# Auditory Localization in Low-Bitrate Compressed Ambisonic Scenes
## 2 Background
### Binaural-Based Ambisonics  
If the binaural localization cues (ITD, ILD) and spectral cues are reproduced correctly, the perceived spatial and timbral attributes of presented sound should be the same in comparison to the real sound source. This can be achieved through the controlled headphone-based reproduction of binaural signals. These signals can be recorded using binaural microphones or artificially synthesized employing HRTF sets. Readers are referred to [10, 11, 12] for more complete references on binaural recording technique and synthesis. HRTF-based signal processing is a key element of all interactive binaural reproduction systems, as it can accommodate head-tracking, enabling dynamic spatial audio rendering using information on the listener's head movements. If the signals fed to each ear are modified accordingly, providing localization cues based on the head displacement and rotation, presented virtual sound sources will remain at their positions in space. According to [13,14] perception of virtual sound sources is dramatically improved with head-tracking enabled systems. The simplest head-tracking devices provide information on the rotation of the listener's head. An accurate approximation of the head orientation can be derived using inertial and magnetic sensors. To track head displacement, usually additional optical tracking is required. An alternative to direct HRTF convolution is to use HRTFs as virtual loudspeakers. Here the same signals that would be used in a real-world 3D loudspeaker array are convolved with the HRTFs corresponding to specific loudspeaker positions to give a virtualized presentation of the array over headphones. The accuracy of sound field reproduction then becomes dependent on the spatialization method used, for example, Vector-Base Amplitude Panning [15], Wave Field Synthesis [16] or Ambisonics [1]. The latter spatialization method is an approach to deliver an approximation of the full-sphere sound field at the listener's ears. The theory of Ambisonics is well documented and the reader is directed to [17, 18, 19] for good explanations of the topic. A succinct review is provided here. Ambisonics is based on the spherical harmonic representation of the sound field. A sound source can be encoded to Ambisonics format through matrix multiplication with spherical harmonic weights that represent the source position on the sphere. Ambisonic sound field representations employing 0 th and 1 st-order spherical harmonics are known as First-Order Ambisonics (FOA). Sound field representations that extend beyond first order are referred to as Higher-Order Ambisonics (HOA). In practice, a limited number of Ambisonic components can be transmitted and exploited. The required number of components \(N\) for a peripohmic system of \(m\)th order can be calculated by \(N=(m+1)^{2}\). Increasing the order results in a higher spatial aliasing frequency \(f_{\text{alias}}\) and results in a larger sweet spot [18]. A limited number of spherical harmonic components leads to truncated representation of the sound field and a decrease in spatial resolution. Therefore, to achieve higher spatial resolution, higher orders must be used. Above \(f_{\text{alias}}\) Ambisonic decoding introduces timbral alterations to the original encoded signals [20] degrading overall timbral fidelity. Ambisonics has been widely adopted for immersive applications for mobile media since it can be easily manipulated and transformed [21] to facilitate stable sound sources when using dynamic binaural rendering. In this case, the Ambisonic scene is rotated counter to head movements by scaling the Ambisonic channels by correct coefficients adjusted according to the head-tracking data. Please note that the directions of virtual loudspeakers (simulated by HRTFs) remain unchanged and it is the loudspeaker feeds to the virtual loudspeakers that are updated in real time. Figure 2 shows the basic audio signal chain for loudspeaker-based and binaural-based Ambisonic rendering.