## 4 Numerical Results and Discussion
However, we may observe that the OP performance at relay \(R_{2}\) and devices in even transmission blocks (Figure 4) achieved better results than OP performance at relay \(R_{1}\) and devices in odd transmission blocks (Figure 3). The analysis results of OP performance for relay \(R_{2}\) are given by (30) or (34) and for devices \(D_{n}\) by (36) or (38), where \(\mathcal{R}=R_{2}\) and \(\theta=even\). The analysis results were verified with Monte Carlo simulations for relay \(R_{2}\) given by (31) or (35) and for devices by (37) or (39), where \(\mathcal{R}=R_{2}\) and \(\theta=even\). We may observe that the OP performances at relay \(R_{2}\) and devices in even transmission blocks outperform those at relay \(R_{1}\) and devices in odd transmission blocks at high SNRs such as \(\rho_{S}=\rho_{\mathcal{R}}=20\) dB. The present study thus exploits the advantages of a massive MIMO-NOMA network compared to a MIMO-NOMA network. We equipped a greater number of antennas on relay \(R_{2}\) (\(A_{1}=16\)) than on relay \(R_{1}\) (\(A_{1}=4\)). As a result, we obtained the respective pre-coding channel matrix sizes of \([4\times 16]\) and \([16\times 2]\) for \(\mathbf{G}_{0}\) and \(\mathbf{G}_{n}\), which, in the even transmission blocks, were much larger than the pre-coding channel matrix sizes of \([4\times 4]\) and \([4\times 2]\) for \(\mathbf{H}_{0}\) and \(\mathbf{H}_{n}\) in odd transmission blocks. From Expressions (8), (9), (14), (15), (21), (22), (27), and (28) and by applying the TAS protocol, only the best channels from the pre-coding channel matrices are selected for data \begin{table}
\begin{tabular}{l l l} \hline \hline
**Variables** & **Values** & **Units** \\ \hline N & 3 & \\ \(d_{R_{1}}=d_{R_{2}}\) & \(10\) & metres \\ \(d_{1}=v_{1}\) & 5 & metres \\ \(d_{2}=v_{2}\) & 7 & metres \\ \(d_{3}=v_{3}\) & 10 & metres \\ \(a_{1}\) & 0.1667 & \\ \(a_{2}\) & 0.3333 & \\ \(a_{3}\) & 0.5 & \\ \(\omega\) & 4 & \\ \(\sigma_{\mathcal{R}_{1}}^{2}=\sigma_{R_{2}}^{2}\) & \(1\times 10^{-4}\) & \\ \(\sigma_{1}^{2}\) & \(16\times 10^{-4}\) & \\ \(\sigma_{2}^{2}\) & \(4.1649\times 10^{-4}\) & \\ \(\sigma_{3}^{2}\) & \(1\times 10^{-4}\) & \\ \(R_{1}^{2}=R_{2}^{*}=R_{3}^{*}\) & \(0.1\) & bps/Hz \\ \(\rho_{S}=\rho_{R_{1}}=\rho_{R_{2}}\) & \(\{0,\ldots,30\}\) & dB \\ \(\eta\) & 1 & \\ \(A_{0}\) & 4 & \\ \(A_{2}\) & 2 & \\ \hline \multicolumn{3}{c}{Odd transmission block} \\ \(A_{1}\) & 4 & \\ \(\lambda\) & 0.4 & \\ \hline \multicolumn{3}{c}{Even transmission block} \\ \(A_{1}\) & 16 & \\ \(\lambda\) & 0.6 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table of parameters. decoding. Therefore, the relay \(R_{2}\) and devices in even transmission blocks have better OP performance than relay \(R_{1}\) and devices in odd transmission blocks under the same simulation parameters. Figure 4: OP at relay \(R_{2}\) and devices \(D_{n}\) for \(n=\{1,\ldots,N\}\) in an even transmission block, where the number of antennas equipped at the BS, relay \(R_{2}\) and devices \(D_{n}\) are \(A_{0}=4\), \(A_{1}=16\), and \(A_{2}=2\), respectively, and the PS factor \(\lambda=0.6\). Figure 3: OP at relay \(R_{1}\) and devices \(D_{n}\) for \(n=\{1,\ldots,N\}\) in an odd transmission block, where the number of antennas equipped at the BS, relay \(R_{1}\) and devices \(D_{n}\) are \(A_{0}=4\), \(A_{1}=4\), and \(A_{2}=2\), respectively, and the PS factor \(\lambda=0.4\). Figures 5 and 6 plot the system throughput performance at devices in odd and even transmission blocks, respectively. Even though device \(D_{3}\) has the farthest distance from coupled relays (\(d_{3}=v_{3}=10\) m), device \(D_{3}\) always achieved the best throughput performance compared to other devices. It is interesting that the system throughput results of relay \(R_{1}\) and devices in odd transmission blocks (Figure 5) are similar to the system throughput results of relay \(R_{2}\) and devices in even transmission blocks (Figure 6) at the same SNR. To illustrate, we extract the investigated results from Matlab software.