## 4 Simulation Results and Discussion  
This section investigates the downlink NOMA systems' energy efficiency performances with the proposed user clustering and power allocation schemes. In our simulations, we consider a scenario where the user terminals are randomly deployed near a BS. A path loss model is adopted to calculate the channel gain between the BS and users. Using SIC in our simulation scenario, the total system bandwidth of 20 MHz and the maximum transmission power \(P_{B}\) of 46 dBm are evenly divided into 100 frequency resources. In addition, the minimum power difference for SIC \(P_{T}\) and the minimum assignable unit \(\xi\) are respectively set to 10 dBm and \(0.0001\times P_{B}\) in our simulations. To reduce the demodulating complexity of the SIC receiver, the average number of users in each cluster is upper bounded to 2, 3, and 4 by appropriately setting the cluster number \(c\). Specifically, in 2-user NOMA systems where the cluster number \(c\) is set to \(\frac{n}{2}\), each cluster is only allocated with two users. In 3-user and 4-user NOMA systems, the cluster number \(c\) is set to \(\left[\frac{n}{5}\right]\) and \(\left[\frac{n}{4}\right]\), respectively. Note that the constraint of cluster size is a compromise with the current imperfect SIC implementation in practice. Due to the additional system overhead for channel feedback coordination and error propagation, the simultaneous multiple transmissions are infeasible to apply to a large number of users [52]. However, our algorithmic solutions can be adopted to optimize NOMA systems' energy efficiency without this assumption. By applying our user clustering strategy and power allocation algorithms, we collect the energy efficiency performance of 2-user, 3-user, and 4-user NOMA systems and compare them with the customary orthogonal frequency division multiple access (OFDMA) based systems. Figure 3 shows the system's overall energy efficiency versus the number of users between 10 to 60. It can be observed from Figure 3 that the energy-efficient performance with our proposed solutions in 2-user, 3-user, and 4-user increase when the number of users grows, and all of them are much better than the OFDMA scheme. In more detail, the average energy efficiency of 2-user, 3-user, and 4-user NOMA systems at different user numbers are 47%, 49%, and 51% more than the OFDMA scheme. This is because the Lagrangian multiplier-based dynamic programming model can effectively allocate power resources so that the systems can fully use the limited energy to achieve better throughput. To further compare our schemes' performance with conventional OFDMA, simulations for two specific scenarios are conducted. In scenario 1, the number of users deployed near the BS is set to 12. Scenario 2 illustrates a more unpleasant situation. In this simulation scenario, there are also 12 user terminals randomly deployed with a BS. However, half of the users are intended to be set away from the BS to make their channel gains extremely low. To meet the QoS requirements of these users, higher transmission power is needed. Figure 4 shows the system energy efficiency performance versus maximum transmission power of BS between 29 dBm to 46 dBm while other simulation parameters are the same as Table 1. The energy efficiency is expressed as 0 in the case that not all constraints are met. As another benchmark, MaxSE denotes the optimal solution's energy efficiency to maximize spectrum efficiency, which has obtained a lot of attention in the previous work. We can find from Figure 4 that NOMA systems will achieve low energy efficiency at a meager system power budget. However, the OFDMA scheme can not work under the circumstances. After the power budget reaches a certain level, the NOMA systems with our solutions can always outperform the OFDMA scheme significantly.