Energy-Efficient Hybrid Beamforming for Multilayer RIS-Assisted Secure Integrated Terrestrial-Aerial Networks

The integration of aerial platforms to provide ubiquitous coverage and connectivity for densely deployed terrestrial networks is expected to be a reality in the emerging sixth-generation networks. Energy-effificient and secure transmission designs are two important components for integrated terrestrial-aerial networks (ITAN). Inlight of the potential of reconfigurable intelligent surface (RIS) for significantly reducing the system power consumption and boosting information security, this paper proposes a multi-layer RIS-assisted secure ITAN architecture to defend against simultaneous jamming and eavesdropping attacks, and investigates energy-efficient hybrid beamforming for it. Specifically, with the availability of imperfect angular channel state information (CSI), we propose a block coordinate descent (BCD) framework for the joint optimization of the user's received decoder, the terrestrial and aerial digital precoder, and the multi-layer RIS analog precoder to maximize the system energy efficiency (EE) performance. For the design of the received decoder, a heuristic beamforming scheme is proposed to convert the worst-case design problem into a min-max one and facilitate the developing a closed-form solution. For the design of the digital precoder, we propose an iterative sequential convex approximation approach via capitalizing the auxiliary variables and first-order Taylor series expansion. Finally, a monotonic vertex-update algorithm with a penalty convex-concave procedure (P-CCP) is proposed to obtain the analog precoder with satisfactory performance. Numerical results show the superiority and effectiveness of the proposed optimization framework and architecture over various benchmark schemes.