An Anti-Jamming Game between Dynamically-Sensing Jammer and Legitimate User with Faking-Slot Transmission

This paper considers an adversarial scenario with limited channel resources between a pair of legitimate transmitter-receiver communicated with frequency hopping and an intelligent reactive jammer, where the reactive jammer works in a sensing-then-jamming mode and it requires a time interval (or a sensing-slot) for robust sensing of the legitimate signal. More specifically, the legitimate transmitter can mislead the jammer with a faking-slot transmission in each hop due to the repeated appearance of sensing slots. On the other hand, the intelligent reactive jammer performs a sensing-then-jamming action in each hop, and a dynamically-sensing scheme is employed to estimate the action of the legitimate user, which subsequently prompts the jammer to attack one or multiple channels based on the sensing. Taking into account the intricated interactions between the user and the jammer pair, the anti-jamming problem in each hop is formulated under a bi-matrix game framework, and the necessary and sufficient condition for its Nash equilibrium (NE) is derived. Additionally, we prove that the NE solution of the proposed bi-matrix game is equivalent to the global maximum of the corresponding quadratic programming. Finally, we use the quadratic programming method to find the optimal transmission and jamming strategies for the proposed anti-jamming game in several cases. The numerical results show that the user's and the jammer's actions are mainly concentrated in the first half of the hop, and the randomized sensing strategies can make the jammer less sensitive to the legitimate user's faking-slot transmission