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In many multi-microphone algorithms for noise reduction, an estimate of therelative transfer function (RTF) vector of the target speaker is required. Thestate-of-the-art covariance whitening (CW) method estimates the RTF vector asthe principal eigenvector of the whitened noisy covariance matrix, wherewhitening is performed using an estimate of the noise covariance matrix. Inthis paper, we consider an acoustic sensor network consisting of multiplemicrophone nodes. Assuming uncorrelated noise between the nodes but not withinthe nodes, we propose two RTF vector estimation methods that leverage theblock-diagonal structure of the noise covariance matrix. The first methodmodifies the CW method by considering only the diagonal blocks of the estimatednoise covariance matrix. In contrast, the second method only considers theoff-diagonal blocks of the noisy covariance matrix, but cannot be solved usinga simple eigenvalue decomposition. When applying the estimated RTF vector in aminimum variance distortionless response beamformer, simulation results forreal-world recordings in a reverberant environment with multiple noise sourcesshow that the modified CW method performs slightly better than the CW method interms of SNR improvement, while the off-diagonal selection method outperforms abiased RTF vector estimate obtained as the principal eigenvector of the noisycovariance matrix.

Relative Transfer Function Vector Estimation for Acoustic Sensor Networks Exploiting Covariance Matrix Structure