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Direction-Preserving Active Noise Control with a Conditional Control-Filter Estimation Network

Ziyi Yang, Zhengding Luo, Boxiang Wang, Libin Zhang, Woon-Seng Gan

arXiv:2609.07173v1eess.AS

TL;DR

Direction-preserving ANC aims to attenuate noise from other directions while preserving sound from a specified desired direction, a goal not jointly addressed by existing approaches without repeated optimization or desired-signal reconstruction. This paper trains a direction-conditioned network to estimate feedforward control filters from mixed-reference observations; it reports higher mean noise reduction than analytical SSANC at matched mean desired-signal distortion, with measured-transfer-function validation.

  • Problem

    Conventional ANC minimizes total disturbance without distinguishing desired sound from noise, while existing approaches do not jointly balance cancellation and preservation without repeated analytical optimization or desired-signal reconstruction.

    Source: §I · p. 1

  • Method

    A direction-conditioned network estimates a complete multichannel FIR control-filter bank from a mixed-reference observation and desired direction, trained with a component-separated cancellation–preservation objective.

    Source: §I · p. 2, B. Directional Signal Decomposition · p. 2

  • Results

    DP-ANC achieved higher mean noise reduction than analytical SSANC at matched mean desired-signal distortion, and Hearpiece validation demonstrated performance under measured primary-path conditions.

    Source: A. Average Cancellation and… · p. 8, §VI · p. 10

  • Takeaways & Limitations

    The cancellation–preservation trade-off is shaped by reference-array spatial separability, with consistent trends reported for learning-based and analytical designs across simulated and measured configurations.

    Source: §VI · p. 10

    Evaluation focuses on static scenes with one desired and one noise source; reverberation, moving sources, path mismatch, and closed-loop hardware remain for future work.

    Source: F. Limitations · p. 10

Abstract

from arXiv · show

Conventional active noise control (ANC) minimizes the total disturbance at the error microphone without distinguishing desired sound from noise. Direction-preserving ANC (DP-ANC) instead aims to attenuate a noise component arriving from a direction other than the specified desired direction while preserving sound naturally arriving from that direction. Existing approaches typically either require analytical optimization to be repeated for each new observation or estimate and reproduce the desired component through a hear-through secondary-source path. To address these limitations, this paper formulates DP-ANC as a direction-conditioned cancellation-preservation optimization problem. A component-separated objective jointly penalizes residual noise energy and the control response induced by the desired component, with a scalar weighting parameter controlling the cancellation-preservation trade-off. A convolutional network conditioned on the specified desired direction through feature-wise linear modulation (FiLM) is trained using a differentiable secondary-path-aware forward model. At deployment, the network estimates the complete multichannel finite impulse response (FIR) control-filter bank directly from a mixed-reference observation and the specified desired direction in a single forward pass, while retaining the conventional feedforward ANC signal path. Over 3300 evaluation cases, the selected operating point achieves 22.8 dB mean noise reduction with a desired-signal distortion of -11.4 dB. Validation using measured in-ear-device transfer functions further demonstrates consistent performance under measured acoustic configurations.

I. INTRODUCTION

DP-ANC addresses the need to suppress sound arriving outside a desired direction while preserving sound from that direction. The paper combines a cancellation–preservation objective with a network that estimates feedforward control filters from a mixed-reference observation and desired direction.

I. INTRODUCTION

  • Existing approaches do not jointly provide this balance without predesigned filter banks, repeated analytical optimization, or desired-signal reconstruction.Analytical SSANC recomputes a matrix solution for each observation, while hear-through systems reproduce the desired component through secondary sources.Source: §I · pp. 1–2
  • A scalar weighting parameter balances noise cancellation against desired-signal preservation without imposing a prescribed desired-direction response constraint.This is formulated as a direction-conditioned cancellation–preservation optimization problem.Source: §I · p. 2
  • The proposed network estimates a complete multichannel FIR control-filter bank from a short mixed-reference observation and desired direction, retaining the conventional feedforward ANC path.It is trained offline and estimates the filters in one forward pass at deployment.Source: §I · p. 2

A. Multichannel Feedforward ANC Model

  • Conventional feedforward ANC uses tapped reference-signal vectors and control filters to drive a secondary source, with the secondary-path-filtered control contribution designed to reduce the residual disturbance.The conventional objective minimizes residual energy without distinguishing desired sound from noise.Source: A. Multichannel Feedforward ANC Model · p. 2

B. Directional Signal Decomposition

The method separates desired and noise components by direction to formulate direction-selective ANC. The same control-filter bank is intended to cancel noise while producing little secondary response to the desired component.

B. Directional Signal Decomposition

  • The disturbance and reference signals are decomposed into directional components for offline objective evaluation, while deployment uses mixed-reference observations and the specified desired direction.The evaluated setting contains one desired source and one noise source.Source: B. Directional Signal Decomposition · p. 2
  • For a source arriving from direction θ, acoustic paths model its contributions at each reference microphone and at the error microphone.The paths are q_k(θ, n) for the reference signal and p(θ, n) for the primary disturbance.Source: B. Directional Signal Decomposition · p. 2
  • The control-filter bank must reduce the residual noise component while keeping the desired component after control small.These are the separate noise-attenuation and desired-signal-preservation requirements.Source: B. Directional Signal Decomposition · p. 3

C. Cancellation–Preservation Objective

The cancellation–preservation objective penalizes residual noise and the control response induced by the desired component. A scalar weight sets their trade-off without requiring a fixed desired-direction response.

C. Cancellation–Preservation Objective

  • Penalizing rather than constraining the desired-induced control response preserves a continuous trade-off and avoids substantially reducing the filter degrees of freedom available for noise cancellation.The formulation does not prescribe a target response or delay.Source: C. Cancellation–Preservation Objective · p. 3
  • The objective combines normalized noise reduction and desired-signal preservation terms, with λ controlling their relative weight.Larger λ places more weight on limiting the desired-induced control response; smaller values permit more aggressive cancellation.Source: C. Cancellation–Preservation Objective · p. 3
  • The preservation term penalizes the desired-induced control response evaluated through the secondary path, rather than deviation from a prescribed desired-direction response.The component-separated terms are evaluated at the ANC error microphone.Source: C. Cancellation–Preservation Objective · p. 3
  • Direct analytical evaluation requires separated components and a new normal-equation solution for each observation; the learning-based realization instead trains directly with the weighted objective.The closed-form counterpart clarifies that the preservation term acts as a direction-dependent quadratic regularizer.Source: C. Cancellation–Preservation Objective · p. 3

III. PROPOSED DP-ANC FRAMEWORK

The framework maps a mixed-reference observation and desired direction to a feedforward control-filter bank. Offline training evaluates the filters with separated components, while deployment retains the conventional ANC signal path.

III. PROPOSED DP-ANC FRAMEWORK

  • Given a mixed-reference observation and specified desired direction, the estimation network produces the complete feedforward control-filter bank.The multichannel reference observation is transformed to a complex STFT network input.Source: A. Framework Overview · p. 3
  • Separated desired and noise components are used to evaluate the offline objective, but the network receives the mixed-reference observation and desired direction at deployment.The noise direction is not supplied explicitly; the desired direction identifies the component whose control response is limited.Source: A. Framework Overview · p. 3
  • Training minimizes expected objective over a distribution of scenes, learning one mapping shared across scenes instead of repeating a matrix solve for each deployment observation.The scene distribution spans directions, paths, source levels, and waveform realizations.Source: A. Framework Overview · p. 3
  • At runtime, the estimated filters drive the secondary source within the retained feedforward ANC structure to attenuate noise while limiting response to the desired component.The convolutional encoder uses adaptive pooling to accept different observation durations.Source: Figure 1 · p. 4, A. Framework Overview · p. 4

B. Direction-Conditioned Control-Filter Estimation Network

The network combines multichannel acoustic features with the specified desired direction, then decodes them into a complete causal FIR control-filter bank. FiLM injects direction information into each convolutional block, while frequency-domain estimation serves as a compact filter parameterization for time-domain feedforward control.

B. Direction-Conditioned Control-Filter Estimation Network

  • The real and imaginary parts of all reference-microphone STFTs are stacked, preserving inter-microphone phase relationships needed for directional discrimination.The network input retains the complex multichannel representation.Source: B. Direction-Conditioned… · p. 4
  • A periodic desired-direction code passes through a two-layer encoder and block-specific FiLM heads to modulate convolutional features after batch normalization and before ReLU.The FiLM modulation starts as an identity mapping because its weights and biases are initialized to zero.Source: B. Direction-Conditioned… · p. 4
  • Adaptive pooling and a decoder produce normalized real and imaginary coefficients for every control filter, which are de-normalized and reshaped into one-sided complex spectra.The stated configuration uses K = 6 reference channels, nf = 129 frequency bins, and Lw = 256 filter taps.Source: B. Direction-Conditioned… · p. 4, Table I · p. 5
  • Hermitian completion and a 256-point inverse FFT convert each estimated spectrum directly into a real causal FIR filter without truncation.Frequency-domain estimation is only a compact parameterization; runtime control uses time-domain feedforward convolution.Source: B. Direction-Conditioned… · p. 5

C. Differentiable Training with Independent Signal Realizations

Training estimates filters from one mixed-reference realization and evaluates their cancellation and preservation responses on independent waveforms sharing the same directions and acoustic paths. The simulated configuration uses a six-microphone circular array and fixed secondary-path model, with evaluation conditions including sensor noise and angular separation.

C. Differentiable Training with Independent Signal Realizations

  • Independent waveform realizations share source directions and acoustic paths: one supplies the mixed-reference filter-estimation observation, and the other supplies loss evaluation.This separation is intended to encourage filters to remain effective beyond the waveforms used for estimation.Source: C. Differentiable Training with… · p. 5
  • A differentiable secondary-path-aware forward model applies the estimated filters to separately rendered desired and noise components, then propagates gradients through the filters and secondary path.The resulting control responses enter the cancellation and desired-signal preservation terms.Source: C. Differentiable Training with… · p. 5

A. Main Simulated Acoustic Configuration

  • The simulated setup uses six reference microphones around a central error microphone, a nearby secondary source, 8 kHz sampling, a 20–2500 Hz band, and 0.5 s observations.The secondary path is modeled as a known, fixed 16-tap causal response; evaluation uses 30 dB sensor SNR and angular separations of at least 15°.Source: A. Main Simulated Acoustic Configuration · p. 5, Figure 2 · p. 5
  • Array spatial coherence limits the joint achievement of high noise reduction and low desired-signal distortion; the stated resolution scales vary with frequency and the main-evaluation separation criterion is not a fixed physical boundary.For a 0.20 m radius, the approximation gives about 36°, 18°, 12°, and 9° at 500, 1000, 1500, and 2000 Hz, respectively.Source: A. Main Simulated Acoustic Configuration · pp. 5–6

B. Data Generation and Directional Sampling

Training scenes pair a desired source with a noise source at independently sampled azimuths, while training data vary pre-control SNR and noise type. Separate network instances are trained for different trade-off weights, and a validation criterion selects the representative operating point.

B. Data Generation and Directional Sampling

  • Each training scene contains one desired source and one noise source whose azimuths are independently drawn uniformly over 0°–360° and fixed within the 0.5 s realization.The desired waveform is a band-limited Gaussian sequence; noise is sampled equally from band-limited Gaussian sequences and UrbanSound8K recordings.Source: B. Data Generation and Directional… · p. 6
  • Training samples pre-control error-microphone SNR independently from U[−15, 5] dB and uses separate waveform realizations for filter estimation and loss or metric computation.The two realizations share directions and acoustic paths but use independent source waveforms.Source: B. Data Generation and Directional… · p. 6

C. Network Training

  • Separate 956,540-parameter networks are trained for λ ∈ {0, 0.03, 0.1, 0.3, 1}, with the best epoch selected by lowest validation LDP on 1024 synthetic scenes.All candidates use the same fixed validation set generated under the training-scene protocol with separate recordings.Source: C. Network Training · p. 6
  • The representative operating point is λ = 0.1, chosen as the candidate nearest the ideal point after NR and −Ddes are independently min–max normalized across the five candidates.The models are optimized with AdamW.Source: C. Network Training · p. 6

D. Compared Methods

The compared methods span uncontrolled ANC, conventional cancellation, hear-through reconstruction, analytical constrained control, and the proposed estimated-filter approach. The analytical SSANC comparison uses a cancellation–preservation frontier, while the proposed method predicts filters for use in the conventional feedforward path.

1) ANC Off:

  • ANC Off uses the uncontrolled error-microphone signal as the noise-reduction reference at 0 dB.Source: 1) ANC Off · p. 6

2) Conventional Wiener ANC:

  • Conventional Wiener ANC minimizes total error-microphone energy without separating desired sound from noise, representing the maximum-cancellation endpoint.Source: 2) Conventional Wiener ANC · p. 6

3) Beamformer Hear-Through:

  • Beamformer hear-through extracts the desired-direction signal with a 384-tap least-squares beamformer and reproduces it through the secondary source after ANC attenuation.The beamformer uses a 4.0 ms target delay.Source: 3) Beamformer Hear-Through · p. 6

4) Analytical SSANC:

  • Analytical SSANC recomputes control filters from each 0.5 s mixed-reference observation using desired-direction path information, then sweeps rf over 13 values to form its cancellation–preservation frontier.The same 256-tap-per-channel filters and processing band are used across the sweep; Table III and Fig. 3 show the representative setting rβ = rf = 104.Source: 4) Analytical SSANC · p. 6

5) DP-ANC (Proposed):

  • The proposed DP-ANC network estimates the complete control-filter bank from the mixed-reference observation and desired direction without a new matrix solution, then uses the conventional feedforward control path.The computational comparison counts network multiply–accumulate operations and converts analytical SSANC eigendecomposition and inversion operations to MACs.Source: 5) DP-ANC (Proposed) · pp. 6–7

E. Evaluation Metrics

The evaluation metrics distinguish noise reduction, desired-signal preservation, and output SNR, while the protocols test independent signals in simulated and measured-path configurations.

E. Evaluation Metrics

  • Ddes measures the desired-induced control-response energy normalized by the naturally arriving desired-component energy; it is not a perceptual distortion score.More negative values indicate a weaker response, while 0 dB indicates equal energies without distinguishing cancellation, reinforcement, or phase alteration.Source: E. Evaluation Metrics · p. 7
  • SNRout measures the energy balance between the controlled desired component and residual noise, but does not measure waveform fidelity by itself.The evaluation interprets it jointly with Ddes and component-resolved time-frequency and envelope comparisons.Source: E. Evaluation Metrics · p. 7

F. Evaluation Protocol

  • The main evaluation uses 3300 cases across 11 balanced content groups, with a −10 dB pre-control SNR and at least 15° source separation.Filter estimation and metric computation use independent 0.5 s signal realizations under the same directions and acoustic paths.Source: F. Evaluation Protocol · p. 7
  • The full-azimuth coverage experiment uses a common −5 dB pre-control SNR and 30 dB sensor-noise level; desired direction is fixed, with a control-filter bank estimated separately for each noise direction.It reports frequency-resolved results in four analysis bands centered at 200, 500, 1000, and 2000 Hz, plus broadband “Overall” values averaged over all 48 noise directions.Source: F. Evaluation Protocol · p. 7

G. Measured Hearpiece-Path Validation

  • Measured-path validation uses KEMAR transfer functions at 48 horizontal azimuths and a four-reference model, with the right eardrum as the error position.The Hearpiece protocol fixes the desired direction at 0°, sweeps noise over the measured azimuths, and evaluates each filter on four independent 0.5 s signals.Source: G. Measured Hearpiece-Path Validation · pp. 7–8
  • The illustrative fixed-record comparison uses a 0° tonal alarm and 90° air-conditioner noise; filters are estimated from the first 0.5 s of a 2.0 s record.The complete record supplies the displayed signals.Source: Figure 3 · p. 8

V. RESULTS AND DISCUSSION

Across the evaluated settings, DP-ANC improves mean noise reduction at matched mean desired-signal distortion relative to analytical SSANC, while its preservation weight and directional input shape the cancellation–preservation balance.

A. Average Cancellation and Desired-Signal Preservation

  • 0.68–3.06 dB: DP-ANC achieves higher mean noise reduction than analytical SSANC at matched mean desired-signal distortion across five settings.Figure 4 reports the cancellation–preservation frontiers over 3300 evaluation cases.Source: Figure 4 · p. 8, A. Average Cancellation and… · p. 8
  • DP-ANC provides higher NR and the highest output SNR among the methods, while analytical SSANC has mean Ddes approximately 8 dB lower.Conventional Wiener ANC has the highest NR, but its Ddes near 0 dB indicates a desired-induced control response nearly as energetic as the desired component.Source: A. Average Cancellation and… · p. 9

B. Effect of the Preservation Weight λ

  • As λ increases from 0 to 1, mean noise reduction falls from 25.1 to 18.8 dB while mean desired-signal distortion falls from −2.2 to −20.1 dB.The weight controls this balance across separately trained models.Source: B. Effect of the Preservation Weight λ · p. 9

C. Angular Resolution and Directional Selectivity

  • As source separation increases from 0° to 30° in the first setting pair, DP-ANC noise reduction rises from 21.5 to 23.3 dB and desired-signal distortion falls from −0.6 to −9.4 dB.Analytical SSANC follows a similar trend; the comparison includes two cancellation–preservation settings and averages 64 cases per point.Source: C. Angular Resolution and Directional… · p. 9, Figure 5 · p. 9
  • Across the simulated circular array, broadband overall NR is 22.6 dB, while preservation is angle-dependent and −Ddes is only about 1–3 dB at coincident directions.The experiment evaluates each noise azimuth with a filter bank estimated for that direction, making it a directional-coverage map rather than a fixed-filter beampattern.Source: C. Angular Resolution and Directional… · p. 9
  • When the specified desired direction aligns with either physical source, that source has approximately −10 dB Ddes while the other is attenuated by over 24 dB.Responses vary continuously as the specified direction sweeps between the sources.Source: C. Angular Resolution and Directional… · p. 9

D. Validation on Measured Hearpiece Primary Paths

The Hearpiece model achieved 16.6 dB broadband noise reduction with −7.7 dB desired-signal distortion, and DP-ANC required fewer operation counts than analytical SSANC to obtain a control-filter bank. The evaluation remains limited to static one-desired-source, one-noise-source scenes, while future work targets multi-source and time-varying scenes.

D. Validation on Measured Hearpiece Primary Paths

  • Directional coverage evaluates 48 swept noise azimuths at a fixed desired direction, while the sensitivity test changes only the specified direction across fixed two-source scenes.The coverage uses four broadband evaluations per azimuth; sensitivity averages 32 scenes with sources at 0° and 135°.Source: Figure 6 · p. 10, Figure 7 · p. 10
  • 16.6 dB broadband noise reduction with −7.7 dB desired-signal distortion was achieved by the separately trained Hearpiece model.The results support applicability to measured acoustic paths and different microphone-array configurations.Source: D. Validation on Measured Hearpiece… · pp. 9–10

E. Computational Comparison

F. Limitations

  • The evaluation focuses on static scenes with one desired source and one noise source; reverberation, moving sources, path mismatch, and closed-loop hardware remain untested.The network also uses a 0.5 s observation block and is trained for a specific microphone geometry.Source: F. Limitations · p. 10

VI. CONCLUSION

  • In simulation, the proposed method achieved higher mean noise reduction than analytical SSANC at matched mean desired-signal distortion.Angular-resolution results show that reference-array spatial separability shapes the cancellation–preservation trade-off.Source: §VI · p. 10
  • Future work will extend the objective to multi-source and time-varying scenes and develop streaming updates and cross-device adaptation.Source: §VI · pp. 10–11
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