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.
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.
Methods are proposed for modifying the reverberation characteristics of sound fields in rooms by employing a loudspeaker with adjustable directivity, realized with a compact spherical loudspeaker array (SLA). These methods are based on minimization and maximization of clarity and direct-to-reverberant sound ratio. Significant modification of reverberation is achieved by these methods, as shown in simulation studies. The system under investigation includes a spherical microphone array and an SLA, comprising a multiple-input multiple-output system. The robustness of these methods to system identification errors is also investigated. Finally, reverberation and dereverberation results are validated by a listening experiment.
Spatial analysis of room acoustics is an ongoing research topic. Microphone arrays have been employed for spatial analyses with an important objective being the estimation of the direction-of-arrival (DOA) of direct sound and early room reflections using room impulse responses (RIRs). An optimal method for DOA estimation is the multiple signal classification algorithm. When RIRs are considered, this method typically fails due to the correlation of room reflections, which leads to rank deficiency of the cross-spectrum matrix. Preprocessing methods for rank restoration, which may involve averaging over frequency, for example, have been proposed exclusively for spherical arrays. However, these methods fail in the case of reflections with equal time delays, which may arise in practice and could be of interest. In this paper, a method is proposed for systems that combine a spherical microphone array and a spherical loudspeaker array, referred to as multiple-input multiple-output systems. This method, referred to as modal smoothing, exploits the additional spatial diversity for rank restoration and succeeds where previous methods fail, as demonstrated in a simulation study. Finally, combining modal smoothing with a preprocessing method is proposed in order to increase the number of DOAs that can be estimated using low-order spherical loudspeaker arrays.
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