Grid-Based Exclusive Region Design for 3D UAV Networks: A Stochastic Geometry Approach

This paper presents a stochastic geometry analysis of radio interference and a grid-based design of a primary exclusive region (PER) for spectrum sharing in the 3D unmanned aerial vehicle (UAV) networks. When a UAV network shares frequency bands with a primary system (e.g., a weather radar system), the UAVs must avoid harmful interference with the primary system. To facilitate the design of a complex-shaped PER according to a primary user's antenna pattern, spatial grid models, namely cylindrical and cubic grid models, are introduced. In the cylindrical grid model, to approximate the distribution of the interference at the radar, the cumulants of the interference are expressed by expressions with simple integrals or even closed-form expressions based on the assumption that the distributions of the UAVs in each grid cell follow an inhomogeneous 3D Poisson point process (PPP). In the cubic grid model, the shape of the grid cell is approximated by the cylindrical grid cell to derive the cumulants of the interference because they cannot be calculated in the same manner as in the cylindrical grid model. Using the derived interference cumulants to determine a PER to satisfy the radar's outage probability target, an optimization problem that minimizes the number of the UAVs forbidden from transmitting signals is formulated. The numerical results confirm that the approximated interference distribution using cumulants is in acceptable agreement with the simulation results and the PER obtained from the proposed optimization problem improves the number of the transmitting UAVs by reducing the volume of grid cells.