# Minimum Audible Angle in 3 rd-Order Ambisonics in Horizontal Plane for Different Ambsonic Decoders
###### Abstract  
As immersive audio is gaining popularity, the perceptual aspects of spatial sound reproduction become relevant. The authors investigate a measure related to spatial resolution, the Minimum Audible Angle (MAA), which is understudied in the context of Ambisonics. This study examines MAA thresholds in the horizontal plane in three ambisonic decoders--the Sample Ambisonic Decoder (SAD), Energy-Preserving Ambisonic Decoder (EPAD), and All-Round Ambisonic Decoder (AllRAD). The results demonstrate that the decoder type influences spatial resolution, with the EPAD exhibiting superior performance in MAA thresholds (1.24\({}^{\circ}\) at 0\({}^{\circ}\) azimuth) compared to the SAD and AllRAD. These differences reflect the discrepancies in the decoders' energy vector distribution and angular error. The MAA values remain consistent between decoders up to 30\({}^{\circ}\) azimuth but diverge significantly beyond this range, especially in the 60\({}^{\circ}\)-135\({}^{\circ}\) region corresponding to the cone of confusion. The findings of this study provide valuable insights for spatial audio applications based on ambisonic technology. Ambisonics; ambisonic decoding; perception; psychoacoustics; Minimum Audible Angle (MAA); spatial audio +
Footnote †: journal: Applied sciences  
0000-0002-4000-0002-387X/0000-Level Difference (ILD), a fundamental auditory localisation mechanism [2]. The manipulation of the gain between two loudspeakers creates a phantom source between them, with its position determined by the specific gain ratios [3]. Among different spatial sound reproduction techniques, Ambisonics is commonly used due to its \"first-person\" perspective, as well as the ease of audio-scene translation, such as rotation [4; 5; 6]. It therefore allows for the use of head-tracking for the purpose of natural navigation in the virtual scene and increased localisation accuracy. Ambisonic technology represents a scene-based approach to spatial audio reproduction, distinct from channel-based and object-based methodologies. It does not rely on a predefined playback system, offering greater flexibility [6]. It enables the encoding of directional information about sound sources in a three-dimensional space and facilitates reproduction through spherical harmonic representation. It is also used as a foundation for an emerging open-source Immersive Audio Model and Format [7] known also as Eclipsa Audio [8], which makes Ambisonics more commercially accessible for a wider audience and therefore the perceptual evaluation is even more justified. Auditory spatial sound location is a complex phenomenon, highly dependent on the environment, the acoustics of the room, and the familiarity with the sound source, among others [2]. It varies significantly within individual cases and changes with age. Of the three planes depicted in Figure 1, the accuracy of localisation is the highest on the horizontal plane (azimuthal angle), which also exhibits less inter-subject variability. Several different measures refer to the acuity of sound localisation in a three-dimensional space. Quantitative metrics include localisation, localisation blur, MAA [9], and Minimum Audible Moving Angle (MAMA) [10]. On the other hand, qualitative measures comprise locatedness (ease of localisation) or the source image spread [11]. The focus of this study is the MAA, defined as the smallest angle at which a listener can discriminate between two successively presented stationary sound sources [2]. It is part of the spatial resolution attribute, is relatively easy to measure, and can provide useful insight into the perceptual quality of the system and the decoder. Figure 1: Coordinate system convention in spatial sound reproduction. Several studies have investigated the localisation of sound sources in ambisonic scenes reproduced using virtual or real microphones [12]; at times studies also included synthesised scenes [13]. Ref. [14] explored the MAA in the context of reverberation, establishing that reverberation impairs the MAA threshold.