# Hybrid Active-Passive Reconfigurable Intelligent Surface for Cooperative Transmission Systems
## 4 Simulation Results  
In the following section, we validate the derived formulas for mathematics utilizing Monte Carlo simulations and compare the outage probabilities of the three RIS systems. The system parameters are configured as follows: \(P_{S}=P_{RIS}=[-5,7]\) dBm, where \(P_{S}\) and \(P_{RIS}\) are the transmitting power and the total power of HAPR, respectively. The noise generated by the active RE is \(\sigma_{R}^{2}=0.01\). The receiving noise is \(\sigma_{D}^{2}=1\). The outage threshold is \(\gamma_{th}=20\) dB.  
Firstly, we examine how the quantity of REs affects the passive RIS's OP. For various values of \(N\), the OP curves of the passive RIS-assisted system are displayed, as shown in Figure 2. It can be seen that the OP is smaller as \(P_{S}\) increases, and the increase in \(N\) can also significantly reduce the OP and improve the system performance, a conclusion that is in perfect agreement with the theoretical values we have derived.  
In Figure 3, we present the OP curves of the active RIS-assisted system under different \(N\), It can be seen that the factors affecting the OP of the system are similar to those of the passive RIS-assisted system, in that the OP is reduced by increasing \(P_{S}\) and \(N\).  
In Figure 4, the OPs of the HAPR system are compared for \(N=5,10,20\). The results indicate that as \(P_{S}\) and the quantity of REs rise, the OPs of the HAPR system continue to fall. Furthermore, we compare Figure 2, Figure 3, and Figure 4, which clearly reveal that HAPR requires a lower number of REs than A-RIS and P-RIS to achieve the same target OP value. This proves that HAPR requires a small physical size to achieve the desired communication target, which is advantageous in space-constrained situations. Compared with traditional RISs, HAPR has a wider range of application scenarios.  
Figure 3: OP versus \(P_{S}\) for A\(-\)RIS with a different number of \(N\).  
Figure 2: OP versus \(P_{S}\) for P\(-\)RIS with different numbers of \(N\).  
In Figure 5, we compare the OP curves of the three RISs when \(N=5\) and \(P_{\rm S}=[-4,4]\) dBm. As the OP curves of the three RISs at \(N=10\) and \(N=20\) follow the same trend as at \(N=5\), except that the OPs are smaller, we only provide the simulations at \(N=5\) here for the sake of overall aesthetics. Comparing these three curves, we find that the OP of the HAPR system is always lower than that of the A-RIS system and the P-RIS system, regardless of the value of \(P_{\rm S}\). We also know from the figure that HAPR requires less \(P_{\rm S}\) than the two RISs to achieve the same OP, which means that the transmitter consumes less power and reduces the power consumption of the system, making it more energy efficient. Meanwhile, we also find an attractive phenomenon that the OP curves of A-RIS and P-RIS intersect near \(P_{\rm S}=-1.802\) dBm. In other words, when \(P_{\rm S}\) is small, the OP of P-RIS is lower than that of A-RIS, in which case a better communication performance can be obtained by using P-RIS; however, when \(P_{\rm S}\) increases to greater than \(-1.802\) dBm, it is more sensible to use A-RIS to assist in signal transmission. This is because the array gain of the P-RIS is \(N^{2}\), while the gain of the active RIS is less than \(N^{2}\), so the SNR of the P-RIS is greater than that of the A-RIS when \(P_{\rm S}\) is small. As \(P_{\rm S}\) increases, A-RIS has enough power to amplify the signal, and this improves the gain, at which point A-RIS performs significantly better than P-RIS.  
Figure 4: OP versus \(P_{\rm S}\) for HAPR with different number of \(N\).