# Interaural Level Difference Optimization of Binaural Ambisonic Rendering
## 6 Conclusions and Future Work  
ILD reproduction of binaural Ambisonic rendering has been shown as inaccurate at low orders of Ambisonics. This paper has presented a method for Ambisonic interaural level difference optimization, aiming to improve the ILD reproduction of low-order binaural Ambisonic rendering using virtual loudspeakers. This has been achieved through an iterative pre-processing stage whereby the ILD of the HRIRs for binaural rendering are measured and then augmented accordingly at frequencies above \(f_{alias}\) by applying a gain to the contralateral signal of the HRIR such that when used for binaural Ambisonic rendering, the resulting rendered ILD matches that of the original HRIR more closely.  
The effect of AIO has been evaluated both objectively and perceptually. Objective evaluation compared binaural Ambisonic rendering, both without and with AIO, to HRIR references for Ambisonic orders \(\{M=1,M=2,...,M=5\}\) in three ways: change in ILD, both over direction and over frequency, and spectral difference over all directions on the sphere. In all three, AIO was shown to produce overall improvements, with greater improvements in ILD reproduction being shown to produce the most significant improvements in spectral reproduction. Perceptual evaluation in the form of listening tests using both simple and complex acoustic scenes largely corroborated the results of the objective evaluation. General findings showed AIO is most effective at \(M=1\) and \(M=2\) where Ambisonic ILD reproduction is inherently the least accurate. Implementing AIO produces an improvement in lateralization, which helps to reduce the perceptual differences between orders. As AIO pre-processing of HRIRs can be implemented offline, it is hence recommended for improving lateralization and spaciousness for all orders of Ambisonics, without producing a reduction in timbal quality.  
Future work will look at adapting the AIO algorithm to implement frequency-dependent gains for each loudspeaker instead of a single gain as is the current case. Planned subsequent work will also look at integrating the presented AIO method with other pre-processing techniques for improving high-frequency reproduction of binaural Ambisonic rendering using virtual loudspeakers, such as diffuse-field equalization [59], direction-bias equalization [58] and time-alignment [25; 26; 27]. Preliminary tests have shown that combining AIO with these equalization methods can produce even greater improvements to high-frequency reproduction, and possibly allow for the perceptual experience of a higher Ambisonic order without an increase in convolutions. Finally, comparisons with other state-of-the-art pre-processing techniques such as magnitude least squares [28] will be made, both objectively and perceptually.  
Conceptualization, T.M. and G.K.; Methodology, T.M.; Software, T.M.; Validation, T.M., D.T.M. and G.K.; Formal Analysis, T.M.; Investigation, T.M.; Resources, T.M.; Data Curation, T.M.; Writing--Original Draft Preparation, T.M.; Writing--Review & Editing, T.M., D.T.M. and G.K.; Visualization, T.M.; Supervision, D.T.M. and G.K.; Project Administration, T.M.; Funding Acquisition, G.K.  
This research was supported by a Google Faculty Research Award and the Engineering and Physical Sciences Research Council (EP/M001210/1).  
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.