# NOMA Clustering for Improved Multicast IoT Schemes
## 3 System Model and Problem Formulation
### Formation of Coalitions
Users are randomly distributed in the cell area. The distances in the figures are in meters. First, the coalition heads are selected and marked using different color and mark. Then, coalitions are formed as described in Algorithm 1. Users in the same coalition are marked using the same color and mark as their coalition head (which can be distinguished by their bigger mark size and colored marker face). We provide an indication about the D2D coverage area for some coalition heads by drawing circles to show how the algorithm works. We observe in the figures that the coalition heads are located next to the BS and at the cell edges. This configuration allows to encircle the rest of the users in the cell. In the first tentative connection, D2D users connects to the nearest coalition head or neighbor as described in Algorithm 2. Coalitions are, hence, formed leaving some users \"disconnected\". In a second tentative connection, these users join the coalition of their preferred neighbor as in Algorithm 2. We remark from Figure 3 that after two tentative connections, only one user

Figure 3: Coalition formation: \(N=120\) users and 10 coalitions; 2 tentative connections. Figure 2: Coalition formation: \(N=120\) users and 10 coalitions; only one tentative connection. is left \"disconnected\" in this system configuration, who will be detected and connected to the BS. In order to see how Algorithm 2 works, we focus on the coalition number 9 and we draw the resulting transmission tree connecting the D2D users. We observe from Figure 4 that each user is relying on its best D2D link to maximize its rate. As stated previously, we do not take into account the generated delay due to the multi-hop in the transmission tree construction, as we are considering, in our model, IoT application not sensitive to this measure. ### SE and EE Simulations

We compare the system spectral and energy efficiency with OMA and NOMA models for different signal to noise ratio (SNR) values and for different users' speed profiles \(v_{1}=0.01\) km/h, \(v_{2}=0.1\) km/h and \(v_{3}=1\) km/h, representing different cases of coherence time values. In this simulations, we consider \(\lambda=4\times 10^{4}\) (\(N=1566\)) and 60 coalitions. Users join the coalitions as described in Algorithm 1 in one tentative connection. We present the SE and EE results in Figure 5 and Figure 6, respectively. We compare the simulation results and the outcome of the formed coalitions with the theoretical values, for a quasi-static mobility scenario. The proposed NOMA-D2D scheme is better than the multicast NOMA and OMA models, in terms of system SE and EE, especially for low mobility profiles. However, for medium and high mobility figures, the EE of the proposed system is worst than NOMA one due to the high rhythm of channel change versus the consumed time needed in the execution of the coalition algorithms. Though, the proposed system remains better than OMA for all considered speed profiles. Figure 4: Transmissiontree of coalition number 9. ### Optimal Number of Coalitions

In this subsection, we analyze the impact of the number of coalitions on the system performance. For a given configuration of \(\lambda=5\times 10^{3}\) (\(N=172\) users), we illustrate the evolution of the system SE and EE according to the number of coalitions in Figure 7. We consider different iteration cases of Algorithm 2; one tentative connection, two tentative connections, and three tentative connections. We also provide the number of cellular and D2D users for each case of \(M\). Figure 5: SE comparison between OMA, NOMA and proposed cooperative NOMA. \(N=1566\) and \(M=60\). Figure 6: EE comparison between OMA, NOMA and proposed cooperative NOMA. \(N=1566\) and \(M=60\). From the figures, we observe that the overall shape of the SE function is similar to the evolution of the D2D users and is decreasing versus the number of coalitions.