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

Abstract

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.

Modal smoothing for analysis of room reflections measured with spherical microphone and loudspeaker arrays

“…A model for a system positioned in a room is then formulated. Finally, the radial-function elimination is applied to the spherical microphone array, as it has been shown to be beneficial in room acoustics applications [18,14]. For further details regarding the complete formulation of MIMO systems, including a study of system properties and of limitations, the reader is referred to Refs.…”

“…which holds λ l (ω) for all reflections. An important characteristic of the room system transfer matrix is that its rank is bounded by the number of significant reflections or by its dimensions (the lower of the two) [14], i.e., min(L, (N L + 1) 2 , (N M + 1) 2 ), which will be useful in the formulation of modal smoothing in the next section. Note that the number of reflections in a room can be high; thus, the limitation on matrix rank presented in this section constrains the method to work in practice only when the reflections are relatively sparse, i.e., for the early reflections.…”

“…A(ω), the MIMO system transfer matrix, has been studied in Ref. 14, providing insight into the expected performance and limitations of modal smoothing: its rank was proposed as an estimator for the number of significant reflections, and an analysis of this matrix's singular values was provided. The singular values were shown to be comprised of two distinct groups: the signal singular values, equal in number to the number of reflections (when using high enough SH orders of the arrays), and the noise singular values, which include all singular values that are not included in the first group.…”

“…Expanding on this relation between the eigenvalues of SA (ω) and singular values of A(ω), the performance of modal smoothing, i.e., the ability to successfully restore the rank of SA (ω), is expected to be similar to that of the estimation of the number of reflections, which was extensively studied in Ref. 14. In particular, one limitation that arises from the analysis in Ref.…”

Spherical Decomposition of Arbitrary Scattering Geometries for Virtual Acoustic Environments

“…In regards to modeling the effects of scattering of entire finite geometries into virtual environments, not much research exists. Though analytical models for basic geometries such as the sphere exist [9], and methods have been proposed to estimate scattering using machine learning [10,11], still flexible methods for In this paper we propose a method for encoding the scattering properties of entire arbitrary complex geometries through a multiple-input multiple-output (MIMO) spherical decomposition [12,13] approach of the scattering function. We show how this encoding format is flexible and allows for various manipulations of the scattered field (rotation, scaling, translation).…”