Spatial Reverberation and Dereverberation using an Acoustic Multiple-Input Multiple-Output System

TL;DR

The study addresses modifying room reverberation using a compact spherical loudspeaker array (SLA) in confederation with a spherical microphone array (SMA) within a MIMO framework. It develops a normalized spherical-harmonics MIMO model and derives beamformers that optimize direct-to-reverberant ratio ($DRR$) and the early-to-late energy index ($C50$), validated through extensive simulations and a listening test with head-tracked binaural rendering. Key contributions include a comprehensive system model, a SH-domain normalization scheme, a generalized Rayleigh-quotient formulation for DRR$^{MIMO}$ and $C50^{MIMO}$, robustness analysis to RIR estimation errors, and perceptual evidence that directional SLAs can achieve spatial dereverberation. The work has practical implications for room acoustics and hearing-aid/augmented listening applications by enabling spatial control of reverberation with compact, collocated sources.

Abstract

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.

Figures (10)

• Figure 1: System block diagram with SLA beamforming coefficients, $\gamma_1(k), ..,\gamma_L(k)$, and SMA beamforming coefficients, $\lambda_1(k),..., \lambda_M(k)$.
• Figure 2: System diagram in the x-y plane; X and O represent the SLA and SMA, respectively. The solid line represents direct sound and the dashed lines represent reflections (only two reflections are illustrated). $\psi_{0 }$ and $\phi_{0 }$ are the azimuth angles of the DOR and DOA for the direct sound, respectively. $\psi_{1 }$ and $\phi_{1 }$ are the corresponding angles for the sound reflected by the wall at the bottom of the figure. In this case, $\omega_{0 } = \theta_{0 } = \omega_{1 } = \theta_{1 } =90^\circ$.
• Figure 3: EDCs for $room\,1$ with RT $=1.14\,$s, for SLA beamforming vectors $maxDRR$, $minDRR$, $maxC50$, $minC50$, $maxFIX$, and $minFIX$, employing SLA SHs order $N_L = 2$, and beamforming vector $omni$.
• Figure 4: EDCs for $room\,1$ with RT $=1.14\,$s, for SLA beamforming vectors $maxC50$ and $minC50$, employing SLA SHs orders $N_L = 2,3,$ and $4$, and beamforming vector $omni$.
• Figure 5: PWD around the SMA for $room\,1$, using $N_M = 5$ and for beamforming vector $omni$. The DOAs of direct sound and first order reflections are plotted using 'x' and 'o's, respectively.