Statistical-CSI Precoding for OTFS-Based Multi-Satellite Cooperative Transmission

Abstract

Multi-satellite cooperative transmission (MSCT) enabled by low-Earth-orbit (LEO) constellations is a promising technique for 6G non-terrestrial networks (NTNs), since it can improve coverage reliability and system throughput. However, the high mobility of LEO satellites causes severe Doppler shifts and rapidly varying channel phases, making instantaneous channel state information (CSI) difficult to acquire and maintain. This paper studies statistical-CSI delay-Doppler (DD)-domain precoding for orthogonal time frequency space (OTFS)-based MSCT. We formulate a statistical-CSI weighted sum-rate (WSR) maximization problem based on a covariance-based approximation of the expected rate. To evaluate the desired and interfering receive covariances, we construct a receive covariance operator that maps cooperative transmit covariance matrices to UT-side receive covariance matrices while preserving Rician second-order statistics in the satellite-antenna-DD domain. We further show that expected-channel weighted minimum-mean square error (WMMSE) criterion is not equivalent to WSR objective under Rician statistical CSI. Based on the covariance operator and its adjoint mapping, we derive the covariance gradient and propose a projected covariance-gradient precoding algorithm with per-satellite power projection, backtracking line search, and deterministic multi-start refinement. Numerical results verify the monotone convergence of the proposed algorithm and demonstrate consistent WSR performance gains over baselines.