Jamming the Relay-Assisted Multi-User Wireless Communication System: A Zero-Sum Game Approach

Recently, various wireless Internet-of-Things devices and unmanned aerial vehicles have been frequently used to facilitate daily life. On the other hand, they can also pose serious threats to public security if maliciously used. A countermeasure against these threats is to transmit jamming signals to break the communication links between attacker and wireless devices. However, this is not easy since modern multi-device (multi-user) wireless communication systems are smart in avoiding jamming. Moreover, a relay is widely used to improve the jamming resistance. To successfully jam those malicious devices, we consider a jamming and anti-jamming zero-sum game, in which the attacker tries to maximize the sum-rate of a relay-assisted wireless system and the jammer tries to minimize it. Finding the equilibrium is challenging due to its non-convexity and complex structure. We address this problem in two cases. Specifically, in the single-device (single-user) case, we show that putting the whole jamming power to either relay or device achieves the Nash equilibrium. In the multi-device case, an efficient method is developed, which transforms this game into a min-max optimization problem and decouples it into two sub-problems by the hybrid block successive approximation method. The resultant sub-problems are solved by the multi-block alternating direction method of multipliers and the block successive upper-bound minimization method of multipliers, respectively. Then, a stationary point of the original problem can be iteratively achieved. Numerical results demonstrate that the two proposed jamming methods outperform many traditional methods.