Active Noise Control With a Gain Constraint for Micro-Loudspeakers

TL;DR — This paper proposes a fixed-filter active noise control (ANC) method with frequency-response gain constraints (ANC-FRC) to prevent mechanical over-excursion in micro-loudspeakers without introducing the group delay associated with cascaded filters. The approach achieves superior noise reduction across frequency bands compared to unconstrained Wiener filters and traditional high-pass cascading methods.

Key contributions

• Identifies that unconstrained fixed-filter ANC methods cause mechanical over-excursion and nonlinear distortion when deployed on resource-constrained micro-loudspeakers.
• Proposes an ANC method with low-frequency frequency-response constraints (ANC-LF-FRC) using an infinity norm bound to limit low-frequency gain without adding electronic latency or group delay.
• Demonstrates that strict low-frequency-only constraints induce the Gibbs phenomenon at band discontinuities, degrading noise reduction performance.
• Introduces the ANC-FRC method combining low-frequency infinity norm constraints with an L2-norm regularization term toward the unconstrained Wiener optimum across target bands, forming a convex optimization problem with guaranteed global convergence.

Problem

Compact smart devices like smartphones and smart glasses utilize micro-loudspeakers with severely limited low-frequency reproduction capability. Traditional unconstrained fixed-filter ANC methods, such as the standard Wiener-Hopf solution, apply excessively high gain at low frequencies to cancel high-energy disturbances, leading to mechanical over-excursion, hardware overload, and signal distortion. While cascading high-pass filters can suppress low-frequency output power, the induced group delay increases electronic latency and lowers the upper bound of effective noise reduction. This work addresses the trade-off between hardware safety and noise reduction efficiency without sacrificing latency.

Method

The single-channel feedforward ANC system processes a reference signal x(n) through a control filter w to generate anti-noise y(n), which propagates through secondary path s(n) to cancel disturbance d(n) at the error microphone. The unconstrained optimal Wiener filter minimizes mean squared error (MSE) E{e^2(n)}, but fails for micro-loudspeakers. To prevent saturation, the ANC-LF-FRC method enforces a hard infinity-norm constraint ||F_h w||inf <= delta_th on low-frequency bins (DC to h) via a DFT matrix F_h. Because sharp rectangular constraints in the frequency domain trigger the Gibbs phenomenon and oscillations in unconstrained bands, the proposed ANC-FRC method introduces a soft L2-norm regularization term lambda ||F{H} (w - w_opt)||_2 over the remaining frequency bins (h+1 to Nyquist).

The final objective function combines the MSE cost function with this regularization term, resulting in a convex optimization problem with a linear inequality constraint that guarantees a unique global minimum solved via standard convex solvers like CVX. The regularization factor lambda is set to 0.2 and the low-frequency gain limit delta_th is 10 dB. This structure restricts low-frequency gains to protect the micro-loudspeaker while forcing the unconstrained band's filter response to closely track the optimal unconstrained Wiener filter, preserving phase and magnitude characteristics without adding electronic group delay.

Experimental setup

Experiments were performed in an anechoic chamber using a Brühl & Kjær 4100-D dummy head placed 0.75m away from a KEF X300A primary loudspeaker. Noise signals included stationary white noise from the Noisex-92 database and non-stationary real-world train noise, captured via an error microphone in the artificial ear and a reference smartphone microphone sampled at 48 kHz (16 kHz in simulations). Baselines compared include the unconstrained ANC-Wiener method, a traditional High-pass method (first-order Butterworth with a 400 Hz cutoff), and the intermediate ANC-LF-FRC method. Evaluation uses noise reduction (NR) levels measured via power spectral densities (PSD) across specific frequency bands over 10 independent Monte Carlo runs.

Results

The proposed ANC-FRC method consistently outperforms traditional high-pass filtering and unconstrained configurations. For train noise, the ANC-FRC method achieves average noise reduction levels of 1.54 dB (100-500 Hz), 13.96 dB (500-1000 Hz), and 18.55 dB (1000-2000 Hz), compared to the high-pass method which yields negative attenuation (-1.85 dB) in the 100-500 Hz band due to destructive phase distortion and group delay. For white noise, ANC-FRC achieves 1.54 dB, 14.06 dB, and 19.23 dB across the same respective frequency bands. While the unconstrained Wiener filter achieves higher low-frequency reduction (4.08 dB), it does so by demanding illegal physical excursions that exceed micro-loudspeaker hardware limits. Ablations comparing ANC-LF-FRC against ANC-FRC prove that adding the L2-norm regularization eliminates the Gibbs phenomenon, lifting mid-band performance from 11.01 dB up to 13.96 dB on train noise.

Limitations

The evaluation is limited to a single-channel feedforward ANC setup tested in controlled anechoic conditions with simulated and playback loudspeaker setups. The approach relies on a fixed-filter pre-training regime, meaning it assumes static or slowly varying secondary paths and acoustic environments rather than tracking highly dynamic real-time plant changes via fully adaptive algorithms. Performance bounds depend heavily on precisely identifying the secondary transfer function and selecting appropriate constraint thresholds delta_th and regularization parameters lambda for specific hardware.

Why read this

Read this paper if you design audio firmware or hardware-constrained active noise control systems for portable devices like smartphones and wearables and need to circumvent micro-loudspeaker clipping and over-excursion without adding latency-inducing high-pass filters.

Code

None released (as of this page's updated date). If you are an author with a repo, please claim this entry — see CONTRIBUTING.md.

Applications

Active noise control systems for smartphones, smart glasses, portable audio devices, and consumer electronics utilizing compact micro-loudspeakers.

Institutions

Chongqing University of Posts and Telecommunications

Funding / 經費: National Key Research and Development Program of China, National Natural Science Foundation of China, Natural Science Foundation of Chongqing

Related

• Predictive Directional Selective Fixed-Filter Active Noise Control for Moving Sources via a Convolutional Recurrent Neural Network — same problem · relatedness 2.3/3
• A Sparsity-Aware Robust Nonlinear Active Noise Control for Impulsive Noise Environments — same problem · relatedness 2.0/3
• Active Constructive Interference for Speech — shared technique · relatedness 2.0/3
• NCPSZ: A Nonlinear Control Network for Miniature Loudspeakers in Personal Sound Zone Applications — same problem · relatedness 1.9/3
• A Causal Reference-Enhanced Keep-Speech Active Noise Control Method — same problem · relatedness 1.8/3

All 950k paper pairs scored by TypeSafe Jev (scripts/related/); relatedness 0 = unrelated … 3 = directly comparable.