# Energy-Efficient Resource Allocation for Downlink Non-Orthogonal Multiple Access Systems
## 4 Simulation Results
subchannel allocation algorithm proposed in this paper ensures that the subchannels are not matched to users with poor channel gain and that the channel gain of the paired users is as high as possible, which can help to increase the system rate. We took 10 users randomly distributed in the cell. Figure 5 shows the system energy efficiency trend as the base station's total transmission power increases. We can clearly see that the system energy efficiency increases in the early stage as the power of the base station increases. However, the system energy efficiency is most excellent when the base station's total transmission reaches 33 dBm. After that, even if the transmitting power of the base station is increased, the system's energy efficiency no longer grows and tends to decrease gradually. This is because the total transmission power of the base station puts a significant constraint on the system's energy efficiency at the beginning. Still, the base station consumes more power as the available power increases. This phenomenon shows that increasing the available power does not guarantee an increase in system energy efficiency; on the contrary, it may lead to a waste of resources. To assess the fairness of our proposed SSA-MPSO scheme and other NOMA schemes and OFDMA allocation among users, we introduce [PERSON]'s fairness index F from [38] to characterize the fairness per pair of users. \[\text{F}=\frac{\left(\sum_{n=1}^{N}R_{n}\right)^{2}}{N\sum_{n=1}^{N}R_{n}^{2}} \tag{25}\]  
In Figure 6, we first observe that the system's fairness becomes progressively smaller as the number of users increases, both with the NOMA system scheme and OFDMA. In particular, due to subchannels being assigned to only one user, OFDMA-based systems lose access to many subchannels. Therefore, all NOMA system solutions are higher than OFDMA solutions. In addition, the SOMSA-MPSO scheme selects the user with the best channel conditions at each step of the sub-channel matching process. It ensures that the user with the best channel gain matches the subchannel. However, users in the later matching order tend to lose the right to choose, which may result in the combination of the user with the worst channel gain and the subchannel. On the other hand, our proposed  
Figure 4: Energy efficiency versus the number of users. subchannel assignment algorithm avoids matching the worst subchannel to a user with low channel gain. Figure 7 shows the probability of interruption versus SNR for a user count of 36. It is known that the lower the interruption probability, the better the system performance. From Figure 7, we can observe that the outage probability of applying our proposed sub-channel assignment algorithm is better than that of the random matching algorithm and OFDMA. This is because, when matching subchannels to users, we prioritize the worst subchannel to avoid reaching the worst subchannel to a user with low channel gain and check the user with high channel gain on the current subchannel. This operation helps to increase the data rate of the paired users. In addition, by looking at Figure 8, we can see that our  
Figure 5: Energy efficiency versus maximum transmission power of BS. Figure 6: The fairness index versus SNR. proposed SSA-MPSO scheme has the best BER performance. The BER performance of the Random-EPA-FTPA scheme is slightly better than that of the OFDMA but much worse than the BER performance of our proposed method. This is because the Random-EPA-FTPA scheme may result in some users with close channel gains being assigned to the same subchannel. This will make it more difficult for the receiver to decode. Figure 9 illustrates the decreasing energy efficiency of the system as the user minimum data rate gradually increases, regardless of the resource allocation scheme adopted. In particular, we can see that our proposed SSA-MPSO scheme achieves a higher energy efficiency compared to Random-EPA-FTPA, SOMSA-MPSO, and SSA-EPA-FTPA.