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The perception of sound by human listeners in a room has been shown to be affected by the spatial attributes of the sound field. These spatial attributes have been studied using microphone and loudspeaker arrays separately. Systems that combine both loudspeaker and microphone arrays, termed multiple-input multiple-output (MIMO) systems, facilitate enhanced spatial analysis compared to systems with a single array thanks to the simultaneous use of the arrays and the additional spatial diversity.

Using MIMO systems, room impulse responses (RIRs) can be presented using matrix notation, which enables a unique study of a sound field’s spatial attributes by employing methods from linear algebra. In the study, a theory of the spatial analysis of a sound field using a MIMO system comprised of spherical arrays is developed and a simulation study is presented. For example, a system matrix’s rank and null space are studied to reveal spatial information on a room, such as the number of dominant room reflections and their directions of radiation and arrival from the loudspeaker array to the microphone array, respectively.

Finally, limitations on the use of MIMO systems are studied by incorporating errors in the system model. These include spatial aliasing and model mismatch errors of both of the arrays. Based on the analysis of the errors, guidelines are proposed for designing MIMO systems such that both arrays enjoy directivity and robustness in the same range of frequencies. Such systems are referred to as matched systems, and their superiority over unmatched systems is demonstrated via an additional simulation study.