A Discrete-Time Mean Field Game in Multi-UAV Wireless Communication Systems

Unmanned aerial vehicles (UAVs) are foreseen as a promising solution to deal with sophisticated communication scenarios, which can be used as aerial mobile base stations to enhance terrestrial wireless communication systems. Due to the wide range of serviced ground users, a large number of UAVs need to be deployed. In this paper, we study a multi-UAV downlink communication system with the UAVs acting as the aerial mobile base stations, and investigate the probability of successful transmission between the UAV and its served users, with consideration of both energy availability and mobility effects. We propose the optimal control law based on a discrete-time mean field game (MFG) with power control and velocity control. Furthermore, the optimal controls generate an almost surely asymptotic Nash equilibrium according to the estimate of population state average, meaning that the long time average cost reaches its minimum. Simulation results show that the proposed control policy can effectively improve the probability of successful transmission.