Deployment and Trajectory Optimization for UAVs: A Quantization Theory Approach

Optimal deployment and movement of multiple unmanned aerial vehicles (UAVs) is studied. The scenarios of variable data rate with fixed transmission power, and variable transmission power with fixed data rate are considered. First, the optimal deployment of UAVs is studied for the static case of a fixed ground terminal (GT) density. Using high resolution quantization theory, the corresponding best achievable performance (average data rate or transmission power) is determined in the asymptotic regime of a large number of UAVs. Next, the dynamic case where the GT density is allowed to vary periodically through time is considered. For one-dimensional networks, an accurate formula for the total amount of UAV movement that guarantees the best time-averaged performance is determined. In general, the tradeoff between the total UAV movement and the achievable performance is obtained through a Lagrangian approach. A corresponding trajectory optimization algorithm is introduced and shown to guarantee a convergent Lagrangian. Numerical simulations are also carried out to confirm the analytical findings.