# Power Allocation and User Grouping for NOMA Downlink Systems
## 4 Numerical Results  
In this section, we evaluate the performance of the proposed resource allocation algorithms through simulation. We use MATLAB (R2017a) to simulate the performance of FTPA and FPA. Furthermore, the simulation environment of the DL algorithm is as follows: Python 3.5 with TensorFlow 1.15.0 an a NVIDIA GeForce GTX 960M. In the simulations, we consider a situation in which the users are uniformly distributed in a circle range with a radius of 500 m. We set the minimum distance from the users to the BS as 50 m. It is supposed that the instantaneous CSI of each user can be obtained. The methods introduced in this paper have been simulated in this section. Table 1 shows the system parameters [1,13,18]. Figure 4 shows the sum rate for two user grouping schemes. When the total power changes from 50 mW to 55 mW, we compare our method with the maximum channel gain difference method [9]. We assume that 12 users are randomly and evenly distributed in a cell. We want to reduce the complexity of the power allocation algorithm; thus, equal power allocation is adopted among subcarriers. In other words, the total transmit power is equally distributed to each subcarrier. The users within the subcarriers adopt the FTPA algorithm. We can see that the sum rate of the system increases with the increase in transmit power. Compared with the method in [9], the improved user grouping method in this paper avoids users with similar channel gain in a group and slightly improves the sum rate. Figure 5 shows the sum rate comparison of different power allocation methods among subcarriers. They are the deep learning power allocation (DLPA) method proposed in this paper, water-filling power allocation (WFPA) [27], FTPA, and FPA. We assume that there are 20 users and 10 subcarriers. The total power ranges from 5 W to 10 W. With the increase in transmit power, the sum rate obtained by the three methods is improved. We can see that the WFPA method is better than the other methods in the sum rate. However, WFPA may allocate the power of subcarriers with particularly poor channel conditions as zero. The sum rate of DLPA is about 2.2% higher than that of FTPA and about 19% higher than that of FPA. The reason is that DLPA maximizes the sum rate according to the channel gain. Although FTPA considers the channel gain, it only allocates more power to users with lower channel gain and less power to users with higher channel gain. The FPA algorithm does not take into account the influence of channel conditions and allocates power according to a fixed allocation factor, so this method has the worst performance. Figure 6 illustrates the sum rate obtained by the four methods with different numbers of users. The total power is 10 W and the number of users ranges from 20 to 40. As we can see, the DLPA algorithm is still better than FTPA and FPA. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Cell Radius/m & 500 \\ Minimum Distance from User to BS/m & 50 \\ Overall System Bandwidth/MHz & 10 \\ Noise Power Spectral Density/(dBm/Hz) & \(-\)174 \\ Path Loss/dB & 128.1 + 37.6 log(d) \\ Fading Model & Rayleigh Fading \\ Minimum Rate/Mbps & 1 \\ FTPA Factor & 0.7 \\ FPA Factor & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System Parameters  
Figure 4: System sum rate comparison of two user grouping methods. The DLPA algorithm is used among subcarriers and CFE of power allocation is used between multiplexed users. We call this power allocation method DLPA-CFE. Similarly, DLPA is used among subcarriers and FTPA is used between multiplexed users. We call it DLPA-FTPA. FTPA-CFE is the power allocation method that uses FTPA among subcarriers and CFE between multiplexed users. FTPA is used among subcarriers and multiplexed users, which we call FTPA-FTPA. Figure 7 shows the sum rate comparison of different power allocation algorithms. We used the method proposed in Section 3.1 to implement user grouping.