This paper investigates the uplink covert communication in a multiple-input multiple-output (MIMO) satellite-terrestrial system consisting of an Earth station transmitter Alice, a geosynchronous Earth orbit (GEO) satellite receiver Bob, and multiple GEO satellite wardens around Bob, where each node in the system is equipped with an array of directional antennas. Based on beamforming and the default antenna orientation setting, we first propose a scheme for covert Alice-Bob uplink transmission. Under the perfect channel estimation scenario, we provide theoretical modeling for the system performance in terms of detection error probability (DEP), transmission outage probability (TOP) and covert rate (CR), and then explore the optimal beamforming (OB) design as well as the joint optimal beamforming and antenna orientation (JO-BA) design for CR maximization. We then extend our study to the imperfect channel estimation scenario, and conduct related performance modeling and OB/JO-BA designs for CR maximization. We also apply the techniques of semidefinite relaxation, alternating optimization, Rodrigues' rotation formula and 1-D search algorithm to develop efficient algorithms to solve the above optimization problems. Finally, extensive numerical results are presented to verify our theoretical results and to illustrate the efficiency of beamforming and antenna orientation design for supporting the uplink covert communication in MIMO GEO satellite-terrestrial systems.

翻译：本文研究由地面站发射机Alice、地球同步轨道卫星接收机Bob以及Bob周围的多个GEO卫星监测站组成的多输入多输出卫星-地面系统中的上行链路隐蔽通信，其中系统各节点均配备定向天线阵列。基于波束成形与默认天线指向设置，我们首先提出一种隐蔽的Alice-Bob上行传输方案。在完美信道估计场景下，我们建立了系统在检测错误概率、传输中断概率与隐蔽速率方面的理论模型，进而探索了最大化隐蔽速率的最优波束成形设计以及波束成形与天线指向联合优化设计。随后将研究扩展至非完美信道估计场景，并建立了相应的性能模型及最大化隐蔽速率的最优波束成形/联合优化设计。同时应用半定松弛、交替优化、罗德里格斯旋转公式与一维搜索算法等技术，开发了求解上述优化问题的高效算法。最后，通过大量数值结果验证了理论分析，并阐明了波束成形与天线指向设计对支持MIMO GEO卫星-地面系统中上行链路隐蔽通信的有效性。