# Adaptive Binaural Cue-Based Amplitude Panning in Irregular Loudspeaker Configurations
## 4 Experiments
### Objective Experiments
This implies that, for irregular loudspeaker placements, the time delay must be carefully adjusted to ensure that sounds from both loudspeakers arrive at the listening area nearly simultaneously, thereby enabling virtual sound source creation through amplitude panning. The proposed method can accurately reproduce virtual sources by incorporating ITD into the gain calculation using measured BRIRs. Figure 8b shows the IACC values of virtual sound sources reproduced by the three methods at various azimuth angles. The IACC of the real sound source in a free field approaches unity. In the listening room, acoustic reflections induce a reduction in IACC for all virtual sound sources. The IACC differences among the three methods are minimal, except for the DBAP algorithm, which exhibits lower values at azimuth angles of \(20^{\circ}\) and \(25^{\circ}\). The comparison of mean SPL at the left and right ears for different virtual sound source azimuth angles across the three methods is shown in Figure 8c. In the VBAP algorithm, the mean SPL tends to increase with the azimuth angle because the left  
Figure 8: (**a**) ITD, (**b**) IACC, and (**c**) mean SPL of the virtual sound sources reproduced by three methods at various desired azimuth angles in the experiment. loudspeaker, being closer to the listener, generates a higher direct sound pressure level than the right loudspeaker. However, the reflected sound and reverberation levels from both loudspeakers are similar. After compensation for direct sound, the reflected and reverberated pressure levels fall below those of the right loudspeaker, thereby reducing the total SPL from the left. Consequently, as the azimuth angle increases, the contribution from the right loudspeaker grows, leading to an overall increase in the SPL. In the DBAP algorithm, the left loudspeaker produces a higher mean SPL than the right loudspeaker due to disparities in distance. As the virtual sound source moves from left to right, the distance to the listening position increases, causing the mean SPL to decrease with the increasing azimuth angle. In the proposed method, the mean SPLs of both loudspeakers are equalized during the compensation stage. As a result, the mean SPL remains relatively stable across different azimuth angles, ensuring perceptually consistent loudness as the virtual sound source moves. The VBAP and DBAP methods assume that each loudspeaker behaves as an omni-directional point source in a free field, thereby overlooking frequency-dependent factors such as room modes, loudspeaker directivity, and inter-loudspeaker variability. These methods rely on direction- or distance-based approximations, which are insufficient to ensure accurate ITD reproduction across arbitrary virtual source azimuths and irregular loudspeaker configurations. In contrast, the proposed method predicts the ITD corresponding to each gain pair and incorporates the acoustic characteristics of the listening environment by leveraging measured RIRs and BRIRs in the gain computation. The algorithm adaptively adjusts the inter-loudspeaker gains based on the resulting ITD and IACC values. Furthermore, inverse filtering of the RIRs, which capture both direct and reflected components, including reverberation, ensures that the two loudspeakers exhibit matched magnitude frequency responses at the listening position. As a result, the virtual sound source maintains a consistent mean SPL across a wide range of desired azimuth angles.