Anti-Jamming Games in Multi-Band Wireless Ad Hoc Networks

For multi-band wireless ad hoc networks of multiple users, an anti-jamming game between the users and a jammer is studied. In this game, the users (resp. jammer) want to maximize (resp. minimize) the expected rewards of the users taking into account various factors such as communication rate, hopping cost, and jamming loss. We analyze the arms race of the game and derive an optimal frequency hopping policy at each stage of the arms race based on the Markov decision process (MDP). It is analytically shown that the arms race reaches an equilibrium after a few rounds, and a frequency hopping policy and a jamming strategy at the equilibrium are characterized. We propose two kinds of collision avoidance protocols to ensure that at most one user communicates in each frequency band, and provide various numerical results that show the effects of the reward parameters and collision avoidance protocols on the optimal frequency hopping policy and the expected rewards at the equilibrium. Moreover, we discuss about equilibria for the case where the jammer adopts some unpredictable jamming strategies.