Optimized Loudspeaker Panning for Adaptive Sound-Field Correction and Non-stationary Listening Areas

TL;DR

The paper tackles sound-field errors arising from irregular loudspeaker layouts in multichannel systems by introducing a measurement-free framework that combines Bayesian loudspeaker normalization with OPSE-driven panning optimization. A normalization filter $G_n(ν)$ aligned to an axial reference at the listener is derived from a relative-transfer-function $Q_n(ν)$, while non-stationary listening locations are handled via a circular-conjugate prior on normalization angles with Bayesian updates. The OPSE formulation maximizes panning sensitivity under spatial VBAP-like constraints, non-negativity, electrical headroom, and acoustic-power limits, solvable as a second-order cone program and reducible to kernel-space for real-time use. Acoustic covariance is modeled as a mix of direct and diffuse-field contributions, enabling adaptation across anechoic to diffuse environments and across various loudspeaker layouts. Experiments demonstrate robustness of the normalization and effectiveness of OPSE for center-channel emphasis, diffuse-field behavior, and layout-aware circular panning, with practical guidance on layout choices to optimize directional panning fidelity.

Abstract

Surround sound systems commonly distribute loudspeakers along standardized layouts for multichannel audio reproduction. However in less controlled environments, practical layouts vary in loudspeaker quantity, placement, and listening locations / areas. Deviations from standard layouts introduce sound-field errors that degrade acoustic timbre, imaging, and clarity of audio content reproduction. This work introduces both Bayesian loudspeaker normalization and content panning optimization methods for sound-field correction. Conjugate prior distributions over loudspeaker-listener directions update estimated layouts for non-stationary listening locations; digital filters adapt loudspeaker acoustic responses to a common reference target at the estimated listening area without acoustic measurements. Frequency-domain panning coefficients are then optimized via sensitivity / efficiency objectives subject to spatial, electrical, and acoustic domain constraints; normalized and panned loudspeakers form virtual loudspeakers in standardized layouts for accurate multichannel reproduction. Experiments investigate robustness of Bayesian adaptation, and panning optimizations in practical applications.

Figures (7)

• Figure 1: Acoustic transfer function $G_n(\nu)$ in \ref{['EQ:PT:ANECHOIC_TF_LISTENER']} normalizes the direct acoustic path between the listener and loudspeaker at $\boldsymbol{u}_n$ to be its on-axis response $S_A(\nu, 0)$ at the normalized coordinate $\boldsymbol{v}_n$.
• Figure 2: Circular distribution prior (FWHM $90.2^{\circ}$) contains $\left \{ {50, 90, 95} \right \} \%$ of normalization angles within $\left | {\theta} \right | \leq \left \{ {27.4,\, 72,\, 90} \right \} ^{\circ}$ of the mean angle.
• Figure 3: We equalize a sample loudspeaker with acoustic responses over the horizontal plane (left) between Bayesian estimates of the normalization angle $\boldsymbol{\bar{\theta}}$ in \ref{['EQ:PT:PDF_STAT']} (center) and the axial windowed power average. The acoustic power averages (right) over the posterior circular distribution windows $f(\theta \, | \, \mu = \mu^{\left \{ {t} \right \} }, \ell = \ell^{\left \{ {t} \right \} } )$ update across time-steps to yield a sequence of quotient correction targets in \ref{['EQ:PT:RAT']}.
• Figure 4: VBAPS (left) constrains the feasible steering direction $\boldsymbol{s}$ to lie between the minor-arc of the loudspeaker pair coordinates $\boldsymbol{x}_L, \boldsymbol{x}_R$. Sample voltage constraints (right) are proportional to differences in loudspeaker-to-listener distance, orientation, and selection.
• Figure 5: OPSE center content more uniformly distributes across $5.0$ ITU loudspeakers for increasing acoustic power targets $\rho$, and constant electrical headroom.