  Spatial attributes of room acoustics have been widely studied using
microphone and loudspeaker arrays. However, systems that combine both arrays,
referred to as multiple-input multiple-output (MIMO) systems, have only been
studied to a limited degree in this context. These systems can potentially
provide a powerful tool for room acoustics analysis due to the ability to
simultaneously control both arrays. This paper offers a theoretical framework
for the spatial analysis of enclosed sound fields using a MIMO system
comprising spherical loudspeaker and microphone arrays. A system transfer
function is formulated in matrix form for free-field conditions, and its
properties are studied using tools from linear algebra. The system is shown to
have unit-rank, regardless of the array types, and its singular vectors are
related to the directions of arrival and radiation at the microphone and
loudspeaker arrays, respectively. The formulation is then generalized to apply
to rooms, using an image source method. In this case, the rank of the system is
related to the number of significant reflections. The paper ends with
simulation studies, which support the developed theory, and with an extensive
reflection analysis of a room impulse response, using the platform of a MIMO
system.
