Game Theory-Based Anti-Jamming Strategies for Frequency Hopping Wireless Communications

In frequency hopping (FH) wireless communications, finding an effective transmission strategy to properly mitigate jamming has been recently considered as a critical issue, due to the inherent broadcast nature of wireless communications. Recently, game theory has been proposed as a powerful tool for dealing with the jamming problem, which can be considered as a player (jammer) playing against a user (transmitter). Different from existing results, in this paper, a bimatrix game framework is developed for modeling the interaction process between the transmitter and the jammer, and the sufficient and necessary conditions for Nash equilibrium (NE) strategy of the game are obtained under the linear constraints. Furthermore, the relationship between the NE solution and the global optimal solution of the corresponding quadratic programming is presented. In addition, a special analysis case is developed based on the continuous game framework in which each player has a continuum of strategies. Finally, we show that the performance can be improved based on our game theoretic framework, which is verified by numerical investigations.