Finite Point Processes in a Truncated Octahedron-Based 3D UAV Network

In this paper, stochastic geometry tools are utilized to analyze the performance of a wireless network with Unmanned Aerial Vehicles (UAVs). The evaluation is based on the concept of a truncated octahedron that is the fundamental three-dimensional (3D) shape that models the basic cell in an entirely aerial cellular structure with UAV nodes only. The spatial locations of the aerial users, are modeled as a 3D Binomial Point Process (BPP). Subsequently, stochastic geometry analysis in a reference truncated octahedron located at the origin is performed and exact expressions for the distances between aerial users, are derived. To this end, expressions for evaluating the volume of the regions of the 3D cell in which an aerial user may fall, are derived. Then, by defining the signal-to-interference-plus-noise (SINR) ratio at the reference UAV-base station (UAV-BS) receiver, a performance analysis in terms of coverage probability is conducted under two interference scenarios, i.e., a pure intra-cell interference and an intra- plus inter-cell interference case. As intermediate step in the coverage probability analysis, expressions for relevant distance distributions and the Laplace transform of the aggregate interference power distribution are derived. For the sake of completeness, coverage probability analysis under intra-cell interference is also performed and compared to a 3D cell modeled as a sphere. The analytical expressions are also compared to simulation results to validate the accuracy of the proposed framework and reveal valuable insights.