  Spatial analysis of room acoustics is an ongoing research topic. Microphone
arrays have been employed for spatial analyses with an important objective
being the estimation of the direction-of-arrival (DOA) of direct sound and
early room reflections using room impulse responses (RIRs). An optimal method
for DOA estimation is the multiple signal classification algorithm. When RIRs
are considered, this method typically fails due to the correlation of room
reflections, which leads to rank deficiency of the cross-spectrum matrix.
Preprocessing methods for rank restoration, which may involve averaging over
frequency, for example, have been proposed exclusively for spherical arrays.
However, these methods fail in the case of reflections with equal time delays,
which may arise in practice and could be of interest. In this paper, a method
is proposed for systems that combine a spherical microphone array and a
spherical loudspeaker array, referred to as multiple-input multiple-output
systems. This method, referred to as modal smoothing, exploits the additional
spatial diversity for rank restoration and succeeds where previous methods
fail, as demonstrated in a simulation study. Finally, combining modal smoothing
with a preprocessing method is proposed in order to increase the number of DOAs
that can be estimated using low-order spherical loudspeaker arrays.
