# Energy-Efficient Device Discovery Mechanism for Device-to-Device Communications in 5G Networks +
## 5 Evaluation Results  
In this section, the performance of the proposed hybrid D2D discovery mechanism is evaluated using both analyses and simulations. The simulation program is developed by ourselves using C++ Builder. In our simulation scenario, there are 19 homogeneously hexagonal cells, as shown in Figure 3. The cell radius \(R\) of each cell equals 200 m. The BS of the innermost cell in Figure 3 is located at the origin (0, 0). For the cell whose BS is located at the coordinates \((x,y)\), the BSs of its six adjacent cells are located at \((x,y+\sqrt{3}R)\), \((x,y-\sqrt{3}R)\), \((x+\frac{3}{2}R,y+\frac{\sqrt{3}}{2}R)\), \((x-\frac{3}{2}R,y+\frac{\sqrt{3}}{2}R)\), \((x+\frac{3}{2}R,y-\frac{\sqrt{3}}{2}R)\), and \((x-\frac{3}{2}R,y-\frac{\sqrt{3}}{2}R)\), respectively. UEs arrive at a cell according to the Poisson process with rate \(\lambda_{UE}=0.5\) s\({}^{-1}\) and are uniformly distributed over a cell, i.e., following a Poisson point process (PPP). The ratios of UEs whose target UEs are located in the same cell as themselves and in adjacent cells are denoted by \(r_{1}\) and \(r_{2}\), respectively. In simulations, we assume that \(r_{1}=0.9r\) and \(r_{2}=0.1r\), where \(r\) is defined in (1). In Wi-Fi Direct, the maximum propagation range of the transmitted signals is assumed to be \(d=100\) m and the retry limit \(R_{T}\) is set to 5 if not specific mentioned. The length of a slot time in Wi-Fi Direct is set to 50 s. Whenever a UE successfully discovers its target UE, D2D communications start. During D2D communications, the data flow is always from the source UE (GO) to the target UE (client) and the full load condition is assumed. That is, the source UE (GO) always has data packets for transmission. The sojourn time of each D2D link in the system is exponentially distributed with the mean time \(1/\mu=300\) s.  
This section aims to evaluate and compare the energy consumption (in terms of the number of transmitted beacons), discovery delay, and discovery success rates of different D2D discovery mechanisms such as the direct D2D discovery scheme and the proposed one. In the direct D2D discovery scheme, all UEs entering the cell directly initiate D2D discovery procedure and the legacy Wi-Fi Direct is used. The length of the search state lasts 45 ms (i.e., 15 ms for each channel) and the length of the listen state is random and can be 100, 200, or 300 TUs (time units), where a TU equals 1.024 ms [21]. The total duration of a search state and its subsequent listen state is called a discovery cycle. Each UE executes at most two discovery cycles in the find phase. While in the proposed hybrid D2D discovery mechanism, after the stage of Phase 1 only the ratio \(r\) of UEs will trigger the D2D discovery procedures in Phase 2. Additionally, the optimal search and \begin{table}
\begin{tabular}{l l l l l l} \hline
**Rounds** & \(\sigma\) & \(\mathbf{p_{s}}\) & \(D\) & \(N\) & \(\mathbf{P_{\text{S}}}\) \\ \hline
1 & 4.534495 & 0.442625 & 1.397300 & 5.150993 & 0.216241 \\
2 & 0.980543 & 0.752858 & 1.358715 & 4.958488 & 0.222874 \\
3 & 1.010621 & 0.788811 & 1.357113 & 4.945034 & 0.222905 \\
4 & 1.010762 & 0.810988 & 1.356260 & 4.937319 & 0.222915 \\
5 & 1.010806 & 0.810982 & 1.356261 & 4.937321 & 0.222915 \\ \hline \end{tabular}
\end{table} 
Table 2: Analytic Results by Iterations. listen channel for a D2D link is assigned by the BS according to the minimum channel interference criterion given by the algorithm in Figure 4. In the direct D2D discovery scheme and the proposed one, when a source UE does not receive any response from its target UE within a slot time, the binary exponential backoff algorithm is executed to retransmit the discovery beacon. Notably, the binary exponential backoff algorithm without frozen backoff time is used in the proposed mechanism in order to shorten the discovery delay. On the other hand, to validate the performance of the binary exponential backoff algorithm, the inverse proportional transmission probability algorithm proposed in [16] is compared as well.