MVDR Beamforming for Cyclostationary Processes

TL;DR

The paper addresses denoising with harmonic-like, cyclostationary noise by extending MVDR to a cyclic, frequency-shifted domain. It introduces cMVDR, a multi-band beamformer based on FRESH filtering that jointly exploits spatial and spectral correlations, and a data-driven procedure to estimate resonant frequencies via the periodogram and to select effective frequency shifts using coherence filtering. Theoretical analysis shows that noise reduction improves with spectral correlation, and experiments on synthetic and real data demonstrate consistent SI-SDR and STOI gains, including scenarios with a single microphone and low SNR. The work provides open-source code and demonstrates practical impact for robust acoustic beamforming in non-stationary noise environments where harmonic structure is present.

Abstract

Conventional acoustic beamformers assume that noise is stationary within short time frames. This assumption prevents them from exploiting correlations between frequencies in almost-periodic noise sources such as musical instruments, fans, and engines. These signals exhibit periodically varying statistics and are better modeled as cyclostationary processes. This paper introduces the cyclic MVDR (cMVDR) beamformer, an extension of the conventional MVDR that leverages both spatial and spectral correlations to improve noise reduction, particularly in low-SNR scenarios. The method builds on frequency-shifted (FRESH) filtering, where shifted versions of the input are combined to attenuate or amplify components that are coherent across frequency. To address inharmonicity, where harmonic partials deviate from exact integer multiples of the fundamental frequency, we propose a data-driven strategy that estimates resonant frequencies via periodogram analysis and computes the frequency shifts from their spacing. Analytical and experimental results demonstrate that performance improves with increasing spectral correlation. On real recordings, the cMVDR achieves up to 5 dB gain in scale-invariant signal-to-distortion ratio (SI-SDR) over the MVDR and remains effective even with a single microphone. Code is available at https://github.com/Screeen/cMVDR.

Figures (8)

• Figure 1: Spectrum of a cello note with ideal harmonics. Higher harmonics deviate from integer multiples of the fundamental.
• Figure 2: Waveforms of cello (left) and white noise (right) of frequency components $f = n\cdot f_1,~n=1,2,3$ bandpassed and downshifted to 82Hz --- the fundamental frequency of the cello note. While the harmonics of the cello (left) follow almost identical trends, the white noise components (right) resemble independent realizations.
• Figure 3: Overview of the proposed method: harmonic frequency estimation, signal modulation, STFT, coherence filtering, and cMVDR beamforming.
• Figure 4: Comparison of frequency-shift calculation strategies for aligning harmonics to working frequency $\alpha_2$. Column 1: original spectrum. Columns 2–3: integer-multiple downward shifts (\ref{['sssec:down_shift']}); Columns 4–5: difference-based shifts (\ref{['sssec:diff_shift']}). Markers distinguish individual harmonics.
• Figure 5: Comparison of the $\times$ and the $\Delta$ strategies for calculating frequency shifts.