Trajectory optimization for cellular-connected UAV under outage duration constraint

Enabling cellular access for unmanned aerial vehicles (UAVs) is a practically appealing solution to realize their high-quality communications with the ground for ensuring safe and efficient operations. In this paper, we study the trajectory design for a cellular-connected UAV that needs to fly from given initial to final locations, while communicating with the ground base stations (GBSs) subject to a minimum signal-to-noise ratio (SNR) requirement along its flight. However, due to various practical considerations such as GBSs' locations and coverage range as well as UAV's trajectory and mobility constraints, the SNR target may not be met at certain time periods during the flight, each termed as an outage duration. In this paper, we first propose a general outage cost function in terms of outage durations in the flight, which includes the two commonly used metrics, namely total outage duration and maximum outage duration as special cases. Based on it, we formulate a UAV trajectory optimization problem to minimize its mission completion time, subject to a constraint on the maximum tolerable outage cost. To tackle this challenging (non-convex) optimization problem, we first transform it into a tractable form and thereby reveal some useful properties of the optimal trajectory solution. Based on these properties, we further simplify the problem and propose efficient algorithms to check its feasibility and obtain optimal as well as low-complexity suboptimal solutions for it by leveraging graph theory and convex optimization techniques. Numerical results show that our proposed trajectory designs outperform that by the conventional method of dynamic programming, in terms of both performance and complexity.