In this study, the authors proposed the optimal beamforming (BF) design for multiuser broadcast secure transmission under secrecy outage probability constraint with artificial noise technique. Different from former research papers, their model assumes that different users have different priority and importance. Some users are regarded as main users with a stricter constraint, which make the normal BF algorithm not to gain the best performance. For this reason, they proposed a new BF design method for this specific system model. To deal with intractable non-convex problems, they employed a series of optimisation algorithm like Bernstein-type inequality and second-order cone constraints method to transform these problems into solvable functions. After that, they show the feasibility of their new BF algorithm by Monte-Carlo simulation method, and analyse the influence on transmission and security performance caused by different system parameters. Furthermore, they compare the security performance of their method with the normal BF method, which demonstrates the advantage of the new BF method.

中文翻译：

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保密中断概率约束下不同重要性用户的人工噪声多用户广播系统的安全波束形成方法

在这项研究中，作者提出了在保密中断概率约束下采用人工噪声技术的多用户广播安全传输的最佳波束成形（BF）设计。与以前的研究论文不同，他们的模型假设不同的用户具有不同的优先级和重要性。一些用户被认为是具有更严格限制的主要用户，这使得普通的BF算法无法获得最佳性能。因此，他们针对该特定系统模型提出了一种新的BF设计方法。为了解决棘手的非凸问题，他们采用了一系列优化算法，例如Bernstein型不等式和二阶锥约束方法，将这些问题转换为可解函数。之后，他们通过蒙特卡洛模拟方法展示了其新的BF算法的可行性，并分析了不同系统参数对传输和安全性能的影响。此外，他们将其方法的安全性能与常规BF方法进行了比较，从而证明了新BF方法的优势。