MPDR Beamforming for Almost-Cyclostationary Processes

TL;DR

This paper introduces the cyclic MPDR beamformer, which exploits spectral and spatial correlations in almost-cyclostationary noise sources, improving noise suppression in acoustic applications, especially under low-SNR conditions.

Contribution

The paper extends the MPDR beamformer to incorporate spectral correlations via FRESH filtering, addressing inharmonicity and demonstrating improved noise reduction for ACS processes.

Findings

Up to 5dB SI-SDR improvement over MPDR in low-SNR scenarios

Consistent STOI gains with the proposed method

Effective even with a single microphone

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 achieves. 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 5dB 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 is available at https://github.com/Screeen/cMPDR.