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Spatial attributes of room acoustics have been widely studied usingmicrophone and loudspeaker arrays. However, systems that combine both arrays,referred to as multiple-input multiple-output (MIMO) systems, have only beenstudied to a limited degree in this context. These systems can potentiallyprovide a powerful tool for room acoustics analysis due to the ability tosimultaneously control both arrays. This paper offers a theoretical frameworkfor the spatial analysis of enclosed sound fields using a MIMO systemcomprising spherical loudspeaker and microphone arrays. A system transferfunction is formulated in matrix form for free-field conditions, and itsproperties are studied using tools from linear algebra. The system is shown tohave unit-rank, regardless of the array types, and its singular vectors arerelated to the directions of arrival and radiation at the microphone andloudspeaker arrays, respectively. The formulation is then generalized to applyto rooms, using an image source method. In this case, the rank of the system isrelated to the number of significant reflections. The paper ends withsimulation studies, which support the developed theory, and with an extensivereflection analysis of a room impulse response, using the platform of a MIMOsystem.

Theory and investigation of acoustic multiple-input multiple-output systems based on spherical arrays in a room