Technically, the security performance of generalized spatial modulation (GenSM) networks can be enhanced by dynamically adjusting the precoder allocated to the legitimate signal as communication channel varies. For this purpose, our paper proposes a secure transmission strategy upon designing both digital and analog precoders for hybrid GenSM systems, where an eavesdropper is taken into account. The concept of the hybrid GenSM system has arose to improve the spatial multiplexing (SMX) gain for remedying the shortcoming of the limited number of radio frequency chains in traditional GenSM systems. However, this may lead to a great deal of security degradation since the SMX gain of the unintended receiver will be also improved. To this end, we develop a secrecy enhancement scheme by devising both analog and digital precoders for hybrid GenSM networks. Specifically, we derive an efficiently closed-form alternative to the original secrecy rate (SR) expression for reducing the excessive computational complexity of the joint optimization problem over the hybrid precoder. Then, by using this alternative as our cost function, an iterative algorithm is proposed. In particular, we elaborately conceive a pair of concave maximization problems in order to optimize the digital and analog precoders, respectively. Our proposed strategy not only utilizes semi-positive definite relaxing technique over the analog precoder but also invokes a lower bound of the alternative to further simplify the optimization over the vectored digital precoder. Subsequently, both the convergence and computational complexity of the proposed alternating iteration algorithm are analyzed. Compared to existing designs, our proposed strategy strikes a compelling role in balancing the SR performance and complexity. Finally, our simulation results confirm the efficiency of the proposed algorithm in terms of the SR performance achieved.

中文翻译：

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具有有限字母输入的安全广义空间调制的混合预编码设计

从技术上讲，可以通过在通信信道变化时动态调整分配给合法信号的预编码器来增强通用空间调制（GenSM）网络的安全性能。为此，我们在设计混合GenSM系统的数字和模拟预编码器时提出了一种安全的传输策略，其中考虑了窃听者。提出了混合GenSM系统的概念，以改善空间复用（SMX）增益，以弥补传统GenSM系统中有限数量的射频链的缺点。但是，由于意外接收器的SMX增益也将得到改善，因此这可能导致大量的安全性下降。为此，我们通过设计用于混合GenSM网络的模拟和数字预编码器来开发一种保密增强方案。具体来说，我们推导了一种有效的封闭形式替代原始保密率（SR）表达式的方法，以降低混合预编码器上联合优化问题的过多计算复杂性。然后，通过将此替代方案用作我们的成本函数，提出了一种迭代算法。特别地，我们精心构思了一对凹最大最大化问题，以便分别优化数字和模拟预编码器。我们提出的策略不仅在模拟预编码器上利用半正定松弛技术，而且还调用替代方法的下限，以进一步简化对矢量数字预编码器的优化。随后，分析了所提出的交替迭代算法的收敛性和计算复杂度。与现有设计相比，我们提出的策略在平衡SR性能和复杂性方面发挥了引人注目的作用。最后，我们的仿真结果就所实现的SR性能而言，证实了所提算法的效率。