# Interpolating the Directional Room Impulse Response for Dynamic Spatial Audio Reproduction
## 1 Introduction  
Virtual reality (VR) is one of the most fundamental efforts of humans to explore the real world using a simulated environment. With the outbreak of the unprecedented coronavirus disease (COVID-19), the world has progressively and partially changed to virtual workplaces, making VR-related technologies increasingly vital for applications, such as teleconferencing, remote teaching, telemedicine and so on. VR is only viable when creating an immersive experience for people as if they were physically present in the target real-world place. To implement this, VR sessions are required to reproduce the spatial audio that is perceived to provide the three-dimensional (3D) acoustic characteristics of the real environment, including sound source direction and reverberation. This is typically achieved using binaural reproduction techniques over headphones. As VR users are inclined to move around the virtual space, the spatial audio needs to be reproduced dynamically to match the user's location relative to the sound source. Due to the limited storage in real-world products, the dynamic reproduction usually requires continuously transmitting binaural signals through telecommunication to match the user position, which provides practical challenges because the transmission bandwidth can also be limited. Thus, an efficient and effective method is urgently needed for dynamic spatial audio reproduction. Rather than continuously transmitting binaural signals, current approaches reproduce the binaural signals at the user using knowledge of the sound source, the user's head related transfer function (HRTF) and the room impulse response (RIR), both of which describe the acoustic transfer function between a sound source and a receiver, depending on their relative position and depending also on the unique characteristics of the listener for HRTF. In this paper, we assume the sound source is known (e.g., through transmission of dry audio source signals at the start of a VR session) and the HRTF is accurately known for a user. To reproduce the spatial audio, the RIR needs to be convolved with the sound source for all possible positions that the user can walk through, so all RIRs at such positions need to be known. This still presents practical challenges in bandlimited environments. Therefore, this paper focuses on using interpolation approaches that can estimate RIRs at unknown positions using a limited set of known RIRs. A conventional RIR is measured either by recording an impulse signal [1] or synthesized using approaches, such as the well-known image method [2], but these are one-dimensional signals in the time domain and do not contain spatial information, such as the direction of arrival of the source. Hence, researchers have investigated approaches to interpolating RIRs using 3D representations of the RIR, such as first order Ambisonics (FOA) encodings, which are known here as directional RIRs (DRIRs). [PERSON] and [PERSON] [3] utilized a virtual FOA microphone array to achieve a simple implementation, which calculated the weighted average of recorded B-format signals to estimate unknown DRIRs with the weights decided by distances from the source to each microphone. [PERSON] et al. also applied a similar linear approach to real-time acoustic space auralizations [4]. These algorithms require no assumptions or priori knowledge and are straightforward to use, whereas their interpolation accuracy is limited due to the spectral distortion and large localization errors occurring particularly when the sound source is close to both microphones or closer to one microphone than to another [5]. Typical solutions to address this limitation utilize higher order Ambisonics (HOA) representations of the soundfield, which provide improved accuracy over a larger spatial region. Approaches based on HOA representations include extrapolation-based algorithms [6; 7; 8; 9; 10], which extrapolate a finite set of spatial parameters based on measured RIRs and thus allow the RIR to be synthesized outside the region covered by microphones.