  In many multi-microphone algorithms for noise reduction, an estimate of the
relative transfer function (RTF) vector of the target speaker is required. The
state-of-the-art covariance whitening (CW) method estimates the RTF vector as
the principal eigenvector of the whitened noisy covariance matrix, where
whitening is performed using an estimate of the noise covariance matrix. In
this paper, we consider an acoustic sensor network consisting of multiple
microphone nodes. Assuming uncorrelated noise between the nodes but not within
the nodes, we propose two RTF vector estimation methods that leverage the
block-diagonal structure of the noise covariance matrix. The first method
modifies the CW method by considering only the diagonal blocks of the estimated
noise covariance matrix. In contrast, the second method only considers the
off-diagonal blocks of the noisy covariance matrix, but cannot be solved using
a simple eigenvalue decomposition. When applying the estimated RTF vector in a
minimum variance distortionless response beamformer, simulation results for
real-world recordings in a reverberant environment with multiple noise sources
show that the modified CW method performs slightly better than the CW method in
terms of SNR improvement, while the off-diagonal selection method outperforms a
biased RTF vector estimate obtained as the principal eigenvector of the noisy
covariance matrix.
