Wideband Relative Transfer Function (RTF) Estimation Exploiting Frequency Correlations

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 Cramér–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 maximumlikelihood 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.

Related publications

1. Wideband Relative Transfer Function (RTF) Estimation Exploiting Frequency Correlations
   Giovanni Bologni; Richard C. Hendriks; Richard Heusdens;
   IEEE Trans. Audio Speech Lang. Process.,
   Volume 33, pp. 731–747, 2025. DOI: 10.1109/TASLPRO.2025.3533371
   document