--- id: cheng26b_interspeech title: Active Noise Control With a Gain Constraint for Micro-Loudspeakers authors: - Zhenhua Cheng - Yi Zhou - Yin Liu - Yu Zhao - Liming Shi year: 2026 doi: 10.21437/Interspeech.2026-2202 isca_url: https://www.isca-archive.org/interspeech_2026/cheng26b_interspeech.html pdf_url: https://www.isca-archive.org/interspeech_2026/cheng26b_interspeech.pdf session: Active Noise and Echo Control, Sound Zones and Packet-Loss Concealment topics: - speech-enhancement category: enhancement-separation institutions: - Chongqing University of Posts and Telecommunications funding: - National Key Research and Development Program of China - National Natural Science Foundation of China - Natural Science Foundation of Chongqing code: url: "" license: "" open_to_collaboration: false wiki_frontmatter: id: cheng26b_interspeech category: enhancement-separation institutions: - Chongqing University of Posts and Telecommunications updated: 2026-09-29 confidence: full-paper digest: v2 source: https://doi.org/10.21437/Interspeech.2026-2202 pdf: https://www.isca-archive.org/interspeech_2026/cheng26b_interspeech.pdf wiki_url: https://interspeech-2026-wiki.vercel.app/papers/cheng26b_interspeech/ markdown_url: https://interspeech-2026-wiki.vercel.app/papers/cheng26b_interspeech/markdown.md --- # Active Noise Control With a Gain Constraint for Micro-Loudspeakers *Zhenhua Cheng, Yi Zhou, Yin Liu, Yu Zhao, Liming Shi* [PDF](https://www.isca-archive.org/interspeech_2026/cheng26b_interspeech.pdf) · [ISCA page](https://www.isca-archive.org/interspeech_2026/cheng26b_interspeech.html) · [DOI](https://doi.org/10.21437/Interspeech.2026-2202) **Category:** `enhancement-separation` **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. | Method | Noise type | 100-500 Hz | 500-1000 Hz | 1000-2000 Hz | |---|---|---|---|---| | ANC-Wiener method | Train noise | 4.08 | 17.77 | 20.66 | | High-pass method | Train noise | -1.85 | 6.05 | 18.61 | | ANC-LF-FRC method | Train noise | -0.13 | 11.01 | 15.68 | | ANC-FRC method | Train noise | **1.55** | **13.96** | **18.55** | | ANC-FRC method | White noise | **1.54** | **14.06** | **19.23** | ## 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 / 機構 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](wang26e_interspeech.md) — same problem · relatedness 2.3/3 - [A Sparsity-Aware Robust Nonlinear Active Noise Control for Impulsive Noise Environments](xu26_interspeech.md) — same problem · relatedness 2.0/3 - [Active Constructive Interference for Speech](yaish26_interspeech.md) — shared technique · relatedness 2.0/3 - [NCPSZ: A Nonlinear Control Network for Miniature Loudspeakers in Personal Sound Zone Applications](gong26_interspeech.md) — same problem · relatedness 1.9/3 - [A Causal Reference-Enhanced Keep-Speech Active Noise Control Method](rao26_interspeech.md) — same problem · relatedness 1.8/3 All 950k paper pairs scored by TypeSafe Jev (`scripts/related/`); relatedness 0 = unrelated … 3 = directly comparable.