Robust Secrecy-Energy Efficient Beamforming for Jittering UAV in Cognitive Satellite-Aerial Networks

Cognitive satellite-aerial network (CSAN), integrating the satellite (SAT) network with the unmanned aerial vehicle (UAV) network in the same frequency band, is regarded as a promising architecture for next-generation heterogeneous networks. However, the CSAN reliability is compromised by the eavesdropping risks, UAV energy limitations and inherent jitter effects. To overcome these challenges, our aim is to design robust beamforming (BF) schemes to maximize the secrecy energy efficiency (SEE) of jittering UAV while satisfying both UAV transmit power constraint and SAT earth station interference limitation. Specifically, the worst-case robust SEE maximization (WC-RSEEM) and the outage-constrained robust SEE maximization (OC-RSEEM) problems are formulated for the deterministic and the probabilistic jittering models, respectively. For WC-RSEEM, we derive a second-order Taylor series expansion (STSE)-based approach to approximate the complex trigonometric form in terms of jitter errors into a quadratic form. Based on this result, we convert the original non-convex problem into a convex one by utilizing S-Procedure and propose an iterative penalty function-based successive convex approximation (PF-SCA) algorithm to obtain the UAV beamformer. For OC-RSEEM, by combining STSE approximation with Bernstein-type inequalities, the original problem is transformed into a deterministic form that can be handled by a two-level iterative algorithm. In this algorithm, the innerlevel problem is reorganized as a transmit power minimization problem, which is solved by the PF-SCA approach, whereas the outer-level problem is recast as a singlevariable optimization problem, which is solved by the golden search method. Simulation results validate the superiority and robustness of the proposed robust BF schemes.