Robust Multi-Objective Beamforming for Integrated Satellite and High Altitude Platform Network With Imperfect Channel State Information

In this paper, we propose a robust beamforming (BF) scheme for an integrated satellite and high altitude platform network, where a multibeam satellite system shares the millimeter wave spectrum with a high altitude platform system. Specifically, we first exploit the weighted Tchebycheff method and formulate a multi-objective optimization problem to obtain the Pareto optimal trade-off between two conflicting yet desirable objectives, namely, sum rate maximization and total transmit power minimization, while satisfying the quality-of-service constraints of both earth stations and mobile terminals and per-antenna transmit power budget. Then, by using the angular information based imperfect channel state information, we propose a low-complexity discretization method to transform the non-convex objective function and constraints to the convex ones. Furthermore, a monotonic optimization scheme combined with iterative penalty function algorithm is presented to obtain the BF weight vectors with low computational complexity and fast convergence rate. Finally, numerical results are provided to confirm the effectiveness and superiority of the proposed approach in comparison to the existing related works.