Robust Downlink Precoding for LEO Satellite Systems With Per-Antenna Power Constraints

Downlink precoding has been widely accepted as a crucial technique in low-earth-orbit (LEO) satellite communications due to its advantages in improving the space division multiplexing capability and enhancing spectrum efficiency. Because of the strong spatial directivity in the satellite channels, the downlink precoder can be efficiently designed based on the angle of departure (AoD)-based channel state information (CSI). However, acquiring perfect AoD-based CSI is challenging due to the angle estimation error and attitude jitter of the LEO satellites. In light of this, this paper investigates the precoder design for the LEO satellite downlinks with imperfect AoD-based CSI. For robust design, we treat the angle deviations of each user as random variables, which are supposed to exhibit a particular distribution, then integrate them within a certain range to achieve the robustness of the proposed downlink precoder against the angle mismatch. Instead of using the sum-power constraint on the transmit antennas, we adopt a more realistic per-antenna power constraint (PAPC). Accordingly, we formulate the problem to maximize the ergodic sum rate of the system. By leveraging the corresponding Lagrangian formulation and identifying the optimal precoder structure as the solution to a generalized eigenvalue problem, an iterative algorithm for the robust precoder design is derived. To reduce the computational complexity, a low-complexity version of the proposed algorithm is implemented based on deep learning techniques to meet the high demand for real-time applications in LEO satellite systems. Simulation results verify the effectiveness of the proposed precoding approach.