Two-Timescale Joint On-Ground Precoding and On-Board Beamforming Design for Multi-Gateway Multibeam Satellite Systems

This paper studies the joint on-ground precoding and on-board beamforming design problem in multi-gateway multibeam satellite communications with feeder link interference. Compared with pure on-ground systems, the hybrid on-ground on-board architecture provides a good trade-off between the total throughput and the bandwidth requirements of the feeder link. Moreover, we propose a two-timescale design strategy which significantly reduces the computational burden on the satellite payload. To be specific, the long-term on-board beamforming network (BFN) is designed based on the statistical channel state information (S-CSI), while the short-term on-ground precoding matrices are designed to cater to the instantaneous CSI (I-CSI) with optimized on-board BFN. We formulate an average sum rate maximization problem which incorporates the lossless constraint of the BFN, as well as the average power constraints at the satellite. To tackle this two-timescale non-convex stochastic optimization problem, we propose an algorithm called two-timescale joint on-ground and on-board beamforming (TJGBB). At each iteration, the TJGBB algorithm first solves the short-term on-ground precoding subproblem based on the weighted minimum mean square error (WMMSE) method. Then, it constructs convex surrogate functions for the objective and constraints of the long-term on-board beamforming primary problem, creating an approximate version. Finally, the long-term variables are updated by solving this convex approximation problem. The proposed algorithm is proven to almost surely converge to a stationary solution of the original problem within an acceptable error margin. Simulations show that our proposed method can significantly improve the overall system throughput compared to existing schemes.