# Energy-Efficient Resource Allocation for Downlink Non-Orthogonal Multiple Access Systems
## 4 Simulation Results  
In this section, we use MATLAB to simulate the performance of the above power distribution strategy. We assume that the channel states are known and the channels are independently uniformly distributed Rayleigh fading channels. The radius of the cell is 500 m. The base station is located in the center of the cell. We set the minimum distance between users, and the base station is 50 m. The bandwidth of the NOMA systems is 5 MHz. The circuit power consumption is \(p_{c}=27\) dBm. For the MPSO algorithm, we set the population size of \(K=100\) particles. The specific simulation parameters can be detailed in Table 1.  
To further evaluate the system performance of our proposed scheme (SSA-MPSO), we compare it with a scheme using the combination of the subchannel allocation algorithm in [34] and the power allocation algorithm proposed in this paper (SOMSA-MPSO), as well as a scheme combining our proposed subchannel allocation algorithm and the fractional transmission power allocation [37] (SSA-EPA-FTPA), a method combining the random matching algorithm and the the fractional transmission power allocation (Random-EPA-FTPA), and an OFDMA-based scheme. In addition, when allocating power, the FTPA algorithm must vary the power allocation factor to adjust the given power for each user, considering the different channel conditions. When the power allocation factor is zero, all users on the subchannel will receive equal power. As the power allocation factor increases, users with low channel gain will receive more power. For this reason, a power allocation factor of 0.2 is taken as a reference value for the initial allocation. Figure 3 shows the system's energy efficiency versus the number of iterations. We take the base station's transmit power to be 40 dBm and the number of users to be 20. It can be observed that the energy efficiency of the system keeps increasing with the number of iterations. Although the convergence speed is slower with the improved particle swarm algorithm, the power allocation algorithm based on the enhanced particle swarm algorithm is simple compared to the traditional power allocation algorithm on the one hand. Moreover, the modified PSO algorithm has a higher global search capability due to the differential evolution operation we introduce. For \(P_{tot}=40\) dBm, with a fixed total transmit power of d base stations, we can see in Figure 4 that the system's energy efficiency gradually increases with the increasing number of users. Although the overall trend is the same, the NOMA system with all four resource allocation schemes outperforms the conventional OFDMA system due to the higher diversity gain achieved by NOMA compared to conventional OFDMA. In addition, the modified particle swarm algorithm for inter- and intra-subchannel power allocation schemes is more global than the ETP-FTPA algorithm, resulting in a more energy efficient NOMA system. Further, the performance of the NOMA system using the SSA-MPSO scheme is slightly better than that using the SOMSA-MPSO strategy. This is because the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Maximum number of users & 40 \\ Number of subchannels & 20 \\ System bandwidth & 5 MHz \\ BS maximum transmission power & 40 dBm \\ Cell radius & 500 m \\ Min distance between user and BS & 50 m \\ Circuit power consumption & 27 dBm \\ AWGN power density & \(-174\) dBm/Hz \\ Rayleigh fading coefficient & 1 \\ PSO population size & 100 \\ PSO maximum iterations & 100 \\ Inertia weight & \(\omega_{\max}=0.9\), \(\omega_{\min}=0.4\) \\ Inertia adjustment factor & 0.1 \\ Acceleration coefficient & \(c_{\max}=2.5\), \(c_{\min}=0.5\) \\ Crossover probability & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters for downlink NOMA systems. Figure 3: System energy efficiency versus the number of iterations.