# Energy-Efficient Device Discovery Mechanism for Device-to-Device Communications in 5G Networks +
## 5 Evaluation Results
The inverse proportional transmission probability scheme, which is the same as the proposed two-phase hybrid D2D discovery mechanism except that the binary exponential backoff algorithm is replaced by the inverse proportional transmission probability algorithm, is named \"Inverse Proportional\" scheme in the following. In the first example, the performance of different D2D discovery mechanisms versus the ratio \(r\) is investigated. Each data point of simulation results is repeatedly simulated five times and the average and 95% confidence interval of the measured parameter are taken over all the runs. Figure 6 plots the UE's energy consumption performance under the proposed, inverse proportional, and direct D2D discovery mechanisms. The analytic results computed based on Equation (7) are also included in Figure 6 for comparison. According to Figure 6, the analytic results of the proposed scheme almost coincide with the simulation results, demonstrating the accuracy of our analysis. The energy consumption of the proposed and inverse proportional mechanisms is similar and it is much less than that of the direct D2D discovery scheme. For the proposed and inverse proportional mechanisms, the average number of transmitted beacons slightly increases with the ratio \(r\) because the collision probability grows with the number of D2D links, leading to an increase in the number of retransmissions. For the direct D2D discovery scheme, all UEs directly initiate D2D discovery procedures and thus the collision probability is irrelevant to the ratio \(r\). Notably, the value \(r\) represents the ratio of UEs whose target UEs are located in the same cell as themselves or in adjacent cells. Therefore, when \(r\) is small, very few UEs can find their target UEs and the number of retransmissions at each UE almost reaches \(R_{T}\), leading to \(R_{T}\)+1 = 6 beacons being transmitted over each channel. Since the discovery procedures must be executed in all three channels and there are two discovery cycles in the worst case, the worst number of transmitted beacons at each UE is about 36. When \(r\) increases, more target UEs are located within the discovery range to be discovered and thus the average number of transmitted beacons at each UE decreases. Accordingly, the average number of transmitted beacons of the direct D2D discovery scheme decreases with the ratio \(r\). Figure 6: Energy consumption of different schemes. Figure 7 shows the average discovery delay under the proposed, inverse proportional, and direct D2D discovery mechanisms. For the proposed and direct D2D discovery schemes, the discovery delay is almost irrelevant to \(r\). However, the average discovery delay of the inverse proportional scheme significantly increases as the ratio \(r\) grows. This phenomenon indicates that the efficiency of resolving collisions of the inverse proportional transmission probability algorithm is worse than that of the binary exponential backoff algorithm. In Figure 7, the proposed hybrid D2D discovery mechanism significantly outperforms the inverse proportional and direct D2D discovery schemes in terms of discovery delay. Additionally, the analytic discovery delay of the proposed scheme is also accurate. As to the discovery success rate, it is investigated in Figure 8. According to the results in Figure 8, the proposed hybrid D2D discovery mechanism significantly outperforms the direct D2D discovery scheme. While the discovery success rate of the proposed hybrid D2D discovery mechanism is only slightly better than that of the inverse proportional scheme. The accuracy of the analytic results of the proposed scheme is also good. The minor difference between the analysis and simulation mainly results from the approximation that in Figure A1 we use a circular cell for analyzing \(p_{c}\) rather than use a hexagonal cell. In the proposed and inverse proportional schemes, the discovery success rate slightly decreases with the ratio \(r\) because the collision probability increases with \(r\).