Statistical CSI-Based Downlink Precoding for Multi-Beam LEO Satellite Communications

With the rapid development of low-Earth-orbit (LEO) satellite communications, multi-beam precoding has emerged as a key technology for improving spectrum efficiency. However, the long propagation delay and large Doppler frequency offset pose significant challenges to existing precoding techniques. To address this issue, this paper investigates downlink precoding design for multi-beam LEO satellite communications. First, the downlink channel and signal models are established. Then, we reveal that traditional zero-forcing (ZF), regularized zero-forcing (RZF), and minimum mean square error (MMSE) precoding schemes all require the satellite transmitter to acquire the instantaneous channel state information (iCSI) of all users, which is challenging to obtain in satellite communication systems. Subsequently, we propose a downlink precoding design based on statistical channel state information (sCSI) and derive closed-form solutions for statistical-ZF, statistical-RZF, and statistical-MMSE precoding. Furthermore, we propose that sCSI can be computed using the positions of the satellite and users, which reduces the system overhead and complexity of sCSI acquisition. Monte Carlo simulations under the 3GPP non-terrestrial network (NTN) channel model are employed to verify the performance of the proposed method. The simulation results show that the proposed method achieves sum-rate performance comparable to that of iCSI-based schemes and the optimal transmission performance based on sum-rate maximization. In addition, the proposed method significantly reduces the computational complexity of the satellite payload and the system feedback overhead.