# Backscatter Assisted NOMA-PLNC Based Wireless Networks
## 6 Numerical Results  
In this section, sum capacity maximization of the downlink NOMA with ambient backscattering is presented. Furthermore, to enhance the throughput and reliability of each wireless link, outage and BER performance of the proposed wireless network is analyzed in uplink, downlink and then end-to-end level. Simulation parameters are given in Table 2.  
Sum capacity of the downlink NOMA with ABS is shown in Figure 3a. Sum-rate of the proposed wireless network is maximized through the optimal power allocation. Simulation parameters are reflection coefficient \(\beta=0.8\), stopping criterion's \(\epsilon_{1}=\) given SNR and \(\epsilon_{2}=0.01\). It is assumed that the interference from ABS is zero. From this figure, it is clear that the sum capacity of the downlink NOMA with ABS is better than the downlink OMA. At 4 dB SNR, the sum capacity of the proposed network is 4 b/s/Hz whereas the wireless network with OMA achieves 2 b/s/Hz. Therefore, data rate of the proposed network is highly improved when compared to OMA network. Sum capacity of the proposed wireless network is shown in Figure 3b for various reflection coefficient. It is observed that sum capacity of the proposed network is improved when the reflection coefficient is increases. At 6 dB SNR, sum capacity of the proposed network is 3 b/s/Hz at reflection coefficient of 0.2 whereas 4 b/s/Hz is achieved at reflection coefficient of 0.5. The outage probability of the proposed wireless network with ABS is shown in Figure 4a. The channel variances are chosen as \(\eta_{n_{1}}=d_{1}^{-\kappa}\) and \(\eta_{f_{1}}=d_{3}^{-\kappa}\)[18]. Without loss of generality, 2/3 times of the transmit power is allocated to the far node and the rest of the power is allocated to the near node. The threshold data rate \(R=1\) is considered. It is observed that the outage of the far node is highly reduced when the proposed network is operating with ABS. At target outage of \(10^{-2}\), the downlink NOMA with ABS is require 13 dB SNR, whereas the downlink NOMA without ABS need around 25 dB SNR, thus 12 dB gain is achieved in proposed network using ABS. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**S.No.** & **Parameters** & **Symbols** & **Value** \\ \hline
1. & No of nodes & \(N\) & 4 \\ \hline
2. & Distance between the near node 1 and the AP & \(d_{1}\) & 2 m \\ \hline
3. & Distance between the far node 1 and the AP & \(d_{3}\) & 10 m \\ \hline
4. & Path loss exponent & \(\alpha\) & 2 \\ \hline
5. & Reflection coefficient & \(\beta\) & 0.8 \\ \hline
6. & Threshold data rates & \(R\) & 0.5, 1, 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation Parameters. Figure 3: (a) Sum capacity of the downlink NOMA with ABS is compared with downlink OMA. (b) Sum capacity of the downlink NOMA with various reflection coefficients. Outage probability of the proposed network is compared with OMA network in Figure 4b. Data rate is varied from 0.5 to 1. At target outage of \(10^{-2}\), proposed network need 30 dB SNR whereas network with OMA need 35 dB SNR. It is noted that when increase the data rate, outage of the wireless network is increased. The outage performance of the proposed wireless network in uplink OMAC level is shown in Figure 5a. Similarly, the outage performance of the proposed wireless network in downlink NOMA level is shown in Figure 5b. It is observed that the outage performance of the downlink network is better than the uplink network this is because of the better downlink temporal efficiency. At target outage of \(10^{-2}\), proposed uplink network need 25 dB SNR whereas downlink network need 22 dB SNR. Thus, downlink has 3 dB SNR gain than the uplink network. Figure 6a shows the average BER performance of the proposed wireless network. BPSK modulation is considered in this simulation. Power allocation for the near node and the far node is splitted as 2/3 and 1/3 times of the total transmit power. Simulation results are used to validate the analytical results.