# On the Performance of Underlay Device-to-Device Communications
## 5 Simulation Results  
In this section, we present numerical results to verify the accuracy of the proposed mathematical framework. More precisely, we consider a generic cell with a circle shape, where the BS is located at the center and radius \(O=1000\) m. Unless otherwise stated, the following parameters are employed throughout this section: \(N=4\), \(\text{BW}=1\) MHz, \(\eta=3.6\), \(f_{c}=2.1\) GHz, NF = 6 dB, \(P_{\text{tot}}=20\) dBm, \(P_{\text{C}}=20\) dBm, \(R=R_{\text{C}}=1\) bits/s/Hz; and \(\alpha=\{0.3650,0.2628,0.2700,0.1022\}\). The positions of D2D transmitter and D2D receiver are \(P_{dt}=(-441,-92),(146,-33),(734,153),(-639,-633)\) and \(P_{dt}=(-443,-95),(146,-39),(740,148),(-646,-626)\), respectively, while the position of cellular user is \((290,78)\). Figure 2 illustrates the outage probability of all D2D receivers as a function of the target rate \(R\) under the equal power allocation scheme. Firstly, it is evident that the proposed mathematical framework absolutely matches with Monte Carlo simulations, confirming the accuracy of the mathematical frameworks. Secondly, under the current setup, the first D2D receiver achieves the best performance among all D2D receivers. It can be explained that it has the shortest transmission distance and is far away from the cellular user. On the other hand, despite benefiting from a moderate transmission distance, the performance of the second D2D receiver is the worst, owing to the largest interference from the cellular user. Thirdly, it is apparent that the higher the target rate, the worse the OP. The explanation is directly attained from the definition of the outage probability. Figure 3 shows the outage probability of the fourth D2D receiver under all schemes with respect to the targeted rate. We observe that, under the current set up, the path-loss  
Figure 2: Outage probability of D2D receiver vs. \(R\) under the equal power allocation scheme. Solid lines are plotted by employing (12) and markers are Monte Carlo simulation. based scheme is the best one and the random scheme is, on the other hand, the worst one. More precisely, when \(R=1\) [bits/s/Hz], the OP of the path-loss based scheme is approximately 0.0002, while the OP of the random scheme is 0.0008. This means that the path-loss based scheme is 4\(\times\) better than its counterpart. However, all schemes are below 0.001, which means that the successful rate is 99.999%, securing the high-reliability transmission. Once again, the curves from the mathematical framework are perfectly overlapped with the computer-based simulation results. Figure 4 reveals the OP of the second and the fourth D2D receivers versus the total transmit power of the D2D networks under the path-loss based method. It is obvious that increasing the transmit power monotonically decreases the OP, hence confirming our findings in Proposition 1. The performance of the fourth receiver is better than the second receiver, as already shown in Figure 2. Nevertheless, the gap between two curves is moderate, and both schemes are below \(10^{-4}\) when \(P_{\rm tot}>20\) dBm. The coverage probability of the cellular user as a function of \(R_{C}\) is shown in Figure 5. It is straightforward to recognize that raising the total transmit power of the D2D networks evidently degrades the performance of the cellular networks, e.g.,  
Figure 4: Outage probability vs. \(P_{\rm tot}\) under the path-loss based method. Solid lines are plotted by employing (12) and markers are Monte Carlo simulation. Figure 3: Outage probability of the fourth D2D receiver vs. \(R\) under all power allocation methods. Solid lines are plotted by employing (12) and markers are Monte Carlo simulation. goes down. Moreover, the Pcov simply declines with respect to the \(R_{C}\) from the definition of the coverage probability. Figure 6 illustrates the behavior of the Pcov versus the total transmit power \(P_{\text{tot}}\). We experience that increasing \(P_{\text{tot}}\) is harmful to the cellular networks.