Modeling Localization of Amplitude-Panned Virtual Sources in Sagittal Planes

Abstract

Vector-base amplitude panning (VBAP) aims at creating virtual sound sources at arbitrary directions within multichannel sound reproduction systems. However, VBAP does not consistently produce listener-specific monaural spectral cues that are essential for localization of sound sources in sagittal planes, including the front-back and up-down dimensions. In order to better understand the limitations of VBAP, a functional model approximating human processing of spectro-spatial information was applied to assess accuracy in sagittal-plane localization of virtual sources created by means of VBAP. First, we evaluated VBAP applied on two loudspeakers in the median plane, and then we investigated the directional dependence of the localization accuracy in several three-dimensional loudspeaker arrangements designed in layers of constant elevation. The model predicted a strong dependence on listeners' individual head-related transfer functions, on virtual source directions, and on loudspeaker arrangements. In general, the simulations showed a systematic degradation with increasing polar-angle span between neighboring loudspeakers. For the design of VBAP systems, predictions suggest that spans up to 40° polar angle yield a good trade-off between system complexity and localization accuracy. Special attention should be paid to the frontal region where listeners are most sensitive to deviating spectral cues.

Fig. 1

Interaural-polar coordinate system with lateral angle, ϕ ∈ [−90°, 90°], and polar angle, θ ∈ [−90°, 270°).

Fig. 2

Example showing the spectral discrepancies obtained by VBAP. The targeted spectrum is the HRTF for 20° polar angle. The spectrum obtained by VBAP is the superposition of two HRTFs from directions 40° polar angle apart of each other with the targeted source direction centered in between.

Fig. 3

Structure of the sagittal-plane localization model used for simulations. Reproduced with permission from [12]. © 2014, Acoustical Society of America.

Fig. 4

Response predictions to sounds created by VBAP with two loudspeakers in the median plane positioned at polar angles of −15° and 30°, respectively. Predictions for two exemplary listeners and pooled across all listeners. Each column of a panel shows the predicted PMV of polar-angle responses to a certain sound. Note the inter-individual differences and the generally small probabilities at response angles not occupied by the loudspeakers.

Fig. 5

Listener-specific increases in polar error as a function of the panning angle. Increase in polar error defined as the difference between the polar error obtained by the VBAP source and the polar error obtained by the real source at the corresponding panning angle. Same loudspeaker arrangement as for Fig. 4. Note the large inter-individual differences and the increase in polar error being largest at panning angles centered between the loudspeakers, i.e., at panning ratios around R = 0 dB.

Fig. 6

Panning angles for the loudspeaker arrangement of Fig. 4 judged best for reference sources at polar angles of 0° or 15° in the median plane. Comparison between experimental results from [2] and simulated results based on various response strategies: PM, CM, and both mixed—see text for descriptions. Dotted horizontal line: polar angle of the reference source. Horizontal line within box: median; box: inter-quartile range (IQR); whisker: within quartile ±1.5 IQR; star: outlier. Note that the simulations predicted a bias similar to the results from [2] for the reference source at 0°.

Fig. 7

Increase in polar error (defined as in Fig. 5) as a function of loudspeaker span in the median plane with panning ratio R = 0 dB. Black line with gray area indicates mean ±1 standard deviation across listeners. Note that the increase in polar error monotonically increases with loudspeaker span.

Fig. 8

Effect of loudspeaker span in the median plane on coefficient of determination, r², for virtual source directions created by VBAP. Separate analysis for frontal, rear, and overall (frontal and rear) targets. Data pooled across listeners. Note the correspondence with the results obtained by [18].

Fig. 9

Predicted polar error as a function of the lateral and polar angle of a virtual source created by VBAP in various multichannel systems. System specifications are listed in Table 2. Open circles indicate loudspeaker directions. Reference shows polar error predicted for a real source placed at the virtual source directions investigated for systems A, … , F.