## 4 Energy Efficient D2D over Single Frequency Network (EED2D-SF)  
In this work, we design a technique to be implemented in the gNodeB of a 5G network to efficiently deliver multicast traffic by exploiting the benefits of D2D communications and SFN operation. The  aim is to improve the overall energy efficiency of the network. In particular, the subset of devices in better channel conditions are served by the gNodeB through a multicast transmission according to the traditional CMS approach, while devices located far from the gNodeB receive the multicast content via D2D communication by relay nodes, properly selected among those that received the multicast service. The relay nodes behave according to the SFN operation, i.e., they simultaneously transmit the same content to the D2D receivers. The exploitation of D2D communications for providing service to cell-edge devices both improves the network data rate and reduces the energy consumption. Proximity connections between relay nodes and devices located close to the cell border will likely benefit from good channel conditions. Furthermore, as a consequence, the CMS serving area will be reduced, thus allowing the gNodeB to serve multicast devices with a less robust MCS that achieves higher data rates. The signal quality received by the D2D terminals is improved thanks to the Single Frequency paradigm. In fact, the transmitting relay nodes in the cell are synchronized and simultaneously send the same signal received from the gNodeB, over the same uplink frequency to their D2D receivers. The  latter observe multiple delayed versions of the same signal and, through appropriate synchronization, channel estimation, and equalization techniques, benefit from the multipath diversity at the only cost of a slight increase in the computational complexity. The dimension of the CMS serving area (i.e., the choice of the MCS for the multicast transmission) and the set of D2D connections to establish (i.e., the choice of the MCS for D2D transmissions) are chosen by the gNodeB in order to maximize the overall network energy efficiency. Figure 1 shows the scenario considered in this paper. After receiving data from the gNodeB, some devices acting as relay nodes (i.e., R1, R2 and R3) could forward the stored data to nodes left out from the gNodeB transmission. Three possible relay selection options with the related D2D configurations are shown (represented with different colors) corresponding to three levels of energy consumption. The first configuration, depicted with the red color, selects three relays, R1, R2 and R3; the second configuration, with orange links, exploits two relays, R1 and R3; and the third configuration selects only one relay, R2, and is illustrated with green links. The relays simultaneously forward data to cell-edge devices. As can be seen, each configuration is identified by a color according to the overall network energy consumption level. Specifically, the most energy efficient D2D configuration is represented by the green battery, the worst performing D2D configuration in terms of energy efficiency is represented by the red battery, and the D2D configuration with the orange battery is characterized by an intermediate energy consumption level. Our proposed EED2D-SF will select the configuration identified with the green color, since it exhibits the best performance in terms of overall network energy efficiency because of both the number of devices involved and the position of cell-edge devices with respect to the relay node. Various energy efficiency (EE) Key Performance Indicators (KPIs) are defined by Standard Development Organization (SDOs). They can be applied to the whole network (i.e., end-to-end), sub-networks (e.g., the radio access network), single network elements, or to telecommunication sites, which contain network elements and site equipment. In [26] EE metrics and measurement procedures in operational radio access networks are defined.