Queue-Stability Constrained Robust Secure Beamforming in Satellite-Terrestrial Integrated Networks

This letter proposes a robust secure beamforming (BF) scheme for a satellite-terrestrial integrated network (STIN), where earth stations are served by the satellite network in presence of multiple eavesdroppers, and the terrestrial network operating the same spectrum provides multicast services to terrestrial users. Unlike most existing works that merely focused on static networks, we consider the effects of random data arrivals on system performance, and establish queue stability condition based on the data queue. Then, we exploit the imperfect channel state information to formulate an optimization problem, aiming at minimizing the long-term average power, while meeting quality-of service constraints, transmit power budget and data-queue stability constraints. To solve this mathematically complex problem, we apply the Lyapunov optimization technique to convert the original problem to a per-slot penalized power minimization problem, and propose an iterative algorithm combining with Bernstein inequality to acquire the BF weight vectors. Finally, simulation results validate that our proposed scheme enhances the secrecy performance of the STIN, achieving a favorable trade-off between power consumption and queue stability.