Spatial modeling of device-to-device networks: Poisson cluster process meets Poisson Hole Process

This paper combines Poisson Cluster Process (PCP) with a Poisson Hole Process (PHP) to develop a new spatial model for an inband device-to-device (D2D) communications network, where D2D and cellular transmissions share the same spectrum. The locations of the devices engaging in D2D communications are modeled by a modified Thomas cluster process in which the cluster centers are modeled by a PHP instead of more popular homogeneous Poisson Point Process (PPP). While the clusters capture the inherent proximity in the devices engaging in D2D communications, the holes model exclusion zones where D2D communication is prohibited in order to protect cellular transmissions. For this setup, we characterize network performance in terms of coverage probability and area spectral efficiency.