Optimal Beamforming for Uplink Covert Communication in MIMO GEO Satellite-Terrestrial Systems

2026-01-03

arXiv.org

AI Summary

This work addresses the problem of covert communication in the uplink of geostationary Earth orbit (GEO) satellite systems under multi-warden scenarios. To maximize the covert rate, the paper proposes a joint optimization framework that simultaneously designs beamforming and antenna pointing—a novel integration first introduced in the context of GEO satellite covert communications. Two schemes are developed: optimal beamforming (OB) and joint beamforming–antenna optimization (JO-BA), both extended to account for imperfect channel state information. The resulting non-convex problems are efficiently solved via semidefinite relaxation, alternating optimization, Rodrigues’ rotation formula, and one-dimensional search. Theoretical analysis and simulations demonstrate that the proposed approaches significantly increase the wardens’ detection error probability, reduce outage probability, and effectively enhance the achievable covert rate.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

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.

Problem

• covert communication
• MIMO satellite-terrestrial systems
• uplink transmission
• beamforming
• GEO satellite

Innovation

• covert communication
• optimal beamforming
• antenna orientation optimization
• MIMO satellite-terrestrial systems
• imperfect channel estimation