# Resource Allocation in C-V2X Mode 3 Based on the Exchanged Preference Profiles
## 4 Resource Allocation via Matching
### Exchanged Preference Profiles
Under the small \(\alpha\) condition, the \(\alpha\)-fair function (10) at the same ergodic capacity possessed a larger slope value. Hence, VUEs with large transmission capacities were more favored in the matching process. Figure 5: The CDF of achievable total CUEs’ capacities. Moreover, it is noted that the total transmission capacity performance of the MCM algorithm and the random selection schemes were slightly affected by the number of V2I links. Due to the iterative process of the Hungarian algorithm in the MCM algorithm, the final allocation result was limited by the VUE with the worst channel conditions in the network system regardless of the V2I links' numbers. In the random selection scheme, each VUE only randomly matched one CUE. Therefore, the total transmission capacity performance of the random selection scheme was bounded by the number of VUEs. Figure 8 demonstrates the vehicular link's outage ratio performance of the five schemes under different numbers of V2I links. As shown in (8) and (9), the LVP performance was positively related to the SINR of the V2V link. Thus, in our proposed algorithms, with the increase in the number of V2I links, the average SINR of the V2V links also increased, improving the links outage ratio performance. Furthermore, the smaller the value of \(\alpha\), the better the outage ratio performance. This was because the reduction of the \(\alpha\) value increased the proportion of the link's capacity in the VUEs' preference profiles; hence, the average SINR of V2V links rose. In accordance with the analysis in Figure 7, the vehicular link's outage ratio performances of the MCM algorithm and the random selection schemes were less affected by the number of V2I links. Figure 6: The fairness performance of different schemes with varying V2I links. Figure 7: The total capacity performance of different schemes with varying V2I links. ### Impact of Number of V2V Links

In this subsection, we evaluated the fairness, transmission capacity, and the link's outage ratio performance of our proposed algorithm under the dynamic V2V links. The number of V2I links was 30, and the range of VUEs was [30; 100]. The results were obtained by simulating 200 independent trials. Figure 9 studies the fairness performance of the five schemes under dynamic V2V links and shows that there was a marked rise in the fairness performance for all schemes with the increase of V2V links. For our proposed algorithms with \(\alpha=0.5\) and \(\alpha=1\) and the MCM algorithm, their fairness performance rapidly increased when the number of VUEs was less than 60. When the number of VUEs ranged from 30 to 60, the number of VUEs was less than that of V2I links. Thus, in this stage, more CUEs could be assigned to the RBs by reusing the spectrum resources with the V2V links as the number of VUEs increased, leading to a rise in fairness performance. When the number of VUEs was larger than 60, the fairness performance of our proposed algorithm with \(\alpha=1\) and the MCM algorithm could still rise. However, the reasons behind this phenomenon for these two algorithms were different. Since the exchanged preference profiles and the powerful fairness-guaranteed capability when \(\alpha=1\), our proposed algorithm with \(\alpha=1\) could allocate the RBs to the V2I link with less transmission capacity, achieving excellent fairness, while the MCM algorithm only considered the resource allocation of VUEs with the same number of V2I links. Although this allocation method could ensure fairness performance, it was not conducive to improving the total system transmission capacity. For our proposed algorithm with \(\alpha=0\) and the random selection, increasing the number of VUEs provided more reused modes for the CUEs, which could improve the fairness performance. Figure 10 depicts the impact of the number of VUEs on the capacity performance of the five allocation schemes.