# Joint Uplink and Downlink Resource Allocation for D2D Communications System
## 4 Numerical Analysis
### Simulation Results  
Figure 2 illustrates the convergence performance of the proposed scheme under different numbers of users. We can observe that the algorithm converges to a stable solution till four times. In addition, as the number of users increases, the system capacity increases accordingly, which means that our JUAD solution is scalable. The time complexity of traditional Hungarian algorithm is \(O(n^{3})\), while that of the improved Hungarian algorithm is \(O(Cn^{3})\), where \(C\) is a constant slightly greater than \(1\). Figure 3 displays the system capacity of the three algorithms versus maximum transmission power. These three algorithms include JUAD, OU, and OD. From Figure 3, it can be seen that the system capacity of the three algorithms are improved with the increasing maximum transmission power. In addition, our proposed JUAD scheme outperforms the other two methods for all channels (whether uplink or downlink) which can be selected to reuse for the D2D. As maximum transmission power is 17 dBm, the system capacity of the proposed scheme is 176 bps/Hz. The performance of OU scheme is close to that of OD scheme, and it is better than that of the OD scheme. That is because, compared with the OU scheme, in which D2D pairs suffer interference from CUs, the OD scheme brings severe interference to D2D pairs, in which D2D pairs suffer interference from BS. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Cell radius & 500 m \\ Bandwidth & 0.5 MHz \\ Noise spectral density & \(-\)144 dBm \\ Path loss exponent & 4 \\ Path loss constant & 0.01 \\ Maximum transmission power of CU & 21 dBm \\ Maximum transmission power of D2D & 21 dBm \\ Maximum transmission power of BS & 27 dBm \\ SINR threshold of CU & 13 dB \\ SINR threshold of D2D & 13 dB \\ Number of CUs & 10 \\ Number of D2D pairs & 10 \\ Number of uplink (or downlink) channels & 10 \\ D2D distance & 30–90 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 2: The system capacity with different number of iterations. The system capacity of the three resource allocation schemes versus the noise power is displayed in Figure 4. From Figure 4, we note that the output performance of the JUAD scheme is higher than that of the OU and OD schemes for different noise power. Moreover, the system capacity of the three resource allocation schemes decrease as the noise power increases. For the resource allocation schemes, each CU and D2D link decrease its transmission power when the noise power reduces. As a result, the co-channel interference between CU and D2D links also decreases, which improves the capacity of system. The same user density is assumed to be for both \(R=500\) m, \(R=800\) m, and \(R=1000\) m, respectively, in the cell. Figure 5 shows the system capacity of the JUAD algorithm with different  
Figure 4: The system capacity with varying noise power, comparison of the JUAD/ OU/OD resource allocation schemes. Figure 3: The system capacity with varying maximum transmission power, comparison of the joint uplink and downlink (JUAD)/only reuse uplink (OU)/only reuse downlink (OD) resource allocation schemes. size of radius. It can be seen from the Figure 5 that the system capacity of the JUAD algorithm under the radius \(R=1000\) m is better than that of the proposed algorithm under the radius \(R=500\) m. This is because the greater distance between users can reduce the interference between CU and D2D, which can improve output performance. The system capacity of the three resource allocation schemes for different distances of D2D pairs is shown in Figure 6. It can be seen that the system capacity decreases with the increasing radius of the D2D pair. As distance of D2D pairs is equal to 70 m, the system capacity that JUAD scheme can achieve is more than 220 bps/Hz, which is about 125% higher than that of the OU and OD schemes. In the range of the distance D2D pairs from 30 m to 90 m, our JUAD resource allocation scheme has superior performance to the other two schemes.