## 5 Simulation Results  
Simulation results and analysis of the proposed RDUR scheme are shown in this section. Simulation parameters are shown in Table 2. \(\mathrm{C}_{1}\) influents the performance of COM-NOMA systems. When \(\mathrm{C}_{1}\) was less than 0.5, there was not enough SU to be selected as UR by USU, especially when USU was near the cell edge. MG users cannot fully cooperate with each other. However, when \(\mathrm{C}_{1}\) increased and approached to 1, the minimal channel gain of SUs who were served by BS \(H_{2,s_{2}}\) became smaller. In multicast technology, reception rates of all SUs were limited by \(H_{2,s_{2}}\). It was more unfair to the SU with good channel condition. Therefore, we set \(\mathrm{C}_{1}=0.6\) in the simulation. In addition, because the radius of ETR was the maxmum of \(\mathrm{E}_{t}\), \(\mathrm{E}_{t}\leq 100\) m. In order to reduce the complexity of simulation, we gave three optional radii of ERSR. Therefore, \(\mathcal{E}=\left\{75\;\mathrm{m},87.5\;\mathrm{m},100\;\mathrm{m}\right\}\). To simplify simulation, it was assumed that two MGs have the same number of users, \(M_{1}=M_{2}\). This paper mainly focuses on the scenario where there is high-density MG users in the cellular. As with COM-NOMA, it was considered as high-density scenario when \(M_{i}\geq 100\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name** & **Value** \\ \hline Coverage Radius of Cellular & 1000 m \\ Radius of Efficient Transmission Range & 100 m \\ System Bandwidth & 10 MHz \\ Transmission Power of BS & 34 dBm \\ Transmission Power of User Terminal & 17 dBm \\ Noise Power Spectrum Density & \(-174\;\mathrm{dBm}/\mathrm{Hz}\) \\ Path Loss Coefficient & 4 \\ Power Allocation Factor \(\alpha_{1}\) & 0.2 \\ Power Allocation Factor \(\alpha_{2}\) & 0.8 \\ The First-stage Coverage Ratio \(\mathrm{C}_{1}\) & 0.6 \\ Optional Radius Set of ERSR \(\mathcal{E}\) & \(\left\{75\;\mathrm{m},87.5\;\mathrm{m},100\;\mathrm{m}\right\}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. In the original UR selection scheme of COM-NOMA, which makes ETR as the ERSR of USU, i.e., \(r_{n}=100\) m, \(\forall n\in[1,N]\), the probability that USU selects multiple URs is shown in Figure 4a. From the simulated results, when the distance from USU to BS was smaller than 500 m, the probability was no less than 50%. It verifies that an efficient UR selection scheme with optional ERSR to reduce UR redundancy was necessary. In Figure 4a,b, the analytical result was calculated from the Poisson distribution of UR in the ERSR. Poisson distribution parameter is \(\lambda_{s}^{A_{n}}(\gamma_{u})\). Analytical probability that USU selects multiple URs is equal to \(1-e^{-\lambda_{s}^{A_{n}}(\gamma_{u})}-\lambda_{s}^{A_{n}}\left(\gamma_{u} \right)e^{-\lambda_{s}^{A_{n}}(\gamma_{u})}\). It matched well with the simulated one. Therefore, when \(\mathcal{E}=\{75\,\text{m},87.5\,\text{m},100\text{ m}\}\), it was reasonable to use the average number of UR of \(u\), \(\lambda_{s}^{A_{n}}\left(\gamma_{u}\right)\), to analyze the total number of UR. In Figure 4b, when \(\gamma_{u}\) is less than 500 m, simulated results are scattered. It was because that the number of USU near BS was small. In addition, the small ERSR leds to less URs. This results in the simulated probability value fluctuates greatly in the Monte Carlo simulation method. From the simulated result, the closer the USU was to BS, the greater the probability was. The probability increases as \(M_{i}\) rises. The reason is as follows. In the first stage of COM-NOMA, path loss determined whether or not MG user can succesfully receive. Therefore, the location of SU presents a trend of gathering towards BS, and the density of SU decreased as distance increased. In the second stage of COM-NOMA, the small path loss ensures that SU within USU's ERSR can provide greater reception SINR than \(\sigma_{0}\) for USU. Therefore, the number of URs, who have been selected by an USU, is mainly decided by the density of SU.