## 6 Properties Analyses
### Stability
Random allocation scheme indicates that the BS randomly determines the access modes of the CUs and D2D users. Figure 5 shows the system rate versus the number of iterations. From this figure, we can see that the system rate increases with the number of iterations ascending. Furthermore, after a certain number of iterations, the system rate tends to stabilize. Specifically, we can find that the proposed algorithm needs about 153 iterations to converge when \(CU=6\), \(C=3\), \(D=8\), while it takes about 141 iterations to converge when \(CU=5,C=3,D=7\). It can also be found that the number of required iterations increases with the number of users increasing. In addition, we can find that the convergence speed of the proposed algorithm is relatively low. Figure 6 plots the system rate versus the distance between the D2D transmitter and the D2D receiver. In this figure, it can be seen that JUARA algorithm performs better than other algorithms in improving system rate. We can also find that the system rate decreases with the increase of the distance between the D2D pairs. This is because the increase of the distance will degrade the communication quality between the D2D transmitter and the D2D receiver. In Figure 7, we evaluate the system rate versus the number of CUs when \(N=8\). As shown in this figure, we can find that system rate increases with the number of CUs ascending for different algorithms. Specifically, the proposed algorithm can achieve the highest system rate than the other algorithms. Moreover, the proposed algorithm outperforms

Figure 5: Convergence of the proposed algorithm. Figure 6: System rate vs. distance between D2D pairs. JUARA-CUs only algorithm, matching algorithm, and random allocation scheme by 3.1%, 8.2%, 14.5%. Figure 8 shows the system rate versus the number of D2D users when \(M=4\). In this figure, it can be seen that the system rate ascends as the number of D2D pairs increases. Furthermore, the proposed algorithm can achieve higher performance compared to the other algorithms. Specifically, the system rate by the proposed algorithm increases by 5.3%, 9.4%, 13.7% than JUARA-CUs only algorithm, matching algorithm, and random allocation scheme, respectively. The reason is that the other algorithms only consider the access modes of some users rather than all the users in the system. Combining Figures 7 and 8, we can observe that the system rate rises with the numbers of D2D users and CUs increasing. There are two main reasons leading to this increase. First, the increase number of the CU/D2D users would lead to a higher system rate. Secondly, with the number of CUs (D2D users) increasing, the D2D users (CUs) can have more choices to choose the more preferred CU (D2D user) to be matched. From Figures 7 and 8, we can also find that the system rate would be decreasing when the number of CUs (D2D users) exceeds a value which system can provide since the required minimum rate of the users must be guaranteed. Figure 9 shows the maximum number of all users versus the number of the Wi-Fi users. The system with the least number of users is \"D2D assisted CN in LS\", which is because the D2D users and CUs cannot access the unlicensed spectrum. The system \"D2D assisted CN in LS and ULS\" is the system proposed in this paper. This is because the CUs and the D2D users can access the unlicensed spectrum by JUARA algorithm. Simulation

Figure 8: System rate vs. number of D2D pairs. Figure 7: System rate vs. number of CUs. results demonstrate that the proposed iterative algorithm can significantly improve the network capacity and the system rate. ## 8 Conclusions

In this paper, we considered a cellular network where the D2D users can reuse the licensed and the unlicensed spectrum. Furthermore, the CUs and D2D users can access the unlicensed spectrum using the duty-cycle mechanism to achieve high system throughput. We formulated an optimization problem to maximize the system rate by jointly considering user access and resource allocation while guaranteeing the QoS of each user.