Towards a perceptually optimal bias factor for directional bias equalisation of binaural ambisonic rendering

Ambisonics has enjoyed a recent resurgence in popularity due to virtual reality applications, where Ambisonic audio is presented to the user binaurally in conjunction with a head-mounted display. In this scenario however, it is imperative to maximise the coherence between audio in the frontal direction and visuals in order to maintain immersion.Ambisonic reproduction can theoretically be perfect in the centre of the loudspeaker array for frequencies up to the `spatial aliasing frequency', $f_{alias}$. At frequencies above $f_{alias}$ however, the limited spatial accuracy of reproducing a physical sound field with a finite number of transducers causes artefacts such as localisation blur, reduced lateralisation and comb filtering. One approach for improving spectral reproduction of binaural Ambisonic rendering is diffuse-field equalisation. In a previous study, the authors applied this technique to virtual loudspeaker binaural Ambisonic decoders, which improved both the spectral response over the sphere and predicted median plane elevation localisation. However, there still exists a perceivable difference in timbre between diffuse-field equalised binaural Ambisonic rendering and HRTF convolution. By altering the diffuse-field equalisation method by concentrating the equalisation for one specific direction (for the virtual reality application this direction is the front), it is possible to create a hybrid of free-field and diffuse-field equalisation such that frontal reproduction becomes more accurate, at the expense of other directions. This is referred to as directional bias equalisation (DBE) and is a two-stage equalisation process. The first obtains a frontal directionally biased spherical field response and equalises it, and the second re-equalises this response for the ideal corresponding frontal response such that an infinite directional bias will produce frontal Ambisonic audio equivalent to frontal HRTF convolution. DBE is a pre-processing stage that can be implemented offline. Increasing the frontal bias factor (represented in this paper using the letter $\kappa$) improves spectral reproduction of frontal sounds to a greater extent, though this comes at the expense of spectral accuracy at other directions. This paper presents the results of a perceptual listening test that attempts to determine the optimal bias factor for an appropriate trade off between improved frontal fidelity and reduced lateral fidelity. The test follows the multiple stimulus with hidden reference and anchors (MUSHRA) paradigm, ITU-R BS.1534-3. Tests are conducted in a quiet listening room using a single set of Sennheiser HD~650 circum-aural headphones and an Apple Macbook Pro with a Fireface UCX audio interface, which has software controlled input and output levels. Headphones are equalised from the RMS average of 11 impulse response measurements, with 1 octave band smoothing in the inverse filter. All audio is 24-bit depth and 48~kHz sample rate. Listening tests are conducted using first, third and fifth order Ambisonics, with loudspeaker configurations comprising 6, 26 and 50 loudspeakers respectively, arranged in Lebedev grids. Test conditions are as follows:\begin{itemize} \item HRTF convolution (reference) \item Standard Ambisonic \item DBE Ambisonic with $\kappa = 1$ \item DBE Ambisonic with $\kappa = 3$ \item DBE Ambisonic with $\kappa = 5$ \item DBE Ambisonic with $\kappa = 9$ \item DBE Ambisonic with $\kappa = 17$ \item DBE Ambisonic with $\kappa = 33$\end{itemize}Additional stimuli are a low and mid anchor for the simple scenes, comprised of the HRTF reference low-passed at 3.5~kHz and 7~kHz respectively, and a zeroth order Ambisonic render for the complex scenes. Two simple and one complex scenes are used. The simple scenes comprise of a single pink noise source. The first is panned directly in front of the listener at ($\theta,\phi$) = ($0^\circ,0^\circ$), and the second is panned directly to the left of the listener at ($\theta,\phi$) = ($90^\circ,0^\circ$). The complex scene is simulated by mixing a frontal pink noise and a diffuse soundscape. The noise burst consists of 0.5s burst and 0.5s of silence. The diffuse soundscape is synthesised from 24 decorrelated monophonic sound scene recordings of a train station. The 24 sources are panned to the vertices of a 24 pt. T-design quadrature, to ensure minimal overlap between virtual loudspeaker positions in the binaural decoders and the sound sources in the complex scene. The frontal noise is 3~dB~RMS louder than the diffuse soundscape. Results are analysed using non-parametric statistics and discussed in the full manuscript. The conclusion suggests the perceptually optimal bias factor for improved frontal spectral fidelity with minimal perceived lateral degradation for virtual loudspeaker binaural Ambisonic rendering.