# Adaptive Binaural Cue-Based Amplitude Panning in Irregular Loudspeaker Configurations
## 4 Experiments
### Subjective Experiments  
Subjective localization tests were conducted to evaluate the perceived azimuth angles of virtual sources. Stereo audio was generated using three distinct methods and four types of audio content: pink noise low-pass filtered at 1.5 kHz (10 s), pink noise low-pass filtered at 9 kHz (10 s), male and female conversation (6 s), and a song clip from 'The Show' by [PERSON] [34] (10 s). The mean SPL of each method was calibrated to 70 dB. Based on the findings from the objective experiments, the experimental azimuth angles were set at \(-10^{\circ}\), \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\), \(25^{\circ}\), \(30^{\circ}\), \(35^{\circ}\), and \(40^{\circ}\), presented in random order. A total of 12 participants with clinically normal hearing (10 males, 2 females, aged 22 to 27 years) took part in the subjective experiments. Participants were instructed to sit in a chair at the listening position, close their eyes prior to audio playback to mitigate visual cues from the loudspeakers, and then identify the location of the virtual sound source after the audio played in loops. During the experiments, participants were permitted to rotate their heads to improve localization of the virtual sound source. Once the azimuth was determined, they opened their eyes and used a laser pointer to indicate the perceived direction of the virtual sound source. Subsequently, the experimenter used the scales in front of the participants to calculate the azimuth angle based on the position indicated by the laser pointer using geometric relationships. Prior to the formal test, participants underwent training to familiarize themselves with the procedure. To assess the efficacy of the proposed method, the experimental results are evaluated using statistical analysis. The manipulated variables comprise the desired azimuth angles, audio content types and processing methods, with the perceived azimuth angle serving as the dependent variable. As initial assessments revealed that the data did not conform to a normal distribution, a non-parametric method is employed. Specifically, [PERSON]'s tests are conducted to examine the effects of method and audio content. The Friedman test shows a statistically significant difference between the three methods (\(\chi^{2}\) = 394.4, \(p\) < 0.0001). Furthermore, a significant difference is also found when analyzing the effects of audio content as a variable (\(\chi^{2}\) = 61.8, \(p\) < 0.0001). These results, stratified by azimuth angles and audio content types, are shown in Figure 9, offering a comprehensive overview of the localization performance of the three methods. The black dots in the figure represent the desired angle values corresponding to each azimuth angle. The results for the pink noise filtered at 1.5 kHz are shown in Figure 9a. The VBAP method yields perceived angles close to the desired values at \(-10^{\circ}\), \(0^{\circ}\), \(35^{\circ}\), and \(40^{\circ}\), with a median azimuth error within \(5^{\circ}\). However, at \(10^{\circ}\), \(20^{\circ}\), \(25^{\circ}\), and \(30^{\circ}\), the perceived angles deviate by more than \(5^{\circ}\), with the largest error of \(9^{\circ}\) occurring at \(25^{\circ}\). The perceived direction of the virtual sound source reproduced by the DBAP method significantly deviates from the desired direction. Although the perceived angles are within \(5^{\circ}\) of the desired angles at \(-10^{\circ}\), \(35^{\circ}\), and \(40^{\circ}\), the errors exceed \(14^{\circ}\) at other angles. The perceived azimuth angle in the DBAP method tends to bias toward the directions of the two loudspeakers. Below \(20^{\circ}\), it collapses near the left loudspeaker, and above \(35^{\circ}\), it collapses near the right loudspeaker. The virtual sound source is successfully reproduced only at \(25^{\circ}\) and \(30^{\circ}\), with significant perceptual differences observed among subjects at \(30^{\circ}\). Additionally, some participants also reported difficulty in identifying the direction of the virtual sound source during the experiments.