# Performance Analysis of Ambient Backscatter NOMA Systems
## 5 Numerical Results  
In this section, the numerical simulation results verify the accuracy of the above expressions. The simulation results were analyzed, to determine the outage performance of the AmBC-NOMA systems. The number of Monte Carlo repeated was set to \(10^{6}\) iterations. The particular simulation settings are set in Table 1[31; 37], where BPCU denotes the abbreviation for bit per channel use. The fading channel parameters were as follows: \(\lambda_{h1}=5\), \(\lambda_{h2}=8\); \(\lambda_{h3}=10\), \(\lambda_{g1}=3\), \(\lambda_{g2}=4\); \(\lambda_{g3}=5\); \(\lambda_{f}=5\). The parameters in EE were set as follows: \(P_{S}\)= 5 dB, \(P_{ULE,d}\) = 10 dBm; \(P_{BS}(d)\) = 10 dBw; and \(P_{BD}\) = 10 dBm[38]. In addition, the AmBC-OMA systems were examined for this paper, as a comparative benchmark. Figure 2 shows the OP versus the transmitting SNR for three users and the BD, with \(R_{1}\) = 0.4, \(R_{2}\) = 0.5, \(R_{3}\) = 0.6, \(R_{BD}\) = 0.009 BPCU, and \(\beta=0.17\). The OP curves for users in the case of pSIC in the AmBC-NOMA systems were plotted according to (10). The theoretical analysis of the OP is in good accord with the numerical simulation, thus verifying the correctness of the OP expressions in the AmBC-NOMA systems. The asymptotic OP curves of the user were plotted by (18). It can be seen that the asymptotic curves are close to the exact curves of the OP in the high SNR regime. As the transmitting SNR rises, the OP of the user with pSIC gradually converges to an error floor, due to the user suffering hardware impairments and backscatter links in decoding their signals. This is because, as the SNR increases, the received SNR decreases, and decoding becomes difficult for the user. The results listed above support the analysis in Remark 3. As demonstrated in this figure, the farthest user (\(d=1\)) had lower OP compared to the nearest user (\(D=3\)), which can be explained by the property that NOMA achieves user fairness (i.e., the farthest user is allocated a higher power allocation factor). The OP curve of the BD in the case of pSIC was plotted according to (15). The figure demonstrates the agreement between the analytical results and the numerical simulations. Furthermore, the asymptotic analysis curve for the BD was plotted by (21). The OP curve of the AmBC-OMA systems was based on (12), and the curve in the figure is consistent with the simulation results. It is indicated that the outage behavior of AmBC-NOMA systems is better than that of AmBC-OMA systems. Additionally, the OP for both the users and the BD increased with the hardware damage. \begin{table}
\begin{tabular}{l l} \hline \hline Monte Carlo simulation of repeated values & \(10^{6}\) iterations \\ \hline  & \(a_{1}=0.7\) \\ Power distribution factor & \(a_{2}=0.2\) \\  & \(a_{3}=0.1\) \\ \hline reflection coefficient & \(\beta=0.17\) \\ \hline RHIs parameter & \(\kappa_{sd}^{2}=\kappa_{\mu}^{2}=0.03\) \\ \hline Gaussian white noise power & \(N_{0}=-5\) dB \\ \hline ipSIC parameter & \(\varpi=1\) \\ \hline  & \(R_{1}=0.4\) BPCU \\ Threshold data rates & \(R_{2}=0.5\) BPCU \\  & \(R_{3}=0.6\) BPCU \\  & \(R_{BD}=0.009\) BPCU \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The Simulation Parameters. Figure 3 plots the OP for three users and the BD versus the transmitting SNR for different residual interference, with \(R_{1}=0.4\), \(R_{2}=0.5\), \(R_{3}=0.6\), \(R_{BD}=0.009\) BPCU, \(\beta=0.17\) and \(\varpi=1\). The OP curves and asymptotic OP curves for users under the pSIC scheme were plotted according to (9) and (17), respectively. By the nature of SIC technology, the user with the stronger signal was decoded first, so that the user (\(d=1\)) did not need to perform SIC operations. We observed that the NOMA systems with ipSIC achieved better outage behavior than the AmBC-OMA systems [38]. This may mean that AmBC-NOMA can achieve better multi-user user fairness than AmBC-OMA. Unlike the already existing work on backscatter [43], we further analyzed the performance of AmBC-NOMA systems.