Cyclic MPDR Beamforming for Suppression of Almost-Cyclostationary Acoustic Interference
Authors: Giovanni Bologni, Martin Bo M\oller, Richard Heusdens, Richard C. Hendriks
Abstract
Conventional acoustic beamformers typically assume short-time stationarity and process frequency bins independently, ignoring inter-frequency correlations. This is suboptimal for almost-periodic noise sources such as engines, fans, and musical instruments: these signals are better modeled as (almost) cyclostationary (ACS) processes with statistically correlated spectral components. This paper introduces the cyclic minimum power distortionless response (cMPDR) beamformer, which extends the conventional MPDR to jointly exploit spatial and spectral correlations. Building on frequency-shifted (FRESH) filtering, it suppresses noise components that are coherent across harmonically related frequencies, reducing residual noise beyond what spatial filtering alone can achieve. To address inharmonicity, where partials deviate from exact integer multiples of a fundamental frequency, we estimate resonant frequencies from a periodogram and derive frequency shifts from their pairwise spacing. Theoretical analysis yields closed-form expressions for residual noise and proves that output power decreases monotonically with the number of cyclic components. Experiments on synthetic harmonic noise and real UAV motor recordings confirm these findings: in low-SNR scenarios, the cMPDR achieves up to 5 dB improvement in SI-SDR over the MPDR, yields consistent STOI gains, and remains effective with a single microphone. When spectral correlation is absent, the method reduces to conventional MPDR and does not degrade performance. These results suggest that cyclic processing is a viable direction for acoustic noise reduction that deserves further investigation. Code and audio samples are available at https://github.com/Screeen/cMPDR.
Reference-based adaptive interference cancellation is evaluated for stereo audio recordings corrupted by real train noise and environmental background. The observed signal is modeled as a clean stereo program contaminated by an additive disturbance generated by an external acoustic source through unknown propagation paths. A second stereo recording, representing another filtered observation of the same physical noise source, is used as the reference input of a multi-reference recursive least-squares (RLS) estimator. The estimated train-interference component is subtracted from the noisy audio and followed by a finite-impulse-response low-pass postfilter. Three 74.01 s real audio sequences sampled at 11.025 kHz are processed under identical algorithmic parameters. Since clean ground truth is not available, performance is assessed with no-reference indicators: waveform behavior, Welch spectral estimates, RMS change, and residual normalized correlation with the reference. With 30 taps per reference channel, 15 anti-causal taps, and forgetting factor 0.999, the maximum reference correlation is reduced from 0.386--0.832 before processing to 0.011--0.016 after processing. The corresponding correlation-ratio reduction is approximately 30.6--34.1 dB, while the output RMS decreases by 1.8--4.8 dB depending on section and stereo channel. The results demonstrate that real train interference, including environmental acoustic effects, can be substantially attenuated when a correlated reference recording is available.
In dynamic acoustic environments with time-varying interferers, effective beamforming requires identifying stationary regions over time. The Capon beamformer, a whitened matched filter constrained to maintain unity gain in the desired direction, theoretically relies on the instantaneous ensemble covariance matrix. Practical implementations rely on the batch Capon (or Sample Matrix Inversion), which estimates the sample covariance matrix (SCM) by averaging over a block of snapshots. This practical approach implicitly assumes that the data within the batch window is stationary and can be coherently combined. In non-stationary settings, a batch approach that averages over fixed or excessively long windows fails, as moving interferers smear the SCM and degrade the beamformer's nulling capabilities. To address this, this paper introduces a temporally segmented distortionless response beamformer. Inspired by the segmented least squares method, which fits piecewise polynomials to data while penalizing excessive segmentation to prevent overfitting, the framework extends practical Capon beamforming by incorporating data-driven temporal segmentation. This formulation minimizes output power while dynamically adapting the SCM estimation windows to local stationarity, offering a principled approach to tracking time-varying interferers.
The minimum variance distortionless response (MVDR) beamformer is widely used for multichannel speech enhancement due to strong noise suppression while preserving target signals. In practice, its performance is sensitive to microphone self-noise and array mismatches. Existing approaches typically rely on fixed, manually tuned WNG thresholds or diagonal loading, leading to suboptimal performance under unknown or time-varying acoustic conditions. This paper proposes a data-driven MVDR framework that adaptively estimates the WNG constraint using a deep neural network. The network jointly predicts a time-frequency noise mask for covariance estimation and a frequency-dependent WNG threshold, enabling dynamic robustness-directivity control. A differentiable robust MVDR layer is integrated into the framework, allowing end-to-end optimization. Experiments demonstrate consistent improvements in speech quality and intelligibility over conventional fixed-WNG MVDR methods.