###### Abstract  
Dynamic virtual auditory displays (VADs) are increasingly used for generating various auditory objects and scenes in virtual and augmented reality. Dynamic VADs are required to generate virtual sources in various directions and distances by using HRT- or HRIR-based binaural synthesis. In the present work, an algorithm for improving the efficiency and performance of binaural synthesis in dynamic VAD is proposed. Based on tensor decomposition, a full set of near-field HRIRs is decomposed as a combination of distance-, direction-, and time-related modes. Then, binaural synthesis in VAD can be implemented by a common set of time mode-related convolvers or filters associated with direction- and distance-related weights. Dynamic binaural signals are created by updating the weights rather than updating the HRIR-based convolvers, which enables the independent control of virtual source distance and direction and avoids the audible artifact caused by updating the HRIR-based convolvers. An example of implementation indicates that a set of eight common convolvers or filters for each ear is enough to synthesize the binaural signals with sufficient accuracy. The computational efficiency of simultaneously generating multiple virtual sources is improved when the number of virtual sources is larger than eight. A virtual-source localization experiment validates the algorithm. t 16 June 2022  
Accepted: 26 July 2022  
generate virtual sources at different spatial positions in terms of directions and distances. How to synthesize binaural signals with high efficiency is one of the core problems of dynamic VAD. Various signal processing algorithms have been designed for synthesizing binaural signals for virtual sources at different spatial positions in dynamic VAD. A conventional algorithm filters the input signal with a pair of head-related transfer functions (HRTFs) in the frequency domain, or equivalently convolutes the input signal with a pair of head-related impulse responses (HRIRs) in the time domain. To simulate the dynamic variation in binaural signals caused by head turning (or by a moving virtual source), this algorithm requires constantly loading the HRTFs from a database and updating the HRTF-based filters constantly. Constantly loading the HRTFs from a large database reduces the computational efficiency, especially when both directional- and distance-dependent HRTFs are loaded from a large near-field HRTF database. Constantly updating the HRTF-based filters (or HRIR-based convolvers) easily causes audible artifacts in the resultant binaural signals. Moreover, the conventional algorithm requires a pair of HRTFs filters for a virtual source, and, thus, the required number of filters increases linearly with the number of virtual sources. Therefore, the efficiency of the conventional algorithm is low in generating multiple virtual sources simultaneously (for example, multiple direct sources and image sources for environmental reflections). Alternatively, basis function decomposition-based algorithms have been suggested for synthesizing binaural signals of virtual source [2]. In fact, HRTFs vary as functions of frequency and source positions (in terms of direction and distance). They can be decomposed as a linear combination of a set of spatial (position) basis functions associated with frequency-dependent weights (spatial basis function decomposition), or a linear combination of spectral shape basis functions associated with source position-dependent weights (spectral shape basis function decomposition). Therefore, HRTF-based filtering can be implemented by a set of fixed filters (or equivalent convolvers) associated with position-dependent weights or gains. One advantage of basis function decomposition-based algorithms is that the filter set is fixed. It is only required to change the weights of filters to account for the variation in head orientation or source position, avoiding the problems caused by constantly loading HRTFs and updating the filters.