Design framework for spherical microphone and loudspeaker arrays in a multiple-input multiple-output system

Abstract

Spherical microphone arrays (SMAs) and spherical loudspeaker arrays (SLAs) facilitate the study of room acoustics due to the three-dimensional analysis they provide. More recently, systems that combine both arrays, referred to as multiple-input multiple-output (MIMO) systems, have been proposed due to the added spatial diversity they facilitate. The literature provides frameworks for designing SMAs and SLAs separately, including error analysis from which the operating frequency range (OFR) of an array is defined. However, such a framework does not exist for the joint design of a SMA and a SLA that comprise a MIMO system. This paper develops a design framework for MIMO systems based on a model that addresses errors and highlights the importance of a matched design. Expanding on a free-field assumption, errors are incorporated separately for each array and error bounds are defined, facilitating error analysis for the system. The dependency of the error bounds on the SLA and SMA parameters is studied and it is recommended that parameters should be chosen to assure matched OFRs of the arrays in MIMO system design. A design example is provided, demonstrating the superiority of a matched system over an unmatched system in the synthesis of directional room impulse responses.

Sector-Based Encoding and Data Compression of Virtual Acoustic Scattering

“…The resulting (N + 1) 2 × (N + 1) 2 matrix S expresses the scattering of the object as a MIMO system [18] between spherical modes of the incident field and spherical modes of the radiating scattered field. It gives a continuous spatially band-limited expression of the scattering at arbitrary directions.…”

Spherical Decomposition of Arbitrary Scattering Geometries for Virtual Acoustic Environments

“…The resulting (N +1) 2 ×(N +1) 2 matrix S expresses the scattering of the object as a MIMO system [13] between spherical modes of the incident field and spherical modes of the radiating scattered field. It gives a continuous spatially band-limited expression of the scattering at arbitrary directions.…”

“…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).…”

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

“…This is achieved by weighting the loudspeaker array input signal, s(ω), where ω is the angular frequency, with complex beamforming coefficients before applying it to the loudspeakers. In this case, the pressure at the microphone array can be written as [15]:…”

“…The ill-conditioning may then lead to noise amplification and result in erroneous DOA estimations. Lately, multiple-input multiple-output (MIMO) systems, which employ a spherical loudspeaker array instead of a single loudspeaker, have been studied for room acoustics [14,15,16]. Thanks to the additional spatial diversity, the direction of radiation (DOR) of reflections in a room (relative to the loudspeaker array center) can also be estimated, using the same methods used for DOA estimation.…”