# A Throughput and Energy Efficiency Scheme for Unlicensed Massive Machine Type Communications +
## 4 Energy Efficiency
Moving on to the energy efficiency analysis, EE is shown in Figures 8-10 as a function of network density, SIR threshold and number of retransmissions, respectively. As can be seen in Figure 8, EE faces a decrease after some point when \(\lambda\) increases. When the nodes are sparsely located in the network, the level of interference is low but a lot of power is also used to transfer a message between nodes, hence EE is low. As \(\lambda\) gets higher, meaning that the nodes are getting closer to each other,the EE improves since less power is used for the transmission while interference is still low and the transmission is affected only by path loss. However, when the network gets very dense, the level of interference gets so high that in order to prevent outage, a lot of power should again be used for transmissions, which will cause the decrease in energy efficiency after some point in the plot. Figure 8: Energy efficiency \(EE\) versus the network density \(\lambda\) with different outage threshold \(\epsilon\) levels and \(\alpha=4\), \(r_{0}=1\). Figure 9: Energy efficiency \(EE\) versus the SIR threshold \(\beta\) with different network densities \(\lambda\) and \(\alpha=4\), \(r_{0}=1\), \(m=5\) and \(\epsilon=0.001\). It should be noted that when \(\lambda\) is low, the scenario with the loosest outage threshold has the lowest energy efficiency because the SIR in this case is lower compared to the other cases; however, when the network gets denser, the interference level rises, which would eventually decrease the throughput, and hence, the loosest outage threshold would result in the highest energy efficiency since there is more room allowed for having outage and less power is used to do the transmission in the presence of the interference. Although having a denser network also means having a higher level of interference, when there is room for higher levels of outage, less retransmissions are also needed in order to meet the reliability requirements of the network, and hence, less transmission power is used. All of these would eventually result in the system being more energy efficient in the presence of loose outage threshold in a dense network. Figure 9 shows how EE performs as the SIR threshold gets larger while having different network densities. As \(\beta\) increases, it means that the throughput is also increasing, even though power consumption is also increasing at the same time. The rate at which the throughput is increasing is higher, and thus, the energy efficiency also improves during this time. This however means that the outage events are also increasing, which will decrease the throughput and eventually EE will also decrease. That is why we see the maximum point in Figure 9. Moreover, we can see that the denser the network is, the more energy efficient it is. This is due to the fact that while nodes being close to each other means higher interference, less power is used for the transmission since the distances are smaller in denser networks. This figure also shows that the energy efficiency is concave in terms of \(\beta\), which was also proven in the EE optimization problem. Moreover, the effect of increasing the number of retransmissions on EE with different network densities can be seen in Figure 10. While \(\lambda\) is low, lower numbers of retransmission are needed for a successful message delivery, and therefore, the energy efficiency is higher in less dense networks. As the number of retransmissions increases, we can see that while the overall EE starts to decrease, denser networks become more energy efficient as well. The reason behind this is that in networks with high \(\lambda\), less power is used per each retransmission attempt to send the message since the distance between the nodes is smaller. Therefore, although the interference is higher, using less transmit power makes the network more energy efficient. Figure 10: Energy efficiency \(EE\) versus the number of retransmissions \(m\) with different network densities \(\lambda\) and \(\alpha=4\), \(r_{0}=1\) and \(\epsilon=0.001\).