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：本文研究由地球站发射机Alice、地球同步轨道(GEO)卫星接收机Bob及Bob周围多个GEO卫星监测节点构成的多输入多输出(MIMO)卫星-地面系统中的上行链路隐蔽通信，系统中每个节点均配备定向天线阵列。基于波束成形和默认天线朝向设置，我们首先提出一种隐蔽Alice-Bob上行链路传输方案。在完美信道估计场景下，我们针对检测错误概率(DEP)、传输中断概率(TOP)和隐蔽速率(CR)建立了系统性能的理论模型，进而探索了最大化CR的最优波束成形(OB)设计以及联合最优波束成形与天线朝向(JO-BA)设计。随后我们将研究拓展至非完美信道估计场景，并开展了相应的性能建模及最大化CR的OB/JO-BA设计。我们还应用半定松弛、交替优化、罗德里格斯旋转公式和一维搜索算法等技术，开发了高效算法以求解上述优化问题。最后，通过大量数值结果验证了理论分析的正确性，并阐明了波束成形与天线朝向设计对支持MIMO GEO卫星-地面系统中上行链路隐蔽通信的有效性。