  We consider the problem of estimating the direction of arrival of desired
acoustic sources in the presence of multiple acoustic interference sources. All
the sources are located in noisy and reverberant environments and are received
by a microphone array. We propose a new approach for designing beamformers and
DoA estimation methods based on the Riemannian geometry of the manifold of
Hermitian positive definite matrices. Specifically, we show theoretically that
incorporating the Riemannian mean of the spatial correlation matrices into
frequently-used beamformers gives rise to spatial spectra that reject the
directions of interference sources and result in a higher
signal-to-interference ratio. We experimentally demonstrate the advantages of
our approach in designing several beamformers and a recent DoA estimation
method in the presence of simultaneously active multiple interference sources.
