# Interaural Level Difference Optimization of Binaural Ambisonic Rendering
## 1 Introduction
Traditionally, binaural rendering of Ambisonics has involved decoding the Ambisonic sound field to a specified loudspeaker configuration, as one would for loudspeaker listening, followed by the additional step of binaural rendering through convolution of each loudspeaker's signal with head-related impulse responses (HRIRs) corresponding to that loudspeaker's position, and summing the resulting convolved loudspeaker feeds [19; 20]. This is often referred to as the virtual loudspeaker approach. Some recent methods for binaural Ambisonic rendering have moved away from the virtual loudspeaker approach and instead focused on order truncation of an approximately spatially continuous spherical harmonic (SH) represented HRIR dataset [21; 22]. However, this causes severe high-frequency roll-off at low truncation orders, which requires compensation through pre-processing techniques [23] such as equalization [24], time-alignment [25; 26; 27] and more recently magnitude least squares [28]. As this also requires a highly dense dataset of HRIRs measured at points on the sphere distributed by a regular (or at least semi-regular) quadrature such as the Lebedev grid [29], it is, therefore, considered infeasible for individualization at present, despite techniques such as reciprocity [30] and multiple swept sine [31] offering faster measurement times. Hence, this paper focuses on virtual loudspeaker binaural rendering of Ambisonic signals, for the methods presented to be directly applicable to individualized binaural Ambisonic rendering with the current physical measurement capabilities. Certain computational cost savings are employed over the traditional virtual loudspeaker approach, such as pre-encoding of the virtual loudspeaker HRIRs into the SH domain. This allows implementation of dual-band decoding and loudspeaker configurations with more loudspeakers than SH channels while minimizing the number of required convolutions. This paper presents a method for addressing the inadequate ILD reproduction of low-order binaural Ambsonic rendering using virtual loudspeakers through a pre-processing stage of the HRIRs used in the binaural rendering of Ambsonic signals. The method augments the amplitude of HRIRs at frequencies above \(f_{alias}\) such that when used to render Ambsonic signals, the ILD reproduction is improved when compared to the original HRIRs in order to improve spectral reproduction and the effect of lateralization and spaciousness. The paper is laid out as follows. Section 2 details the virtual loudspeaker binaural Ambsonic rendering process and ILD estimation method before introducing the proposed technique of Ambsonic ILD Optimization (AIO). Section 3 presents an objective evaluation of AIO for Ambsonic orders \(\{M=1,M=2,...,M=5\}\), comparing a reference dataset of HRIRs to binaural Ambsonic renders both without and with AIO for all directions over the sphere. Objective metrics include accuracy of ILD reproduction, both over sound source location and frequency, and spectral difference. A perceptual evaluation is then presented in Section 4 through listening tests using both simple and complex acoustic scenes. Finally, results are discussed in Section 5 and the paper is concluded, along with proposed further work, in Section 6.