This letter considers the incorporation of secure directional modulation in reconfigurable intelligent surface (RIS)-aided communication networks. With elaborately selected antenna subsets, secure directional modulation generates randomized signals at undesired directions to assure physical-layer security. One major challenge of introducing RIS is that an additional beam, other than the user-specific beam, is required to align to the RIS. The interplay between the two beams can cause high sidelobe, which is non-trivial to address due to the discrete optimization in antenna subset selection. To tackle this challenge, we propose a novel cross-entropy iterative method to achieve low-sidelobe hybrid beamforming for secure directional modulation in RIS-aided networks. We use maximum sidelobe energy as the objective function to reduce the emission, and deploy Kullback-Leibler divergence as the criterion in the iterative selection of good candidate antenna subsets. Simulation results illustrate that the proposed scheme can reduce the sidelobe energy by 8 dB, and the symbol error rate of the eavesdropper maintains at 0.75 (0.875) for QPSK (8PSK) even when its signal-to-noise ratio increases.

中文翻译：

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RIS 辅助网络中的安全定向调制：一种低旁瓣混合波束成形方法

这封信考虑了在可重构智能表面 (RIS) 辅助通信网络中加入安全定向调制。通过精心选择的天线子集，安全定向调制会在不希望的方向上生成随机信号，以确保物理层的安全性。引入 RIS 的一个主要挑战是，除了用户特定的光束之外，还需要一个额外的光束来与 RIS 对齐。两个波束之间的相互作用会导致高旁瓣，由于天线子集选择中的离散优化，解决这一问题并非易事。为了应对这一挑战，我们提出了一种新的交叉熵迭代方法来实现低旁瓣混合波束成形，以在 RIS 辅助网络中实现安全定向调制。我们使用最大旁瓣能量作为目标函数来减少发射，并部署 Kullback-Leibler 散度作为迭代选择好的候选天线子集的标准。仿真结果表明，该方案可以将旁瓣能量降低8 dB，即使在信噪比增加的情况下，QPSK（8PSK）窃听者的误码率仍保持在0.75（0.875）。