Optimal power control for sensors and DoS attackers over a fading channel network

In this paper, we focus on the optimal power control for the sensors and attackers in a remote state estimation process, which guarantees the achievement of the estimation task under the denial-of-service (DoS) attack. In the remote estimation process under the DoS attack, each sensor observes the target state and transmits its local estimates to the remote estimator via a wireless network, communications in which are disrupted by jamming signals. For the wireless network, while most of the existing works on the resilient remote state estimation consider time-invariant channel state information (CSI) model, we pay attention to the fading channel network, in which the channel state is fixed and the channel model can be characterized by a generalized finite-state Markov chain. We model the conflicting nature among the sensor and the attacker as a general-sum stochastic game, proposing a Nash Q-learning algorithm to find the optimal power control strategies for the two players. Moreover, the monotone structure of these strategies is constructed with a sufficient condition. Taking into account the practical applications, we also consider the case where the sensor and the attacker only know partial information of each other and employ the Bayesian game to model it. Based on the channel information of each player and its believes of the channel distribution of the opponent, the type-contingent energy strategies are obtained. Finally, simulation results are given to verify our results.