  In this article, we introduce a new mathematical framework for the analysis
and design of UAV corridors in cellular networks, while considering a realistic
network deployment, antenna radiation pattern, and propagation channel model.
By leveraging quantization theory, we optimize the electrical tilts of existing
ground cellular base stations to maximize the coverage of both legacy ground
users and UAVs flying along specified aerial routes. Our practical case study
shows that the optimized network results in a cell partitioning that
significantly differs from the usual hexagonal pattern, and that it can
successfully guarantee coverage all over the UAV corridors without degrading
the perceived signal strength on the ground.
