## 7 Simulation Results and Discussion  
In this section, the performance of the proposed pricing-based iterative matching algorithm is validated through simulations. Table 2 presents the simulation parameters. We employ mathematical simulation software MATLAB as our simulation environment. We consider a single cellular networkwith a radius of \(R=300\) m, which contains \(M\) D2D TRs, \(R\) RSs and \(C\) CUEs. The CUEs are randomly distributed around the BS, and the D2D TRs and the RSs are deployed in a circular hot spot area with a radius of \(r=30\) m. The Monte Carlo simulation is used, and in general, we set the number of simulations as 2000. We compare the proposed algorithm with three heuristic algorithms, i.e., the exhaustive search with power control, matching with fixed power and random allocation with fixed power. The exhaustive search algorithm that examines all of the possible combinations to find the optimum solution is used to serve as an upper performance benchmark. In the proposed matching with the fixed power algorithm, the power allocation problem is not considered, and the transmit power for any D2D TX or RS is always fixed as the maximum transmit power \(P^{max}\). The random matching with the fixed power algorithm also employs the maximum transmit power. In addition, the D2D TRs, RSs and RBs are matched in a random way, which is used to indicate the lower performance benchmark. This is a conventional algorithm for the lower bound that is also utilized in many works [12; 27; 30]. For the optimum exhaustive matching algorithm, the computational complexity increases rapidly with the number of users increasing, which makes it impossible to simulate the optimum exhaustive matching algorithm with a large scale of users. For this reason, we use \(2\sim 6\) pairs of D2D TRs as an example to indicate the performance gap between the proposed algorithm and the optimum one. Figure 6 shows a snapshot of user locations with \(M=R=4\) and \(C=8\). Figure 7 shows the overall EE performance of all of the D2D pairs versus the number of D2D TR pairs. The performance gap between the proposed algorithm and the optimum exhaustive matching algorithm is smaller compared with the gaps of the other heuristic algorithms, such as matching with fixed power and random allocation with fixed power. For instance, when \(M=6\), the proposed algorithm achieves more than 80% of the optimum performance, and outperforms matching with fixed power and random allocation with fixed power by 68.75% and 145.45%, respectively. Besides, the computational complexity of the proposed matching algorithm is an order of magnitude lower than that of the exhaustive algorithm. The EE of D2D pairs of matching with fixed power is worse than that with power control. This proves that the matching with fixed power performance gain achieved by maximizing transmit power in an interference-limited environment is not able to compensate the corresponding EE loss. The random matching with fixed power performs the worst due to the following two reasons. Firstly, the relay selection and spectrum allocation are not jointly optimized, and the power control has not been taken into consideration. Secondly, some potential D2D TR pairs are blocked when the QoS requirements of either D2D TR pairs or CUEs are not satisfied under the random matching. \begin{table}
\begin{tabular}{l c} \hline \hline
**Simulation Parameter** & **Value** \\ \hline Cell radius \(R\) & 300 m \\ Radius of the hot zone \(r\) & 30 m \\ Path loss exponent \(\alpha\) & 4 \\ Max transmit power of D2D TXs and RSs \(P^{max}\) & 23 dBm \\ Transmit power of CUEs \(P_{c}\) & 20 dBm \\ Noise power \(N_{0}\) & \(-114\) dBm \\ Number of D2D TR pairs \(M\) & \(2\sim 6\) \\ Number of relay \(R\) & \(2\sim 6\) \\ Number of CUEs \(C\) & \(4\sim 12\) \\ SINR threshold \(\gamma_{min}^{D}\) & 25 dB \\ SINR threshold \(\gamma_{min}^{T}\) & 25 dB \\ Step size \(s\) & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters.