## 1 Introduction
### Acoustic Cues Combination for Auditory Distance Perception  
This study focuses on the auditory distance perception of virtual sound sources presented in front of the listener, in a real environment, and at distances beyond the near-field. Both auditory and nonauditory cues affecting the auditory distance perception of frontal sources have been identified [3; 4]. In the free field, the sound level at the ears decreases as the distance to the source increases. Therefore, sound level is considered as a primary monaural cue for distance perception. Sound level is often classified as a relative cue, as it needs a priori knowledge of the source sound power to be interpreted by a listener.  
The direct-to-reverberant (DRR) energy ratio is often considered as the cue best defining the contribution of reverberation for distance. When the distance to a sound source increases in a reverberant environment, the DRR decreases. DRR has been proposed as an absolute distance cue, contrary to sound level, as it does not require a priori information about the source power to be interpreted as a distance cue. Nonetheless, it can be argued that familiarity with the acoustical environment is necessary to consider this cue as absolute, the reverberation decay being specific to each environment.  
However, it is very unlikely that the auditory system can effectively separate the direct sound from reverberation and compute a physical DRR [5]. Different studies tried to define a more relevant reverberation-related distance cue [5; 6; 7; 8]. Three alternative cues to DRR have already been evaluated: an estimation of the perceived distance with an early-to-late energy power ratio [6], the interaural coherence [9; 10], the initial time delay gap (ITDG) depicting the time of arrival of the first reflections [11], and monaural changes in the spectral centroid or in frequency-to-frequency variability in the signal [9]. [PERSON] and [PERSON] [5] have proposed that the best candidate is most likely an early-to-late power ratio. Concerning the temporal limit between what is considered as the early energy, which contains the direct sound and some early reflections, and the late reverberation, no clear conclusions have been drawn [6]. The relevance of the early-to-late energy ratio as a reverberation-related distance cue, and how this cue is combined with the sound level to process an auditory distance judgment, are examined in this study.  
Moreover, the combination of the sound level and reverberation-related cues is the main factor driving the auditory distance perception of stationary sources. [PERSON] [12] showed that the perceptual system uses weighting strategies of intensity and of reverberation-related cues flexibly to produce a distance percept, depending on the characteristics of the listening situation: the stimulus nature, the angular position, and the source-receiver distance. He also suggested that the weighting of cues may rely on the consistency associated with each cue [4]. Cues that are either unavailable (e.g., reverberation in a free field environment) or unreliable (e.g., a cue that stays constant with distance) are given less perceptual weight in the combination process. To conclude, he suggests that such an individual weighted sum of acoustic cues assessments may yield the final distance percept. In this study, the influence of environmental characteristics on the acoustic cues weighting strategies adopted by participants to produce an auditory distance judgment is investigated.