Correlation of Line-of-Sight Probabilities in Aerial-Terrestrial Communications: Modeling, Analysis, and Application

TThe line-of-sight (LoS) condition is important to the quality of wireless communications, especially for millimeter-wave (mmWave) communications which are more sensitive to blockages than typical radio frequency (RF) communications. Considering that one blockage would obstruct several channels simultaneously, recently, researchers have studied the correlation of LoS probabilities among multiple channels in the horizontal plane and shown its importance in system performance analysis. The main missing aspect of existing literature in this direction is that the heights of transceivers and blockages have not been considered in the analysis of the LoS correlation. However, the emerging hybrid cellular networks with unmanned aerial vehicles (UAVs) and reconfigurable intelligent surfaces (RISs) deployed at various altitudes necessitate the LoS analysis accounting for the vertical dimension. In this paper, using stochastic geometry, we formulate a novel joint-LoS-probability framework of two channels among three aerial/terrestrial devices to analyze the LoS correlation both in the horizontal and vertical dimensions. We derive the expression of the conditional and joint LoS probabilities. The proposed framework combines (i) accuracy (verified in simulation), (ii) generality (from adjustable parameters of the channels and environments), and (iii) fitting ability (from a cylindrical blockage model to a non-cylindrical blockage model). The numerical results show that the correlation is quite strong when the angle between the two communication channels is small, while it becomes weaker as this angle increases. Moreover, we introduce a potential application of the joint LoS probability in the optimal deployment of an aerial device. Compared to optimization based on the independence assumption of the LoS probabilities, the improvement in the coverage probability intuitively clarifies the advantage of the proposed joint-LoS-probability framework on the aerial-terrestrial network design.