# Adaptive Clustering of Users in Power Domain NOMA
## 6 Results and Discussions
### The Experiment  
Initially, a network cell contains ten users served by a BS. Subsequently, new users join the cell, one at a time, totaling 12 users, a typical amount found in similar experiments in the literature and 3 GPP [34]. In a period of \(T\) seconds, the cell's input queue is checked to cluster new users and update who has experienced a significant change in channel gain. In this same period, a request for the final clusters is performed, the power coefficients are defined, and the throughput of each cluster is calculated as shown in Figure 6.  
From Figure 6a-e, an improvement in the spectral efficiency of the system can be observed since the system maintained a high global data rate even with the entry of new users into the cell and with the variation of the users' gain. It is also possible to notice, in Figure 6a-c, that the algorithm can create and delete clusters over time according to the evolution of the input data--that is, the channel gain values of the users. This is due to the cluster maintenance step present in the proposed algorithm, which is not possible in the methods found in the literature, as a fixed number of clusters is necessarily predefined. A particular case occurs in Figure 6b. It is possible to notice that only ten of the twelve users are grouped. This happened because the two users did not satisfy the SIC constraint (Equation (8)) when being added to existing clusters, and a new one was not formed due to the similarity of their channel gains at that instant of time. However, note that, in Figure 6c, users who were outside groups were grouped in the following period due to evolving channel gain values. From Tables 4 and 5, we can analyze the average data rate over time by the number of users in the cluster and, thus, have a better idea of the impact of the channel gain changes over time. In Table 4, the users have channel gains that vary slowly with time, and this behavior allows the formation of clusters with three users, which does not occur in Table 5 when the variation is faster due to the increase in the maximum Doppler frequency shift. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Carrier frequency (\(f_{c}\)) & 2.0 GHz \\ Doppler frequency (\(f_{d}\)) & 80 Hz \\ Base station antenna effective height (\(h_{t}\)) & 30 m \\ Mobile station antenna effective height (\(h_{r}\)) & 1.5 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used to generate channel gain coefficients. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Forgetting factor (\(\lambda\)) & 0.5 \\ Outlier threshold (\(\kappa\)) & 1.2 \\ Sensitivity factor (\(\xi\)) & 5\% \\ Power control parameter (\(\alpha\)) & 0.2 \\ Lower bound for grouping (\(\eta\)) & 30\% \\ Upper bound for grouping (\(\varphi\)) & 10\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of the proposed algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time** & **2-UEs** & **3-UEs** \\ \hline
18.0 & \(6.48\times 10^{8}\) Bits/s & \(6.69\times 10^{8}\) Bits/s \\
27.0 & \(6.52\times 10^{8}\) Bits/s & - \\
37.0 & \(6.43\times 10^{8}\) Bits/s & - \\
48.0 & \(6.50\times 10^{8}\) Bits/s & \(6.72\times 10^{8}\) Bits/s \\
59.0 & \(6.27\times 10^{8}\) Bits/s & \(7.00\times 10^{8}\) Bits/s \\
103.0 & \(6.47\times 10^{8}\) Bits/s & - \\
115.0 & \(6.39\times 10^{8}\) Bits/s & - \\
208.0 & \(6.44\times 10^{8}\) Bits/s & - \\
220.0 & \(6.50\times 10^{8}\) Bits/s & - \\
309.0 & \(6.51\times 10^{8}\) Bits/s & - \\
321.0 & \(6.37\times 10^{8}\) Bits/s & - \\
404.0 & \(6.35\times 10^{8}\) Bits/s & - \\
412.0 & \(6.35\times 10^{8}\) Bits/s & - \\
493.0 & \(6.35\times 10^{8}\) Bits/s & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average data rate and cluster formation in time with a 10 Hz doppler frequency. Figure 6: Time behavior of the throughput of a downlink NOMA system after the channel gain variation. (**a**) Throughput after new users enter the cell. (**b**) Throughput after 125 s of users in the cell.