## 5 Simulation Results  
In this section, we evaluate the performance of the hybrid beamforming scheme proposed for an RHS-aided secrecy communication system through simulation results. The simulation parameters are set as follows. The element spacing of the RHS \(d_{x}\) and \(d_{y}\) are set as 0.25 cm. The carrier frequency \(f\) is 30 GHz, and the propagation vector on the RHS \(|\mathbf{k}_{s}|=\sqrt{3}\left|\mathbf{k}_{f}\right|\), i.e., \(2\sqrt{3}\pi f/c\). The height of the BS is set as 50 m. The number of each user's receive antennas \(J=10\), as well as the noise density \(\sigma^{2}\)= \(-174\) dBm/Hz. We set the propagation environment between the BS and receivers as a millimeter-wave channel with \(l\) paths (we set it as one line-of-sight path and one none-line-of-sight path for simplicity). So, the the channel is denoted as  
\[\mathbf{H}_{l}=\sqrt{\frac{XYJ}{I}}\sum_{i=1}^{l}\alpha_{i}^{i}\mathbf{a}_{r} \left(\phi_{i_{i}}^{l}\right)\mathbf{a}_{t}\left(\theta_{i_{i}}^{l},\varphi_{ i_{i}}^{l}\right)^{H}, \tag{21}\]  
where \(\alpha_{l}^{i}\) is the complex gain of the \(i\)-th path; \(\phi_{i_{i}}^{l}\) and \(\left(\theta_{i_{i}}^{l},\varphi_{i_{i}}^{l}\right)\) are the angle of receive and transmit, respectively; and \(\mathbf{a}_{r}\left(\phi_{i_{i}}^{l}\right)\) and \(\mathbf{a}_{t}\left(\theta_{i_{i}}^{l},\varphi_{i_{i}}^{l}\right)\) are the antenna array response vectors at the receiver and transmitter [25]. The simulation setup is depicted in Figure 3. It is assumed that the RHS is located at (0,0,50) in meters (m). UE is located on the x-axis and is 60 m away from the RHS. Five eavesdroppers are strategically deployed within the domain, with their distances from the RHS uniformly set at 200 m. The difference between the \(\varphi_{0}\) of each eavesdropper is \(30^{\circ}\), and they are symmetrically distributed around the UE with respect to the x-axis. As illustrated in Figure 4, we traverse \(M_{x,y}\) at an interval of 0.5. It can be seen that different values of \(M_{x,y}\) influence the secrecy rate. There is a big difference in the influence of \(M_{x,y}\) when the power is low or high. In instances of low power, the BS digital beamforming signal is slight, and optimizing \(M_{x,y}\) primarily aims to increase the noise experienced by potential eavesdroppers. Conversely, at high power, the primary objective of \(M_{x,y}\) optimization is to enhance receiver rates. The observed curve in the figure generally indicates that secrecy rates ascend with increased power, aligning with expected outcomes. Figure 5 illustrates the communication rate of UE and Eves versus the power of the BS. It can be seen that, as the power increases, the user's rate increases, while the eavesdropper's rate is well suppressed. However, it is worth emphasizing that Eve1's eavesdropping rate exhibits a higher value than the other eavesdroppers. This rate amplifies with the increase in power, which is attributed to the influence of sidelobes. RHS will generate some sidelobes when performing beamforming, and the position of Eve1 is just in the direction of sidelobe propagation, so the suppression effect of RHS on Eve1 is not as pronounced as on the other eavesdroppers. Figure 6 illustrates the secrecy rate versus the power of the BS. It can be seen that, with the increase in the transmit power, the secrecy rate is increasing. In order to show the performance of the holographic surface in secrecy communication, we have also simulated the traditional phased array and the situation without RHS. It can be seen that the communication performance of RHS is better than that of the phased array, reflecting the excellent performance of the holographic surface in terms of beamforming. We compared the effects of surfaces with different numbers of radiation elements, and we can see that the surface with more radiation elements has a higher secrecy rate because the higher spatial DoF makes the suppression effect on eavesdroppers better. Figure 4: The secrecy rate versus the amplitude of the RHS. Figure 3: Simulation setups.