Max–Min Fairness Robust Beamforming for LEO Satellite Multibeam Communication Systems With Two CSI Uncertainty Model

The widespread employ of Internet of Things (IoT) devices relies on the massive deployment of sensor nodes and data collection timely. Benefit from development of low-Earth orbit (LEO) satellite technology, the LEO Satellite is considered an effective way for achieving wider coverage to terrestrial IoT devices in remote area. However, it is challenging to obtain perfect channel state information (CSI) in LEO satellite system because estimation error and longer round trip time in practice. To overcome this problem, we propose max–min fairness (MMF) robust beamforming deterministic uncertainty model of imperfect CSI convex-concave optimization algorithm (D-ICCA) and stochastic uncertainty model of imperfect CSI convex-concave optimization algorithm (S-ICCA) in LEO satellite communication system, respectively. MMF optimization problems are formulated under the constraints of the maximum per-antennas power constraint in the LEO satellite communication system. In deterministic uncertainty model of imperfect CSI, we obtain the lower bound of CSI by the Cauchy–Schwarz inequality first. Then, we transform the formulated MMF optimization problem to a series of standard convex problem and solve convex optimization subproblems by adopting the alternating direction method of multipliers (ADMM) to obtain suboptimal robust beamforming vectors. In stochastic uncertainty model of imperfect CSI, we model the MMF optimization problem with stochastic phase error and solve the MMF optimization problem via ADMM with closed-from solution to obtain suboptimal robust beamforming vectors. Finally, simulation results demonstrate that the proposed D-ICCA and S-ICCA beamforming algorithms can achieve better performance than ConADMM and FFA-SCA without robust design.