Eavesdropping and Anti-Eavesdropping Game in UAV Wiretap System: A Differential Game Approach

Despite its advantages of flexility and low-cost networking, unmanned aerial vehicle (UAV) communications face various attacks such as eavesdropping. Existing studies on secure UAV communications assume fixed-location eavesdroppers and rarely consider interactions between legitimate nodes and eavesdroppers. In this paper, we investigate eavesdropping and anti-eavesdropping interaction between a UAV-enabled eavesdropper (UAV-E) and a UAV-enabled base station (UAV-BS) in a downlink wiretap system. The UAV-E aims to wiretap downlink signals by adaptively adjusting its trajectory while the UAV-BS aims to maximize secrecy-sum-rate with minimum power consumption by jointly optimizing user scheduling, power control, and trajectory. Dynamic differential equations are formulated to characterize motions of UAVs, following which a zero-sum differential game is formulated to model the “pursuit-evasion” interaction between the UAV-BS and the UAV-E. Definition and existence of Nash equilibrium (NE) are provided. To obtain the NE, Pontryagins minimum principle is leveraged to solve the trajectory design problem. Further, Gauss-Seidel-like implicit finite-difference method is leveraged to obtain saddle-point strategies at NE. Finally, numerical results are provided to verify the effectiveness of the proposed game model. It is revealed that the differential game can well-characterize the strategy interactions between UAVs. Moreover, results show that the initial positions and weights of UAVs, the energy consumption factor, and the user scheduling have key impacts on motion interactions between the UAV-BS and the UAV-E and further on UAV-BS’s power control.