# Intelligent Reflecting Surface Aided Wireless Systems with Imperfect Hardware
## 5 Numerical Results and Discussions  
In this section, we present and discuss some results from the mathematical expressions derived in the paper. We set \(\chi=2\), \(\gamma_{th}=5\) dB, \(\mu_{T}=\mu_{R}=1.05\), \(v_{T}=v_{R}=25^{\circ}\), \(d_{1}=5\) m, and \(d_{2}=5\) m.  
In Figure 4, we depict outage performance of RIS-aided system, which benefits from dual-hop transmission. When \(\rho_{S}\) increases, SNR can be enhanced, then outage performance can be improved as well. In this RIS-DH scheme, a higher number of meta-surface \(N\) leads to significant improvement in terms of outage probability. It can be observed that the simulated curves match very tightly with the analytical curves, which confirms the validity of derived expressions. We also compare the outage performance between the NCCS and the \(K_{G}\) distributions, which shows that the \(K_{G}\) distribution exhibits better performance. Under the impact of IQI, we can see a slight reduction in outage probability for such an RIS-DH scheme. It is a valid result when we see clearly that asymptotic lines are matched with exact curves at high SNR at the source. It means that IQI reduces the system performance. However, at high SNR regime, system performance still looks good enough to guarantee that such forms of transmission better serve mobile users. In Figure 5, we illustrate the curves for the outage probability for the RIS-T case. We consider two cases: \(N=2\) and \(N=5\). By varying the number of meta-surface \(N\), a big gap emerges, which confirms the important role of RIS to achieve improvements in such an RIS-T scheme. It is a very valuable result since we observed that the analytical results are highly consistent with the Monte-Carlo based simulation. As observed in Figure 6, the SNR threshold \(\gamma_{th}\) has the main role to limit performance as expected. In this case, the simulation results are also consi  
Figure 4: The outage probability vs. \(\rho_{S}\) (dB) with varying \(N\) for RIS-DH case. Figure 5: The outage probability vs. \(\rho_{S}\) (dB) with varying \(N\) for RIS-T case. results. Similar observations can be seen in Figure 7. Although higher SNRs at source \(\rho_{S}\) contribute to increasing outage performance, it depends on other parameters. From the results reported in Figure 7, one can observe that the slope of the NCCS distribution curves approach saturation regardless of the value of \(\rho_{S}\). The threshold rate holds crucial impact on the system performance. Therefore, depending on the demand of service at users, the system should balance the quality targeted to each user regardless of the impact of IQI. Next, Figure 8 is conceived for the RIS-DH case, we show the ergodic capacity performance versus transmit SNR at the access point. We can see that ergodic capacity can be improved once transmit SNR is higher at the access point. This can be explained by the fact that the formulation of ergodic rate in all scenarios of channel distributions depends on SNR at the destination, which relies on SNR at the source. However, at high SNR regime, the ergodic capacity shows its saturation threshold except for the \(K_{G}\) channel distribution and ideal IQI. It can be observed that it becomes prominent when considering gaps between \(K_{G}\) channel distribution of ideal IQI and other cases when transmit SNR at the access point is greater than 25. This trend of the figure confirms the crucial impact of IQI on the ergodic capacity that occurs at high SNR regimes. Similar observations can be achieved in the RIS-T case, as shown in Figure 9. We show the ergodic capacity of the considered system corresponding to two values of meta-surface, i.e., \(N=2\) and \(N=5\). The most significant difference is a gap between ideal and IQI systems occurring in a entire range of transmit SNR. If we focus on the specific point of SNR 10 dB, the influence of IQI is too significant, and it leads to saturation lines for ergodic capacity regardless of the modification of the number of meta-surface in RIS.