# NOMA Clustering for Improved Multicast IoT Schemes
## 3 System Model and Problem Formulation
### Formation of Coalitions
Indeed, when the number of coalitions increases, the number of D2D users in the system decreases, hence the system sum rate decreases as we are loosing the D2D proximity advantage. On the other hand, more cellular users get access to the BS spectrum resources. As consequence, the system SE decreases together with the number of D2D users as the number of coalitions increases. On the other side, as we are assuming that the BS power budget remains the same regardless of the number of connected users, the consumed power at the D2D users reduces the EE of the system when the number of the D2D users increases. This is explaining the shape of the EE curve in Figure 7b. However, as we are increasing the number of coalitions by 140%, the increase in the system EE remain relatively small, as we are talking about an order of 10%, versus a decrease in the system SE with an order of 70%. This is showing the gain in terms of SE which the proposed coalition approach is offering. A second observation from the figures is regarding the impact of the number of iterations on the system configuration; after a certain value of \(M\) (42 coalitions), the system

Figure 7: Proposed cooperative NOMA vs. number of coalitions. (**a**) System’s SE; (**b**) System’s EE; (**c**) Evolution of the number of D2D and cellular users. becomes stable as regards to the number of iterations; i.e., we get the same system configuration, in terms of D2D users, after the first tentative connection; more iterations will not change the configuration. This is due to the fact that when the density of coalition heads is low, users will need more tentative connections to reach a CH through their D2D neighbors. When the density of CHs is large, users can find a CH in their D2D coverage area and join a coalition from the first tentative connection. In case of low coalition head density in the system, allowing more tentative connections will help saving the BS resources and increase the system SE. However, the size of coalitions will increase, which means there will be more delay in the transmission and more use of the devices' resources. We must highlight that for designing an optimal system, an efficient number of coalitions must be selected based on the number of users, their computing and energy capacities, their mobility patterns and the total accepted delay in the transmission. Indeed, with a fewer number of coalitions, the number of D2D users inside each coalition is higher and hence the delay in transmission is more important. On the other side, for high number of coalitions, the channel uses needed to execute the coalition formation algorithm is more important and can take more than one block (one coherence time). We can suggest, as direction to manage to this concern, splitting the cell into several partitions, based on users' geographical position or mobility profiles, and run the proposed algorithms inside each partition. ## 6 Conclusions

In this paper, we presented a NOMA-D2D system based on the concept of coalitions. First, the coalition heads were identified and served in NOMA mode by the base station. In the second step, the other users joined the different coalitions and formed a transmission tree using their best D2D link with the members of the same group. The proposed system presents great benefits, in terms of system SE, compared to NOMA and OMA systems. From the simulations, we observed an increase of up to 10-times the system SE compared to NOMA system and up to 1000-times compared to OMA one. In low mobility patterns, the proposed system can achieve better results than conventional NOMA and OMA systems in terms of system energy efficiency. However, due to the additional time consumed during the coalition and the transmission tree formation stages, the energy efficiency of the system decreases compared to NOMA in high mobility contexts. We finally discussed how to optimally design the system in terms of selecting efficiently the number of coalition heads based on the system conditions and the relevant IoT use cases.