# Resource Allocation in C-V2X Mode 3 Based on the Exchanged Preference Profiles
## 4 Resource Allocation via Matching
### Exchanged Preference Profiles
The maximum tolerable latency \(D_{max}\) was set to 0.001 s, the time slot length was 0.001 s, and the LVP threshold \(p_{0}\) was 0.001. The bandwidth of each RB \(W\) was 180 kHz, and the number of RBs was 100. The maximum total transmission powers \(P_{max}^{C}\) and \(P_{max}^{V}\) were set to 23 dBm, and the limited transmission power \(P_{n,max}^{C}\) was equal to \(P_{max}^{C}/3\). The power of AWGN was assumed to be \(-114\) dBm, and the generated traffic data rate \(\lambda_{k}\) was 2 Mbps. The minimum ergodic capacity requirement of the CUE \(R_{0}\) was 0.5 bps/Hz. ### Network Capacity Performance

In this subsection, we evaluated the achievable network capacity of our proposed algorithm by a comparison with the MCM algorithm and the random selection scheme over 500 independent trials. The number of CUEs and VUEs were 30 and 60, respectively. Figure 5 studies the cumulative distribution function (CDF) of the total CUEs' capacities. In Figure 5, our proposed algorithms with \(\alpha=0\), \(\alpha=0.5\), and \(\alpha=1\) all obtained better performance in the capacity performance, which reflected the excellent optimality-finding

Figure 4: Simulation scenario setup. capability of our proposed algorithm. Moreover, as \(\alpha\) decreased, the maximum achievable total CUEs' capacities of our proposed algorithm increased while the corresponding minimum capacity value decreased, illustrating that the decrease of \(\alpha\) deteriorated the allocation fairness of the system. ### Impact of Number of V2I Links

In this simulation, a vehicular network with different V2I links was considered to evaluate the fairness, transmission capacity, and links' outage performance of our proposed algorithm. The number of VUEs was set to 60, and the number of V2I links ranged from 30 to 100. The simulation results were obtained by 200 independent trials. As observed in Figure 6, increasing the number of V2I links brought a fairness decline. This was because the VUEs and CUEs could only transmit their messages through the sharing spectrum. As the number of V2I links increased, a portion of CUEs were not allocated to the RBs, leading to the degradation of the system's fairness. For our proposed algorithm, as \(\alpha\) increased, the fairness also increased. The fairness gaps between \(\alpha=0\) and \(\alpha=0.5\) were negligible due to the comparable computation efficiency in the preference metric (14) for these two situations. However, when \(\alpha\) was equal to zero, the fairness performance of our proposed algorithm declined significantly. This was due to the fact that the \(\alpha\)-fair function was out of effectiveness when \(\alpha=0\), and in each matching process, our proposed algorithm with \(\alpha=0\) allocated as many RBs as possible to the users with good channel conditions. In the random selection scheme, each VUE randomly selected the CUEs with equal probability. Thus, the fairness performance of the random selection scheme outperformed our proposed algorithm with \(\alpha=0\). Since the MCM algorithm maximized the minimum network capacity through the iterative Hungarian algorithm and the Hungarian algorithm still searched the allocation results maximizing the network capacity, the fairness performance of the MCM algorithm was worse than that of our proposed algorithms with \(\alpha=0.5\) and \(\alpha=1\). In Figure 7, we compare the achievable total CUEs' capacities of the five algorithms under different V2I link numbers. As the number of V2I links increased, the capacity performance of our proposed three algorithms with different \(\alpha\) values increased. This was because increasing the number of V2I links provided more choices for VUEs in their matching process. VUEs could match the CUEs with better channel conditions, improving the total CUEs' transmission capacities. In contrast to the results in Figure 6, our proposed algorithms' achievable total capacity performance decreased as the \(\alpha\) increased.