Robust Multicast Beamforming for Jittering UAV: A Secrecy Energy Efficiency Perspective

Abstract

In this paper, we investigate an unmanned aerial vehicle (UAV) enabled secure multicast communication system, where a UAV serves multiple legitimate ground users in the presence of multiple coordinated eavesdroppers. Taking into account the inherent jittering characteristics of UAVs caused by the airflow, we aim to maximise the worst-case secrecy energy efficiency (SEE) under a constrained UAV transmission power budget. The formulated optimization problem is inherently non-convex and challenging to solve due to the combined effects of jittering uncertainties and the max–min fractional structure of the SEE metric. To address these challenges, we first simplify the original SEE maximization problem by introducing auxiliary variables. Next, considering the impact of jittering on the antenna array response, we develop a novel second-order Taylor series expansion-based approach to approximate beamforming gains as quadratic functions of the angle-of-departure errors, which can be subsequently transformed into deterministic convex constraints by using S-Procedure. Based on these theoretical results, we design an iterative algorithm that combines the penalty function method with the successive convex approximation to efficiently obtain a suboptimal solution. Finally, the simulation results demonstrate the effectiveness and superiority of the proposed scheme compared to several benchmark schemes, highlighting its potential for practical implementation in UAV-enabled secure multicast communication systems.