  This article focuses on estimating relative transfer functions (RTFs) for
beamforming applications. While traditional methods assume that spectra are
uncorrelated, this assumption is often violated in practical scenarios due to
natural phenomena such as the Doppler effect, artificial manipulations like
time-domain windowing, or the non-stationary nature of the signals, as observed
in speech. To address this, we propose an RTF estimation technique that
leverages spectral and spatial correlations through subspace analysis. To
overcome the challenge of estimating second-order spectral statistics for real
data, we employ a phase-adjusted estimator originally proposed in the context
of engine fault detection. Additionally, we derive Cram\'er--Rao bounds (CRBs)
for the RTF estimation task, providing theoretical insights into the achievable
estimation accuracy. The bounds show that channel estimation can be performed
more accurately if the noise or the target presents spectral correlations.
Experiments on real and synthetic data show that our technique outperforms the
narrowband maximum-likelihood estimator when the target exhibits spectral
correlations. Although the accuracy of the proposed algorithm is generally
close to the bound, there is some room for improvement, especially when noise
signals with high spectral correlation are present. While the applications of
channel estimation are diverse, we demonstrate the method in the context of
array processing for speech.
