## 5 Simulation Results
### Performance of RDUR Scheme  
In RDUR, the probability that each optional radius of ERSR \(E_{t}\) is allocated to AA is illustrated in Figure 6 (In Figure 6, only the case when \(M_{i}=130\) is displayed. Those cases when \(M_{i}\) is equal to other values were similar to that when \(M_{i}=130\), so they were not shown in this paper.). When the circular area covered by BS was divided into four AAs, in order from cell center to cell edge, four AAs are \(A_{1}\)  
Figure 5: UR selection ratio and coverage ratio for RDUR scheme in different \(\theta\). (**a**): UR selection ratio versus the number of users in MG. (**b**): The second-stage coverage ratio versus the number of users in MG.  
\(A_{2}\), \(A_{3}\), \(A_{4}\) and shown on the horizontal axis. Across 2000 Monte Carlo runs, it was found that a small radius of ERSR, \(E_{t}=75\) m, was allocated to the AA nearest to the BS, \(A_{1}\), with the most probability 84%. A large radius of ERSR, \(E_{t}=100\) m, was most likely to be allocated to the cell-edge AA, \(A_{4}\). The probability reached to 83%. It increased as the distance from BS increased. As expected, to reduce unnecessary UR, after RDUR, small ERSR should be allocated to the AA with high density of SU. To ensure that USU can select more URs and had more chances to receive successfully, large ERSR was allocated to the AA with low density of SU. Because the proposed RDUR was an enhanced relay selection scheme aiming at NOMA-based cooperative multicast system, and the other UR selection schemes working for OFDMA-based cooperative multicast system do not make the ETR of user's device as a restriction, which results in that no matter how far the SU is from the USU, it can be selected as UR. We compared RDUR with the original UR selection scheme of COM-NOMA systems and two other UR selection schemes in Figures 7 and 8. The UR selection scheme proposed in [4] made all SUs as URs to forward data for USUs. In the try-best UR selection scheme [5], the nearest SU to each USU was selected as UR. In these two schemes, the ETR of user's device was not taken into consideration. But it indeed impacted the performance of system. Therefore, for fairness, in the simulation, the same as RDUR scheme and original scheme of COM-NOMA systems, ETR was also a restriction for these two schemes. We made the second stage as the focus of performance simulations. Because \(C_{1}\) was a fixed value, after the first stage there are \(C_{1}(M_{1}+M_{2})\) SUs. The total number of successful users was decided by UR selection scheme in the second stage. The comparison of coverage efficiency was conducted in Figure 7.  
In comparison to the original scheme of COM-NOMA systems, via RDUR scheme, the coverage efficiency increased by at least about 14% under the same \(C_{1}\). This is because USU selects URs with changeable ERSR. When the density of SU near the BS was large, the appropriate radius of ERSR was selected from \(\mathcal{E}\) unlike the original UR selection scheme in COM-NOMA. In COM-NOMA, those SUs within the ETR were selected as URs. The area of relay selection was smaller in RDUR than that in COM-NOMA. Some SUs who were URs in COM-NOMA were not selected in RDUR. The number of URs reduced. In comparision to the try-best scheme, when \(C_{1}=0.6\), the coverage efficiency enhances. However, when \(C_{1}=0.7,0.8\), the coverage efficiency gap between the two schemes is small. This was because when \(C_{1}\) became larger, the distance between SU and USU decreased relatively, and the nearest SU to USU was also within his/her ERSR. Hence, via these two schemes, there was little difference in the number of URs or the number of USUs that can be successfully received. All of the SUs were selected as UEs in the scheme proposed in [4], the advantage of RDUR was obvious. For the RDUR scheme, the coverage efficiency decreases with the increase of \(C_{1}\). The reason is that when \(M_{i}\) is not large enough, large \(C_{1}\) means a small number of USU and high density of SU.