# Adaptive Binaural Cue-Based Amplitude Panning in Irregular Loudspeaker Configurations
## 4 Experiments  
### Objective Experiments  
The objective experiments were conducted to validate the effectiveness of the proposed algorithm, using pink noise low-pass filtered at 9 kHz as the input signal. Signal processing was performed using a laptop, and the stimuli were delivered to the loudspeakers through the Fireface UC sound card and a power amplifier. Binaural signals were recorded using a dummy head for analysis. During the audio generation process, the VBAP algorithm first applies a gain to the signal sent to the left loudspeaker and performs a time shift to compensate for the direct sound. The gain pair corresponding to the desired azimuth angle is then applied to the monophonic audio signal to produce a two-channel output. Similarly, the DBAP algorithm directly applies the computed gain pair to the monophonic signal to generate the two-channel audio. The proposed method first filters the monophonic audio signal using inverse filters designed for the left and right loudspeakers, respectively. A time shift is then applied to the left channel, followed by the application of the gain pair to produce the final two-channel output. Compared to the VBAP and DBAP algorithms, the main additional computational cost of the proposed method lies in the two-channel filtering process. In this experiment, each inverse filter is implemented with 1000 taps. For real-time processing applications, the filter length can be reduced through central truncation or the use of higher-order octave-band smoothing. Figure 7: **(a)** ITD and **(b)** IACC of the virtual sound sources reproduced by three methods at various desired azimuth angles in simulation. Figure 8a shows the ITD results for the three methods. After compensating for direct sound, the VBAP algorithm reproduces virtual sound sources with minimal ITD errors (0.02 ms, equivalent to one sample time delay) and corresponding azimuth angle errors within \(5^{\circ}\) for desired azimuth angles ranging from \(-15^{\circ}\) to \(10^{\circ}\) and at \(40^{\circ}\). However, within the range of \(15^{\circ}\) to \(35^{\circ}\), the ITDs of the virtual sound source are demonstrably below the target ITDs. Specifically, at \(20^{\circ}\) and \(25^{\circ}\), the ITD error measures 0.09 ms (four time samples), with associated azimuth errors approaching \(10^{\circ}\). In the case of the DBAP algorithm, the ITDs remain relatively constant at 0.14 ms for azimuth angles spanning from \(-15^{\circ}\) to \(20^{\circ}\). However, at \(25^{\circ}\), the ITD undergoes an abrupt transition, and for azimuth angles of \(30^{\circ}\) and beyond, the ITDs register at \(-0.41\) ms. In contrast, the proposed algorithm reproduces virtual sound sources with ITD values that closely approximate the target ITD. For azimuth angles below \(10^{\circ}\) and at \(40^{\circ}\), the ITDs of the virtual sound source align favorably with those of the real sound source. At other azimuth angles, the ITD errors are minimal at 0.02 ms (a single time sample), with angle errors within \(5^{\circ}\). Compared to the other two methods, the ITDs generated by the proposed algorithm exhibit superior agreement with those of the real sound source. These experimental findings suggest that, notwithstanding direct sound compensation, the VBAP algorithm still produces ITD deviations in irregular loudspeaker placements, with errors exceeding \(5^{\circ}\) at certain azimuth angles. This phenomenon arises because of the VBAP algorithm's inherent limitation of disregarding the unique acoustic environment and treating the loudspeaker configuration as a standard setup. The DBAP algorithm, lacking time delay adjustments, yields two distinct ITD values. The ITD of the virtual sound source shifts directly between these two values within a small angle range, failing to produce intermediate angles characterized by matching ITDs. This behavior mirrors the simulation in the proposed algorithm when time delay values fall outside a reasonable range.