Movable-Antenna-Assisted Dual-Hop FSO/RF Space–Air–Ground Networks With Underlay Spectrum Sharing

This article investigates a movable-antenna (MA)-assisted dual-hop space–air–ground nonterrestrial network (NTN) operating under an underlay spectrum sharing paradigm. A satellite communicates with multiple uncrewed aerial vehicles (UAVs) over free-space optical (FSO) links, while each UAV simultaneously serves a cluster of ground users over radio frequency (RF) channels subject to interference constraints imposed by a primary receiver. To efficiently exploit the complementary advantages of FSO and RF transmission and the additional spatial degrees of freedom offered by MAs, a joint optimization framework is developed to maximize the system sum rate. The proposed framework jointly optimizes satellite and UAV power allocation, multiantenna precoding at the UAVs, and the positions of multiple MAs mounted on each UAV. An alternating-optimization algorithm is employed, where minimum mean square error (MMSE)-based precoding accounts for both communication and interference channels, power allocation is convexified using auxiliary rate variables and successive convex approximation (SCA), and antenna locations are optimized via Taylor-based convex surrogates. Simulation results demonstrate that the proposed approach significantly outperforms benchmark schemes with fixed antenna locations, heuristic optimization, and reinforcement learning methods, while providing robust performance across different system parameters.