Joint Beamforming and Time-Slot Allocation for Spectrum Sharing in Integrated Satellite-Terrestrial Networks

The integration of satellite and terrestrial networks can provide ubiquitous connectivity and efficient spectrum utilization. This paper investigates a spectrum sharing scenario for satellite and terrestrial downlinks. Terrestrial users (TUs) are directly served by small base stations (SBSs) and coexist with satellite users (SUs) under a time division multiple access (TDMA) protocol. To address the severe co-channel interference between satellite and terrestrial transmissions, we formulate a joint beamforming and time slot scheduling problem, aiming to maximize the weighted sum rates of the SU and TU. This problem is highly non-convex due to the coupling between the continuous beamforming vectors and the discrete scheduling variables. To address this challenge, we develop an alternating optimization framework. Specifically, the beamforming subproblem is solved via successive convex approximation (SCA) and second-order cone (SOC) reformulation, while the time slot scheduling subproblem is addressed via integer linear programming (ILP). Simulation results demonstrate that this approach significantly improves the achievable sum rate compared to traditional schemes while ensuring fairness between satellite and terrestrial users.