Game Theoretic Study on Channel-Based Authentication in MIMO Systems

In this paper, we investigate the authentication based on radio channel information in multiple-input multiple-output (MIMO) systems and formulate the interactions between a receiver with multiple antennas and a spoofing node as a zero-sum physical (PHY)-layer authentication game. In this game, the receiver chooses the test threshold of the hypothesis test to maximize its Bayesian risk-based utility in the spoofing detection, while the adversary chooses its attack rate, i.e., how often a spoofing signal is sent. We derive the Nash equilibrium (NE) of the static PHY-layer authentication game and present the condition that the NE exists, showing that both the spoofing detection error rates and the spoofing rate decrease with the number of transmit and receive antennas. We propose a PHY-layer spoofing detection algorithm for MIMO systems based on Q-learning, in which the receiver applies the reinforcement learning technique to achieve the optimal test threshold via trials in a dynamic game without knowing the system parameters, such as the channel time variation and spoofing cost. We also use Dyna architecture and prioritized sweeping (Dyna-PS) to improve the spoofing detection in time-variant radio environments. The proposed authentication algorithms are implemented over universal software radio peripherals and evaluated via experiments in an indoor environment. Experimental results show that the Dyna-PS-based spoofing detection algorithm further reduces the spoofing detection error rates and increases the utility of the receiver compared with the Q-learning-based algorithm, and both performances improve with more number of transmit or receive antennas.