In this article, we investigate robust secure beamforming and power splitting for multiuser secondary terrestrial networks with simultaneous wireless information and power transfer, which coexist with primary satellite networks in the same millimeter-wave bands. In particular, a base station is equipped with a uniform planar array, and a secondary user (SU) employs a power-splitting-type receiver. Under an angle-based channel state information (CSI) error model, we formulate an optimization problem with the aim to maximize the minimal worst-case achievable secrecy rate among all SUs, while satisfying the quality-of-service (QoS) constraints for each SU, the interference limit for a primary satellite earth station, and the power consumption limit for the base station. To handle the intractable problem, we propose an iterative algorithm based on a series of approximations and a concept of the convex hull. Specifically, the former is for jointly designing secure beamformers and power splitting ratios, and the latter is for ensuring robustness to the angle-based CSI uncertainty. Furthermore, we analyze the computational complexity of this algorithm and extend the proposed scheme for solving a weighted sum secrecy rate maximization problem. Numerical results validate the effectiveness and superiority of the proposed scheme compared to the existing approaches, and obtain an insight into different robust designs.

中文翻译：

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利用 SWIPT 为毫米波认知卫星地面网络提供稳健的安全波束成形和功率分配


在本文中，我们研究了具有同步无线信息和电力传输的多用户辅助地面网络的鲁棒安全波束成形和功率分配，该网络与相同毫米波频段的主要卫星网络共存。具体地，基站配备有均匀平面阵列，并且次要用户(SU)采用功率分割型接收器。在基于角度的信道状态信息（CSI）错误模型下，我们制定了一个优化问题，旨在最大化所有SU中最小最坏情况可实现的保密率，同时满足每个SU的服务质量（QoS）约束SU，主卫星地球站的干扰限制，以及基站的功耗限制。为了处理这个棘手的问题，我们提出了一种基于一系列近似和凸包概念的迭代算法。具体来说，前者用于联合设计安全波束形成器和功率分配比，后者用于确保对基于角度的CSI不确定性的鲁棒性。此外，我们分析了该算法的计算复杂性，并扩展了所提出的解决加权和保密率最大化问题的方案。数值结果验证了所提出方案与现有方法相比的有效性和优越性，并深入了解不同的鲁棒设计。