The secrecy capacity based on the assumption of having continuous distributions for the input signals constitutes one of the fundamental metrics for the existing physical layer security (PHYS) solutions. However, the input signals of real-world communication systems obey discrete distributions. Furthermore, apart from the capacity, another ultimate performance metric of a communication system is its symbol error ratio (SER). In this article, we pursue a radically new approach to PHYS by considering rigorous direct SER optimization exploiting the discrete nature of practical modulated signals. Specifically, we propose a secure precoding technique based on a multi-objective SER criterion, which aims for minimizing the confidential messages’ SER at their legitimate user, while maximizing the SER of the confidential messages leaked to the illegitimate user. The key to this challenging multi-objective optimization problem is to introduce a priority factor that controls the priority of directly minimizing the SER of the legitimate user against directly maximizing the SER of the leaked confidential messages. Furthermore, we define a new metric termed as the security-level, which is related to the conditional symbol error probability of the confidential messages leaked to the illegitimate user. Additionally, we also introduce the secure discrete-input continuous-output memoryless channel (DCMC) capacity referred to as secure-DCMC-capacity, which serves as a classical security metric of the confidential messages, given a specific discrete modulation scheme. The impacts of both the channel’s Rician factor and the correlation factor of antennas on the security-level and the secure-DCMC-capacity are investigated. Our simulation results demonstrate that the proposed priority-aware secure precoding based on the direct SER metric is capable of securing transmissions, even in the challenging scenario, where the eavesdropper has three receive antennas, while the legitimate user only has a single one.

中文翻译：

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基于多目标符号误码率优化的优先级感知安全预编码

基于对输入信号具有连续分布的假设，保密容量构成了现有物理层安全性（PHYS）解决方案的基本指标之一。但是，实际通信系统的输入信号服从离散分布。此外，除了容量之外，通信系统的另一个最终性能指标是它的符号错误率（SER）。在本文中，我们通过考虑利用实际调制信号的离散特性进行严格的直接SER优化，来寻求一种全新的PHYS方法。具体来说，我们提出了一种基于多目标SER准则的安全预编码技术，旨在将机密消息在其合法用户处的SER最小化，同时最大化泄露给非法用户的机密消息的SER。解决这一具有挑战性的多目标优化问题的关键是引入一个优先级因子，该优先级因子控制直接最小化合法用户的SER与直接最大化泄露的机密消息的SER的优先级。此外，我们定义了一个新的度量标准，称为安全级别，它与泄露给非法用户的机密消息的条件性符号错误概率有关。此外，我们还介绍了安全离散输入连续输出无记忆信道（DCMC）容量，称为安全DCMC容量，在给定特定离散调制方案的情况下，它用作机密消息的经典安全度量。研究了信道的Rician因子和天线的相关因子对安全级别和安全DCMC能力的影响。我们的仿真结果表明，即使在窃听者具有三个接收天线而合法用户只有一个天线的挑战性场景中，基于直接SER度量的建议优先级感知安全预编码也能够确保传输的安全。