# Interaural Level Difference Optimization of Binaural Ambisonic Rendering
## 5 Discussion  
The evaluation showed that AIO successfully improves the ILD reproduction of virtual loudspeaker binaural Ambisonic rendering, when compared to HRIRs. In most cases this comes in the form of an increase in ILD, but not all - some places show AIO reduces ILD of the Ambisonic rendering. The evaluation of the AIO algorithm in ILD reproduction for all directions over the sphere showed that AIO improves ILD reproduction for all tested Ambisonic orders. Though AIO improved ILD reproduction even at \(M=5\), the greatest benefits were obtained where ILD is inherently reproduced the worst: at \(M=1\) and \(M=2\). Where AIO produced greater improvements in ILD reproduction, more substantial improvements were also observed in PSD and listening test results. \(M=2\) produced the largest improvement in ILD reproduction over the sphere, and this was followed by the biggest improvement in PSD. With AIO, \(M=2\) had ILD reproduction better than \(M=3\), and PSD and listening test results were close to \(M=3\). In general, \(\Delta\)ILD between HRIRs and binaural Ambisonic rendering has been shown to increase with frequency, as illustrated in Figure 7. This is likely caused by Ambisonic spatial aliasing, which increases with frequency once above \(f_{alias}\). Implementing AIO reduces \(\Delta\)ILD relatively evenly over all frequency bands, which is likely a result of the AIO algorithm only producing a single gain value for all frequencies. Therefore, implementing frequency specific ILD optimization in a future development, for example, could possibly produce further improvements. Concerning the listening test results, AIO produced notable improvements for \(M=1\) and \(M=2\), and small (but generally not statistically significant) improvements for \(M=3\) and \(M=4\). However, in the simple-scenes test, sound source location was found to be a significant influence on results. In the complex-scenes listening test, the type of soundscape did not affect results with statistical significance. An interesting overall observation is the stark differences between simple and complex-scene results. There was a much greater difference observed in scores between Ambisonic orders in complex scenes, and AIO produced more significant improvements here. Pink noise, used in the simple-scenes tests, focuses the listener on timbre, whereas recorded soundscapes of complex acoustic scenes have more \begin{table}
\begin{tabular}{l c c c c} \hline \hline \(M\) & **1** & **2** & **3** & **4** \\ \hline \(h\) & \(1\)* & \(1\)* & \(0\) & \(0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Significance results of the complex-scene test of the four tested Ambisonic orders over all soundscapes using Wilcoxon signed-rank test (1 indicates statistical significance at \(p<0.05\); * indicates \(p<0.01\)). Values indicate whether AIO produced a statistically significant improvement to binaural Ambisonic rendering. Figure 16: Median complex-scene scores with non-parametric 95% CI across all participants for each soundscape, \(M=0\) results omitted. Score indicates perceived plausibility and spaciousness. of a focus on lateralization and spaciousness due to the numerous simultaneous sources. Further investigation is warranted to conclude the reason for the variation in results between the two tests. Some further observations were made during this study. Despite the iterative pre-processing stage, the ILD augmentation gains for \(M=1\) plateaued, causing the Ambsonic reproduced ILDs to not quite reach those of the HRIR targets (see Figure 3a). This is due to the normalization of HRIRs post-AIO processing using (13), which normalizes the processed HRIR to the same RMS as the unprocessed HRIR. With this normalization, the contralateral signal of the HRIRs with AIO processing for \(M=1\) had a very low amplitude (they were essentially muted). Therefore, a further increase in ILD did not produce any change in results.