Optimal Power Control for DoS Attack over Fading Channel: A Game-Theoretic Approach

In this paper, we investigate remote state estimation against an intelligent denial-of-service (DoS) attack over a vulnerable wireless network whose channel undergoes attenuation and distortion caused by fading. We use the sensor to observe system states and transmit its local state estimates to the remote center. Meanwhile, the attacker injects a jamming signal to destroy the packet accepted by the remote center and causes the performance degradation. Most of the existing works are built on a time-invariant channel state information (CSI) model in which the channel fading is stationary. However, the wireless communication channels are more prone to dynamic changes. To capture this time-variant property in the channel quality of the real-world networks, we study the fading channel network whose channel model is characterized by a generalized finite-state Markov chain. With the goals of two players in infinite-time horizon, we describe the conflicting characteristic between the attacker and the sensor with a general-sum stochastic game. Moreover, the Q-learning techniques are applied to obtain an optimal strategy pair at a Nash equilibrium. Also the monotone structure of the optimal stationary strategy is constructed under a sufficient condition. Besides, when channel gain is known a priori, except for the full Channel State Information (CSI), we also investigate the partial CSI, where Bayesian games are employed. Based on the player's own channel information and the belief on the channel distribution of other players, the energy strategy at a Nash equilibrium is obtained.