# Minimum Audible Angle in 3 rd-Order Ambisonics in Horizontal Plane for Different Ambsonic Decoders
## 5 Results  
The comparative analysis of the SAD, EPAD, and AllRAD revealed large variations in spatial reproduction parameters. For all the results, the highest step in the adaptive procedure--40\({}^{\circ}\)--is assumed to be the recognition threshold. Above that value, the MAA was not determined and the plots are limited on the Y-axis. Figure 8 shows the MAA across the subjects for the SAD case. For most of the participants, two significant peaks are revealed: around 105\({}^{\circ}\) and at 150\({}^{\circ}\). The high values of the MAA at 105\({}^{\circ}\) are preceded by a slow rise starting around 30-45\({}^{\circ}\). For subjects S01 and S15, the first peak is shifted towards 90\({}^{\circ}\), while the second peak is shifted to 135\({}^{\circ}\) for S01 and does not occur at all for S15. The MAA values across the subjects show considerable variability, with three of them (for subjects S05, S14, and S16) extended beyond the maximum analysed range of 40\({}^{\circ}\). Figure 9 shows the outcome of the listening experiment for the EPAD. Similar to the SAD, the variability of the results across the subjects is high, with a few MAA values exceeding the analysis threshold of 40\({}^{\circ}\) (subjects S03, S05, and S11). The trends in the MAA  
Figure 8: MAA results for the SAD. The Y-axis is cut at 40\({}^{\circ}\)—above that value it is assumed that the threshold is not possible to establish, as the biggest angular step in the experiment was 30\({}^{\circ}\). Sab naming convention signifies subjects’ IDs. Figure 7: Example of the course of the staircase procedure for one of the subjects. The threshold oscilates around 1–2\({}^{\circ}\) for a 0\({}^{\circ}\) reference. are also not as visible as in the case of the SAD. However, the majority of the results show a significant peak at 90\({}^{\circ}\), implying a higher MAA in that area. In general, all the results exhibit higher MAA values between 45\({}^{\circ}\) and 165\({}^{\circ}\). The MAA values obtained for the EPAD are generally lower than those for the SAD, cf. Figure 8. This may be a consequence of low fluctuations in amplitude and energy metrics for the EPAD, as shown in Figure 4.  
The MAA values for the AllRAD are depicted in Figure 10. They show that the MAA grows considerably between 60\({}^{\circ}\) and 120\({}^{\circ}\). For subjects S06 and S08, the MAA increases symmetrically with respect to the 90\({}^{\circ}\) azimuth angle, forming two peaks at 75\({}^{\circ}\) and 105\({}^{\circ}\) separated by a trough. Other results exhibit only one peak, either at 75\({}^{\circ}\) (S09) or 105\({}^{\circ}\) (S02 and S10). Conversely, the MAA for S01 and S03 is the highest at 90\({}^{\circ}\). Figure 10: MAA results for the All-Round Ambisonic Decoder. As in Figures 8 and 9, the Y-axis is cut at 40\({}^{\circ}\). Sab signifies subjects’ IDs. Figure 9: MAA results for the EPAD. Similar to Figure 8, the Y-axis is cut at 40\({}^{\circ}\), as above that value it is assumed that the threshold is not possible to establish. Sab signifies subjects’ IDs. The mean values of the MAA parameter determined for all three decoders are shown in Figure 11. The values remain coherent below \(30^{\circ}\). Overall, the EPAD produces the lowest MAA values in relation to the horizontal plane of all the investigated decoders. Furthermore, for reference \(0^{\circ}\), the MAA threshold was the lowest for the EPAD and equalled \(1.24^{\circ}\), which is a value corresponding to those of the investigations with the physical sound source [2]. Overall, the MAA values for all the investigated decoders show a significant increase in the angular range between \(60^{\circ}\) and \(120^{\circ}\). Such a tendency is in line with similar results from the literature [21] and corresponds to the region of indeterminate sound localisation, referred to as the cone of confusion [38]. Figure 12 shows isolated results for subject S01, who is highly familiar with the ambisonic system. For such an experienced person, the MAA values are within a similar range for all investigated decoders.