## 6 Properties Analyses
### Stability
To tackle the formulated problem, we proposed an iteration-based joint user access and resource allocation algorithm. We first obtained a two-dimensional stable matching between the CUs and the D2D users based on the GS algorithm, and then iteratively exchanged D2D users in the licensed and the unlicensed spectrum to maximize the system rate. The properties of the proposed algorithm involving convergence, stability, optimality, and complexity were analyzed in detail. Simulation results demonstrated that the proposed algorithm can achieve high system rate with the excellent QoS of each user. Moreover, the proposed algorithm has a lower complexity as compared to the exhaustive search. Conceptualization, Q.H. and C.X. ; Formal analysis, Q.H. and C.X. ; Methodology, Q.H. and C.X. ; Project administration, C.X. ; Software, Q.H. ; Supervision, G.Z. and C.X. ; Validation, Q.H. and G.Z. ; Writing--original draft, Q.H. ; Writing--review & editing, Q.H., G.Z. and C.X. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not Applicable, the study does not report any data. This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 62071179, in part by the Beijing Nova Program of Science and Technology under Grant Z191100001119124, and in part by the Fundamental Research Funds for the Central Universities under Grant 2019 MS009. The authors declare no conflict of interest. ## References

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