## 4 Simulation Results
### Simulation Configuration
It implies that the transmit power for forwarding EUs' data may be saturated, when the number of D2D transmission pairs is more than 30, as seen in Figure 4. When given the number of D2D pairs is 37, the saturated transmit power for forwarding EUs' data in our RSWW-OSSS is about 2.5 W while the saturated transmit power for forwarding EUs' data in the PSLS is about 3.4 W. The saturated transmit power for forwarding EUs' data in our RSWW-OSSS is 26% less than that in PSLS. In order to evaluate the performance of the proposed RSWW-OSSS, we consider a stable matching with the fixed time allocation (SM-FTA) as the cooperative benchmarker of our RSWW-OSSS. Based on the SM-FTA, an EU shares a fixed portion of the whole time slot to its cooperative partner. Additionally, a stable matching with the fixed power allocation (SM-FPA) is introduced as another cooperative benchmarker of our RSWW-OSSS. Based on the SM-FPA, the transmit power which is allocated by a DT for forwarding EU's data is fixed. Furthermore, we also introduce a random-matching-based overlay spectrum-sharing (RM-OSS) scheme, where both the EUs and the DTs calculate their optimal strategies by playing the proposed two-stage Stackelberg Game. However, according to the RM-OSS scheme, an EU is randomly matched with a D2D transmission pair which is capable of satisfying its transmit rate requirement. Figure 5 shows our comparison between the total rates of EUs achieved by our RSWW-OSSS, the SM-FTA, the SM-FPA as well as the RM-OSS versus different numbers of D2D transmission pairs. Figure 4: D2D pairs consumed power for relaying data versus different numbers of D2D transmission pairs when the number of EUs is 20. Figure 3: Sum-rate of EUs and D2D pairs versus different numbers of D2D transmission pairs when the number of EUs is 20. Furthermore, Figure 6 compares the total rates of D2D transmissions achieved by our RSWW-OSSS, the SM-FTA, the SM-FPA as well as the RM-OSS versus different numbers of D2D transmission pairs. Compared to the benchmarker schemes, the proposed RSWW-OSSS is capable of significantly improving the attainable rates for both the D2D communications and the uplink transmissions from EUs to BS, as shown in Figures 5 and 6. More explicit, when the number of D2D pairs is 20, the achievable rate of EUs in the proposed RSWW-OSSS is 62 b/s/Hz which is about 100% more than that in RM-OSS, 48% more than that in SM-FPA and 22% more than that in SM-FTA, while, the achievable rate of D2D pairs in our RSWW-OSSS is 91 /b/s/Hz which is about 111% more than that in RM-OSS, 52% more than that in SM-FPA and 34% more than that in SM-FTA. Given the number of D2D pairs, the RM-OSS scheme achieves the lowest transmit rate, because that both the EUs and DTs randomly select their cooperative partner without considering the other potential cooperative partners, as seen in Figures 5 and 6. According to the total transmit rate of the uplink transmissions and that of the D2D communications shown in Figures 5 and 6, the SM-FTA outperforms the SM-FPA. Based on the SM-FPA, less DT can afford the total power for successfully forwarding EU's data and for conveying its own data, due to the fixed power allocation and maximum power constraint. Hence, compared to the SM-FTA, the SM-FPA reduces the number of cooperative matching. Observe in Figures 5 and 6 that the total transmit rate of uplink transmissions and that