Distance Distributions and Coverage Probabilities in Poisson-Delaunay Triangular Cells With Application to Coordinated Multipoint Wireless Power Transfer

Abstract

This paper investigates the power coverage probability in cooperative wireless powered communication networks, where multiple access points collaborate to meet the energy demands of low-power devices. Based on the theory of Poisson-Delaunay triangulation, the probability density functions (PDF) of the Euclidean distance between the access points of the Poisson-Delaunay triangular cell and typical devices are derived. By using the theory of stochastic geometry and the obtained PDFs, the closed-form expressions of the wireless power coverage probability are obtained for three typical locations of the devices. As the wireless power coverage probability expressions involve the extended generalized multivariate MeijerG function (EGMMGF), a new implementation enabling numerical calculation of the EGMMGF is also proposed. The impacts of the main network parameters on the performance of the proposed framework are analyzed. In particular, comparative results show the significant gains that can be achieved in the wireless power coverage when multiple access points participate in the wireless power transfer or when the density of the network’s access points is increased, as compared to the non-cooperative scheme.