Iterative Beamforming Method for Phased Array Fed Reflector in 6G Direct-to-Cell Satellite Communications

Direct communication between satellites and terminals, known as direct-to-cell (D2C), is currently in the developmental stage and has become one of the key focuses of satellite communications. However, with the increase of orbital altitude, the aperture size of phased array antennas adopted by low-earth-orbit (LEO) satellite grows, introducing excessively complex hardware requirements. Meanwhile, the beam reconfiguration capability of reflectors adopted by geostationary-orbit (GEO) satellites are limited, making it challenging to meet the D2C demands of non-geostationary orbit (NGSO) satellites due to the mobility of both satellites and terminals. In this paper, we utilize the phased array fed reflector (PAFR), which offers dynamic beamforming capability and reduced hardware complexity advantages, and propose the corresponding beamforming mathematical model. We analyze the relation between the weighted sum rate and the weighted minimum mean square error (WMMSE) within this architecture, and design an iterative beamforming optimization method based on the WMMSE criterion that converges to a local optimal solution. Simulation results demonstrate that the proposed method achieves performance comparable to that of a fully connected structure with an equivalent aperture phased array, while offering superior energy efficiency.