This paper proposes a robust beamforming (BF) scheme to enhance physical layer security (PLS) of the downlink of a multibeam satellite system in the presence of either uncoordinated or coordinated eavesdroppers (Eves). Specifically, with knowing only the approximate locations of the Eves, we aim at maximizing the worst-case achievable secrecy rate (ASR) of the legitimate user (LU), subject to the constraints of per-antenna transmit power and quality of service (QoS) requirement of the LU. Since the optimization problem is non-convex, we first adopt the discretization method to deal with the unknown regions of the Eves and then exploit the log-sum-exp function to approximate the objective function. Afterwards, a BF method joint alternating direction method of multipliers (ADMM) with Dinkelbach iteration is presented to solve this non-convex problem. Finally, simulation results verify that our robust BF algorithm can effectively improve the security of multibeam satellite systems.

翻译：本文提出一个强有力的波束成型(BF)计划,以加强多波束卫星系统在未经协调或协调的监听者(Eves)在场的情况下的物理层安全性(PLS),具体地说,我们只知道夏娃的大致位置,目的是最大限度地提高合法用户(LU)最坏情况可实现的保密率(ASR),但需受LU的Pper-antenna传输功率和服务质量要求的限制。由于优化问题是非对流的,我们首先采用离散法处理Eves的未知区域,然后利用日志总和功能接近目标功能。随后,我们提出了一种BF方法,即与Dinkelbach Iteration共同交替方向法(ADMMM),以解决这个非对流问题。最后,模拟结果证实,我们稳健的BF算法能够有效地改善多波束卫星系统的安全性。