMS).
• Derive update equations for the momentum MNFxLMS, including the forgetting-factor gamma and gradient accumulation parameter gamma.
• Analyze the momentum mechanism as a low-pass filter on fast-changing gradients and an amplifier for slow-changing gradients.
• Use offline system identification to estimate secondary paths and implement the algorithm with specified tap lengths and forgetting factor (gamma = 0.9).
• Conduct simulations using measured primary/secondary paths from a 4-channel ANC setup to compare McFxLMS, MNFxLMS, and momentum MNFxLMS.

Experimental results

Research questions

• RQ1 Does integrating momentum with MNFxLMS improve convergence speed for MCANC without sacrificing robustness to primary noise power variations?
• RQ2 How does momentum MNFxLMS perform with real-world noises (piling, fMRI) compared to conventional McFxLMS and MNFxLMS?
• RQ3 What impact do step-size choices and forgetting factor have on stability and performance of the proposed algorithm?
• RQ4 Can the proposed method handle quickly varying disturbances while maintaining comparable steady-state noise reduction?

Key findings

• Momentum MNFxLMS achieves faster convergence than MNFxLMS and McFxLMS in simulations.
• All algorithms achieve similar steady-state noise reductions around 20–21 dB for the tested noises.
• McFxLMS may diverge with large input power, while MNFxLMS and momentum MNFxLMS remain stable under primary noise power variation.
• Momentum MNFxLMS converges fastest for real piling and fMRI noises in the measured-path scenario.
• The study validates effectiveness in canceling quick-varying noise using measured primary/secondary paths in a 4-channel setup.