Anti-Jamming Transmission for Movable Antennas Enabled Integrated Sensing and Communication Systems: A Stackelberg Game Perspective

This paper proposes a transmission framework for Integrated sensing and communication systems implemented through movable antennas (MAs) in a jamming adversarial environment, which is formulated using a Bayesian Stackelberg game model. As a leader, the base station (BS) aims to maximize the benefit-cost ratio by jointly optimizing the position of the MAs and the transmit beamforming, thereby enhancing communication and sensing performance while reducing transmission power. As the follower, the Jammer attempts to minimize its energy consumption while ensuring that its jamming energy efficiency reaches a predefined threshold. To solve the game equilibrium problem, the optimal jamming power of the Jammer is determined using duality theory. For the BS's optimal response strategy, the jamming power is upper-bounded using the Cauchy-Schwarz inequality, and a flexible mode-switching mechanism between communication priority and sensing priority is introduced. The BS's transmit beamforming is then optimized using quadratic transform methods, while the optimal antenna positions are determined by applying submodular function maximization techniques. Furthermore, the existence and uniqueness of the proposed game's Stackelberg equilibrium have been established. Simulation results demonstrate the proposed model achieves a balance between power control, anti-jamming capability, and the trade-off between communication and sensing performance.