IRS-Assisted Anti-Jamming Transmission for an Integrated Satellite-UAV-Terrestrial Network With Imperfect CSI: A Game-Based Perspective

In this article, an intelligent reflecting surface (IRS)-assisted integrated satellite-unmanned aerial vehicle (UAV)-terrestrial (SUT) Internet of Things (IoT) network faced with a smart jammer under imperfect channel state information (CSI) conditions is considered. We propose a Stackelberg game model to describe the adversarial relationship between the satellite, UAV, and IRS and the jammer, which are modeled as the leader and the follower, respectively. For the follower subgame, the jammer aims to minimize the jamming power while guaranteeing that the jamming energy efficiency surpasses a certain threshold. Under this setup, the Angle of Arrival (AoA)-based discretization method is utilized to address the imperfect CSI issue. Then, the use-and-then-forget method and the Lagrangian function are employed to obtain a closed-form expression for the jammer's power. Finally, a feasible jamming power solution is obtained by means of the Cauchy-Schwarz inequality. For the leader subgame, we aim to optimize the hybrid beamforming design of the satellite, UAV and IRS, with the goal of minimizing the total transmit power, while guaranteeing that the downlink received signal-to-interference-plus-noise ratio (SINR) surpasses the minimum communication threshold. We propose an alternating optimization scheme, in which the Cauchy-Schwarz inequality, the AoA-based discretization method, and nonsmooth penalty functions are employed to alternately obtain the optimal satellite beamforming vector, UAV beamforming vector and IRS phase matrix when the other variables are fixed. Through our analytical and numerical results, the proposed beamforming scheme achieves a reduction of 16.9% in average power consumption compared with other benchmark schemes when obtaining the same anti-jamming performance.