## 2 Theoretical Background  
In ARA, both the real and virtual sound components are equally crucial for achieving an immersive experience [23]. In practice, this notion of \"equality\" is somewhat vague, since it can be interpreted in two ways: the virtual environment energy can either serve as the reference point of the mix adaptation or be adjusted to match a corresponding real environment energy reference. In this research, the second alternative is followed--the ARA mix adaptation is determined by the virtual component adaptation relative to the real environment reference energy and consequently to the natural hearing level of the real acoustic world. This decision was taken due to the fact that the real environment should not be altered in a mix; hence, only the ARA virtual tracks should be adjusted. Regarding perception and sound signal energy, it is well-known that loudness describes how loud the acoustic environment is perceived. In that context, loudness sensation is a subjective attribute of sound that expresses acoustic energy in terms of auditory perception. In the literature, one can find a variety of mathematical models for loudness analytic descriptions [24; 25; 26]. In addition, a set of mapping contours are already derived to describe the loudness of different sound fields [27; 28; 29], while a variety of loudness models, such as binaural loudness [19; 20], aim to predict the loudness of binaural hearing. ARA mainly employs binaural rendering for sound reproduction since it provides a number of implementation advantages: the use of headphones prevents cross-talk between ears, whereas binaural spatialization achieves better localization perception of the virtual  
Figure 1: The legacy ARA mixing process architecture. sound source images and improves the spatial separation in the case of multiple active sources [30]. Hence, following this legacy employment trend, any attempt to provide a dynamic ARA-mixing mechanism should consider binaural loudness. In the past years, a number of models that predict binaural loudness have been proposed [20; 31]. They allow for the quantification of human auditory perception, but their use is impeded by several factors. For example, excessive processing power makes real-time loudness estimation problematic [32]. [PERSON] [33] implements a model based on C-code that could be used to calculate the specific loudness of 8192 sample windows in 20 milliseconds. [PERSON]'s work [32] also emphasizes the efficiency of real-time implementations. Recent research efforts have employed deep neural network architectures [34], where it is noted that training with pure tones and noise ensured that the effects of level, frequency, and spectral loudness summation are adequately represented. The use of pure tones was also investigated by the authors in a previous work [35], in which a preliminary binaural loudness estimation methodology for the dynamic ARA mix model was introduced. Figure 2 illustrates the proposed dynamic ARA mix process using a real-time prototype feature extraction technique based on the binaural loudness model of [PERSON] [19]. The core process is the binaural loudness (_BL_) adaptation algorithm. This aims to control the actual levels of the virtual sound sources based on the desired binaural loudness level difference between the real and virtual sounds. Towards this aim, the feature extraction block exports the auditory excitation bands' matrix through fast Fourier transformation (FFT) analysis. This analysis derives the actual relative level differences and maps them through a precalculated _BL_ matrix to a specific mixing gain of the virtual signal. Signal calibration of the real and virtual audio sources is crucial for the _BL_ adaptation algorithm in the perceptual domain. As a consequence, all input signals are initially calibrated to the desired energy level (dB SPL) according to the system specifications prior to the feature extraction and _BL_ adaptation procedure. The selection of the headphones is a critical factor for ARA.