Distributed Hybrid Beamforming for Downlink Multi-User Space-MIMO Communications

In this correspondence, we propose a graph-based distributed hybrid beamforming scheme for downlink multi-user communications in low earth orbit (LEO) multi-satellite networks. Firstly, we model a reconfigurable holographic surface (RHS)-empowered downlink multi-user satellite-terrestrial communication system, where multiple LEO satellites are collectively integrated into a space multiple-input multiple-output (MIMO) transmitter to coherently transmit data streams to multiple terrestrial user terminals (UTs). Secondly, we formulate a weighted sum rate (WSR) maximization problem, subject to individual transmit power constraints. To address it, a graph-based scheme is developed for the joint optimization of analog and digital beamforming in a distributed manner. Finally, the proposed scheme is extended to support phased array systems. Simulation results show that the proposed scheme significantly outperforms conventional methods such as minimum mean square error (MMSE), zero forcing (ZF), and maximum ratio transmission (MRT), with the phased array configuration achieving a higher WSR than the RHS.