A Unified Disk Scattering Model and Its Angle-of-Departure and Time-of-Arrival Statistics

This paper proposes a novel probability density function (PDF) for the distribution of local scatterers inside a disk centered on the mobile station (MS). The new scattering model is introduced as the unified disk scattering model (UDSM), as it unifies a variety of typical circularly symmetric scattering models into one simple model. By adjusting a designated shape factor controlling the distribution of the scatterers, both the uniform circular and uniform ring scattering models can be obtained as special cases. Furthermore, the original Gaussian and uniform hollow-disk scattering models can be approximated with a high level of accuracy. In addition to these established scattering models, any continuous concentrations of local scatterers from a high density near the MS to a high density close to the outer edge of the disk can also be achieved. Under the assumption of single-bounce scattering, the joint PDF of the angle-of-departure and angle-of-arrival (AoA) and the joint PDF of the time-of-arrival and AoA are derived. Subsequently, the corresponding marginal PDFs are provided in closed form. Finally, the UDSM is validated by several measured channels, showing that the UDSM outperforms several other geometric models proposed in the literature. The proposed model is useful for the designers of cutting-edge vehicular communication technologies to study the system performance under different scattering conditions.