Cooperative Jamming Over DRL-Based Frequency Hopping Wireless Communications: A One-Leader Multi-Follower Stackelberg Game Approach

In wireless communications, traditional malicious jamming attacks that employ a single jammer and focus on a single domain are becoming increasingly ineffective due to the rapid advancements in learning-based anti-jamming technology. To address these issues, this paper proposes a novel multi-domain cooperative jamming method for DRL-based anti-jamming frequency hopping (FH) communications. At the jamming side, intelligent multi-domain attacks could be effectively implemented by coordinating the adjustment of frequency and power parameters among multiple jammers to disrupt the legitimate user’s communication. In this context, the interaction between the legitimate user and multiple cooperative jammers is modeled as a One-Leader Multi-Follower (OLMF) Stackelberg game, where the efficient jamming resource allocation problem among the cooperative jammers is formulated as a potential game. Then, the existence of Nash equilibrium for the potential game is demonstrated, which further ensures the Stackelberg equilibrium for the OLMF Stackelberg game. Additionally, a hierarchical deep reinforcement learning (HDRL) method is introduced to approach the final equilibrium for the cooperative jammers with a high-dimensional action space. Simulation results demonstrate that when facing DRL-based anti-jamming agents, the proposed multi-domain cooperative jamming approach achieves a jamming success rate that is 35% higher than traditional jamming, 20% higher than reactive jamming, and 15% higher than DRL-based non-cooperative jamming. Even when the legitimate user employs the opponent modeling based dynamic best response anti-jamming strategy, our method still converges to the Stackelberg equilibrium and achieves a 10% jamming performance gain compared to the multi-tone intelligent jamming method and the non-cooperative jamming method.