# I/Q Imbalance and Imperfect SIC on Two-Way Relay NOMA Systems
## 4 Numerical Examples and Discussions  
In this section, we provide numerical illustration of our analytical results through Monte Carlo simulations. Unless otherwise specified, the main parameter values used in all our evaluations are provided in Table 2.  
Figure 2 plots the outage probabilities of two users versus transmit SNR with different conditions. The analytical curves for the outage probabilities of the IQI and ipSIC are plotted using (22) and (23). An excellent agreement can be observed between the analytical results and Monte Carlo simulations. We considered five conditions in this simulation: (1) IQI and ipSIC; (2) ONLY ipSIC; (3) NO-IQI and pSIC; (4) OMA; (5) Rayleigh fading channels. In addition, the asymptotic outage probability curves are plotted in accordance using (24) and (25). It is noticed from Figure 2 that the error floors exist for both \(D_{1}\) and \(D_{2}\). The reason is that the IS result in zero diversity order. The outage performance of the system with IQI is worse than that of the system without IQI, which means that IQI has deleterious effects on the system outage performance. Moreover, the outage performance of \(D_{2}\) with ipSIC is worse than that of the system with pSIC, due to the residual interference caused by ipSIC. It can be seen that the outage performances of \(D_{1}\) and \(D_{2}\) for OMA are lower than NOMA. It is also interesting to note that the outage probability of \(D_{1}\) with ipSIC or with pSIC has the same curves. This is due to the fact that the SIC method is not used in the decoding of the signal of \(D_{1}\), which is proven by (22). Therefore, the outage performance of the Rayleigh condition is better than the Rician in \(D_{1}\), and it is worse than the Rician condition in \(D_{2}\). Figure 3 plots the outage probabilities of the two users versus the parameter of ipSIC for the system with IQI and ideal conditions. It is clearly seen that the outage performance of \(D_{2}\) becomes worse with the increase of ipSIC parameter. This is because the residual interference caused by ipSIC is harmful to the outage performance of \(D_{2}\). In addition, the parameter of ipSIC has no effect on the outage probability of \(D_{1}\), which is proven by (22). Finally, the outage performances for both \(D_{1}\) and \begin{table}
\begin{tabular}{l l} \hline \hline
**Monte Carlo Simulations Repeated** & **10\({}^{5}\) Iterations** \\ \hline Power allocation coefficients of NOMA & \(a_{1}=0.7\), \(a_{2}=0.3\), \(b_{1}=0.8\) and \(b_{2}=0.2\) \\ Targeted data rates & \(R_{1}=0.2 BPCU\), \(R_{2}=0.3 BPCU\) \\ The distance between \(R\) and \(D_{1}\) or \(D_{2}\) & \(d_{1}=0.5\), \(d_{2}=1\) \\ Noise power & \(N_{0}=1\) \\ The parameters of ipSIC & \(\varepsilon=0.03\) \\ Ideal RF front end & \(g_{t}=g_{r}=1\), \(\varphi_{t}=\varphi_{r}=0^{\circ}\) \\ The parameters of IQI & \(g_{t}=g_{r}=0.8\), \(\varphi_{t}=\varphi_{r}=5^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Table of parameters used for numerical results. Figure 2: Outage probability versus the transmit SNR of the proposed TWR C-NOMA system for \(D_{1}\) and \(D_{2}\) with data rate thresholds \(\bar{R}_{1}=0.2 BPCU\) and \(\bar{R}_{2}=0.3 BPCU\). \(D_{2}\) with IQI are worse than that obtained without IQI condition. All in all, IQI reduces the system outage performance. In Figure 4, we show the outage probabilities of \(D_{1}\) and \(D_{2}\) with ipSIC under the different levels of phase mismatch. The outage performances of \(D_{1}\) and \(D_{2}\) deteriorate with the increase of the value of phase mismatch. The greater the gap between the value of the phase mismatch and zero degrees, the greater the adverse effect of the phase mismatch on outage performance. Figure 5 plots the outage probabilities of the two users with respect to the amplitude mismatch with ipSIC and pSIC conditions. It is clearly seen that the closer the amplitude mismatch parameter is to one, the better the outage performance of \(D_{1}\) and \(D_{2}\) becomes.