## 2 Psychoacoustic Principles of Auditory Distance Perception
### Cues for Auditory Distance Perception
When a source in the horizontal plane approaches the head, the source azimuth relative to the (ipsilateral) ear changes, even if source azimuth relative to the head center is unaltered. The change in source azimuth relative to the pinnae changes the effect of the pinnae on incident sounds and, therefore, changes the spectrum of a high-frequency HRTF. The parallax effect may provide absolute but weak distance perception information for a proximal source, especially for a frontal source where the ILD cue is unavailable. (4) Direct to reverberation energy ratio  
In a room with diffused reverberation sound field, the direct-to-reverberant energy ratio (DRR) can be calculated as [14]:  
\[\text{DRR}=\frac{D_{S}\Sigma_{S}}{16\pi r_{S}^{2}}\frac{\alpha_{abs}}{1-\alpha _{abs}}\, \tag{4}\]  
where \(r_{S}\) is the distance between the sound source and the receiver position, \(D_{S}\) is the directional factor of the sound source, \(\Sigma_{S}\) is the total absorption area, and \(\alpha_{abs}\) is the average absorption coefficient. Therefore, the DRR is inversely proportional to the square of the source distance. Although the completely diffuse sound field is actually very rare, the DRR serves as an absolute and strong auditory distance perception cue (the absolute distance perception means that the listener can report the exact value of perception distance, not the relative far or near judgement) [15]. This cue is valid for various source distances, and  
Figure 2: ILD versus frequency for a (a) horizontal frontal source at \(\theta_{s}=0^{\circ}\), (b) lateral source at \(\theta_{s}=90^{\circ}\) and three different source distances \(r_{S}\) of 0.25, 0.5, and 1.0 m.  
most effective for a source near the reverberation radius at which the DRR is equal to the unit. However, it is still not completely clear how the auditory system uses the distance information contained in the DRR cue. The possible candidates include the information provided by timbre coloration in the reverberation, the reverberation tails on transients, and interaural coherence in reverberation, although some authors recently argued that interaural coherence may not be used [16]. Inspired by [PERSON] et al. [6], the various auditory distance perception cues and their available conditions are summarized in Table 1. Different cues may be involved. Distance perception is enhanced if multiple cues are available. For example, in a free field, distance perception is more accurate when both HRTF and level cues are available [11]. In a reflective room, distance perception is more accurate if both DRR and level cue are available, although there is some controversy on this issue [15; 17; 18; 19]. However, the information provided by multiple distance perception cues may be somewhat redundant. Distance perception may be still possible in the absence of some cues. For example, distance perception is still possible in a free field in which the DRR cue is absent. Various cues may contribute to distance perception with different weights. These weights vary with multiple factors, such as frequency, source distance and direction, anechoic or reflective environment, etc. Under certain conditions, some cue may be dominant. In summary, auditory distance perception is biased. It is a comprehensive consequence of multiple cues that depend on multiple factors of the sources and acoustic environment. Auditory distance perception cues in a room especially depend on the reflections and, thus, are different from those in a free field. The multiple-factor dependence of distance perception cues, as well as the interaction, cooperation, and redundancy of these cues, complicate the situation. Some mechanisms of distance perception remain unclear. Further research on this issue is needed. These psychoacoustic features of auditory distance perception create challenges for perceived distance control in spatial audio.