Joint Hybrid Beamforming and Trajectory Design for Multi-UAV-Enabled Cell-Free Multi-Static ISAC

This paper investigates a joint hybrid digital-analog beamforming and trajectory design for a cell-free multi-static integrated sensing and communication (ISAC) system supported by multiple unmanned aerial vehicles (UAVs). Specifically, these UAVs cooperatively serve ground users and perform multi-static sensing to detect the target. We formulate a weighted sum-rate (WSR) maximization problem by jointly optimizing the hybrid beamformers and the UAV trajectories. This joint design explicitly accounts for practical constraints, including transmit power budgets, sensing signal-to-noise ratio (SNR) requirements, UAV kinematic constraints, and both continuous and discrete phase shifters. In particular, we reformulate the original complex problem into a solvable form that can be addressed using the penalty dual decomposition (PDD) method. Simulation results demonstrate that the proposed design achieves performance close to that of the fully digital (FD) scheme and significantly outperforms other schemes. Furthermore, leveraging UAV mobility and multi-static cooperation provides crucial spatial degrees of freedom, effectively avoiding WSR degradation under limited transmit power or strict sensing requirements.