Wideband Relative Transfer Function (RTF) Estimation Exploiting Frequency Correlations

TL;DR

This paper introduces a novel RTF estimation method that exploits spectral and spatial correlations, improving accuracy over traditional uncorrelated assumptions, especially in speech processing applications.

Contribution

The paper proposes a new RTF estimation technique leveraging spectral and spatial correlations via subspace analysis, and derives CRBs to understand estimation limits.

Findings

Outperforms narrowband covariance whitening in correlated spectral scenarios

Achieves near-theoretical estimation accuracy in experiments

Potential for further improvement in highly correlated noise environments

Abstract

This article focuses on estimating relative transfer functions (RTFs) for beamforming applications. Traditional methods often assume that spectra are uncorrelated, an assumption that is often violated in practical scenarios due to factors such as time-domain windowing or the non-stationary nature of signals, as observed in speech. To overcome these limitations, we propose an RTF estimation technique that leverages spectral and spatial correlations through subspace analysis. Additionally, we derive Cram\'er--Rao bounds (CRBs) for the RTF estimation task, providing theoretical insights into the achievable estimation accuracy. These bounds reveal that channel estimation can be performed more accurately if the noise or the target signal exhibits spectral correlations. Experiments with both real and synthetic data show that our technique outperforms the narrowband maximum-likelihood estimator, known as covariance whitening (CW), when the target exhibits spectral correlations. Although the proposed algorithm generally achieves accuracy close to the theoretical bound, there is potential for further improvement, especially in scenarios with highly spectrally correlated noise. While channel estimation has various applications, we demonstrate the method using a minimum variance distortionless (MVDR) beamformer for multichannel speech enhancement. A free Python implementation is also provided.