A Bayesian Stackelberg Game Approach to Remote State Estimation Under SINR-Based DoS Attacks with Incomplete Information

With limited energy constraints, the issue of transmission and interference strategies have received considerable critical attention in cyber-physical security. In this paper, for remote state estimation under signal-to-interference-plus-noise ratio-based denial-of-service (DoS) attacks, the Stackelberg game between the sensor and the attacker is investigated. To balance estimation performance and energy consumption, the two players determine the transmission power and interference power sequentially under an incomplete information structure where the sensor does not know the fading channel gain of the attacker exactly. The schedule problem over the infinite-time horizon is first formulated as a Markov decision process with finite state and action spaces. Then, a Bayesian Stackelberg game (BSG) is constructed by incorporating the probability information of the channel interference gain. Based on the definition of best-response, the solution of the BSG is presented and the existence of the Stackelberg equilibrium is proven. Furthermore, a Stackelberg Q-learning algorithm is used to obtain the optimal strategies for the two players. Numerical results demonstrate the effectiveness of the proposed game method when the sensor is unable to access an attacker's channel gain information.