## 6 Perceived Distance Control in Binaural-Based Methods
A continuous direction and distance representation of near-field HRTFs can be obtained by substituting the resultant weights into the decomposition. This method yields near-field HRTFs with appropriate accuracy but usually requires a far-field HRTF dataset in full spatial directions with sufficient directional resolution (usually more than 1000 uniform measured directions are needed to derive the near-field HRTFs up to 20 kHz). Measuring far-field HRTFs with such uniform directional resolution is also difficult. Alternatively, [PERSON] et al. suggested a simplified method for estimating near-field HRTFs by multiplying the distance variation function (DVF) from the far-field HRTFs [70]. The DVF is calculated from a spherical head model. This method yields a rough approximation of near-field HRTFs. The resultant data are appropriate for consumer applications of VADs. Researchers should be careful when applying these data for scientific purposes. (3) Problems with the simplifying signal processing in VADs  
With delicate binaural synthesis processing, a VAD is theoretically able to accurately duplicate the binaural pressures of a target sound field. However, limited by computational resources, the binaural synthesis processing in a practical VAD is usually simplified. Binaural or virtual Ambisonic method is able to simplify the synthesis of free-field virtual sources at different proximal distances in a dynamic VAD [71]. This method includes two stages. In the first stage, the NFC-HOA signals for loudspeaker reproduction are created. In the second stage, the loudspeaker signals are converted into binaural signals for headphone presentation via HRTF-based binaural synthesis. In other words, the NFC-HOA signals are reproduced by virtual loudspeakers. This also provides an example of the mixed use of spatial audio techniques based on different principles. One advantage of the dynamic binaural Ambisonics method is that only the Ambisonics signals, not HRTF-based filters, are needed to be updated in signal processing after head turning, which simplifies signal processing and avoids the artifacts caused by updating the HRTF-based filters in the conventional scheme. Another advantage of the dynamic binaural Ambisonics method is that only the far-field HRTFs in the virtual loudspeaker directions are needed in binaural synthesis, avoiding the difficulty of acquiring near-field HRTFs. The binaural Ambisonics method is mathematically equivalent to estimating near-field HRTFs from known far-field HRTFs by spherical harmonic decomposition to an appropriate order [7]. Our recent experiment indicated that combined with the level cue, fifth-order dynamic binaural ambisonics is able to recreate the auditory perception of a virtual source in various directions and distances closer than 1.0 m [72]. Figure 4: Layout of the second generation of generation of near-field HRTF measurement system with many loudspeakers positioned at different elevation angles in a non-anechoic room. The scheme of synthesizing environmental reflections should also be simplified. The length of a pair of complete BRIRs is in the order of the reverberation time of the target room, which varies from some hundreds of millisecond for an ordinary room to about two seconds in a concert hall. Updating and convoluting with such BRIRs in a dynamic VAD are difficult. Parameterized room acoustics and BRIRs models are often used in practical VADs, in which the binaural signals caused by direct sounds and a few early reflections are accurately synthesized; the later diffused reverberation is approximately synthesized by appropriate artificial reverberation schemes [73]. The distance perception can also be controlled by adjust the DRR in the binaural signals [74; 75]. This simplified processing may also lose some spatial information, including distance perception information related to reflections. Overall, binaural-based methods are theoretically able to create various spatial auditory cues.