Adaptive Coverage Solution in Multi-UAVs Emergency Communication System: A Discrete-Time Mean-Field Game

In emergency situations such as earthquakes, the cellular infrastructure cannot support communication services because of equipment damage. The use of the large number of unmanned aerial vehicles (UAVs) has been drawn significant attentions as an important solution for providing air-to-ground communication services in such situations. In this paper, we research the flight direction policy (velocity vector) of the UAVs where every UAV acts as the base station to serve the multi-users communications. As the trajectory of UAVs have a huge impact on the performance of communication, we investigate an adaptive coverage problem, that all the UAVs can adjust their velocities to increase the number of served users. However, such behavior may cause larger flight energy consumption. We propose a discretetime mean-field game (MFG) framework that each UAV adjusts its velocity in order to minimize the flight energy consumption. In this framework, each UAV evolves according to the dynamic equation and seeks to minimize its flight energy consumption containing the average distribution of all UAVs. We investigate a deterministic function φ to approximate the average distribution of all UAVs as the number of UAVs tends to infinity. Furthermore, the optimal velocity vectors generate a certain asymptotic Nash equilibrium as time tends to infinity, which implies that the flight energy consumption of each UAV can reach its minimal value as the number of UAVs increases to infinity. The simulation results show the optimal trajectory and optimal flight tendency of the UAVs. Moreover, we show that as users move, the amount of the users served is maintained at a relatively stable range, which represents met the demand of user's adaptive coverage.