# Resource Allocation in C-V2X Mode 3 Based on the Exchanged Preference Profiles
## 2 System Model
### Communication Model  
We consider a single-cell C-V2X network with one BS denoted by \(C\) consisting of multiple CUEs and VUEs. Let \(\mathcal{M}=\{1,2,\ldots M\}\) be the set of \(M\) CUEs and \(\mathcal{K}=\{1,2,\ldots R\}\) be the set of \(K\) VUEs. The basic resource allocation unit is defined as the RBs. \(\mathcal{N}=\{1,2,\ldots N\}\) denotes the set of RBs. In our RBs scheduling scheme, due to the high capacity requirement for the V2I links, a CUE can occupy multiple RBs. Moreover, to avoid the interference between different CUEs, each RB can be assigned to only one CUE. As the uplink spectrum is less intensive and the VUEs usually generate tolerable interference with the BS, we stipulate that VUEs can reuse the RBs assigned to CUEs.  
As shown in Figure 1, the channel power gain from CUE \(m\) to the BS on RB \(n\), denoted by \(h_{m,n}^{C}\), is formulated as \(h_{m,n}^{C}=a_{m,n}^{C}g_{m,n}^{C}\), where \(a_{m,n}^{C}\) and \(g_{m,n}^{C}\) account for the corresponding large-scale and small-scale fading, respectively. The channel power gain \(h_{k,n}^{V}\) from VUE \(k\) to its V2V pair on RB \(n\), the interfering channel \(h_{m,k,n}^{V}\) from CUE \(m\) to VUE \(k\) on RB \(n\), and interfering channel \(h_{k,m,n}^{C}\) from the VUE \(k\) to CUE \(m\) on RB \(n\) are defined similarly. Due to the high mobility of vehicles, we assume that the BS can acquire the knowledge of the large-scale fading periodically and only be aware of the statistical characterization of the small-scale components rather than their realizations.  
The signal-to-interference-plus-noise ratio (SINR) of the CUE \(m\) on RB \(n\) is expressed as  
\[\gamma_{m,n}^{C}=\frac{x_{m,n}P_{m,n}^{C}a_{m,n}^{C}g_{m,n}^{C}}{\sigma^{2}+ \sum\limits_{k\in\mathcal{K}}x_{k,n}P_{k}^{V}a_{k,m,n}^{C}g_{k,m,n}^{C}} \tag{1}\]  
where the binary variable \(x_{m,n}\) represents the allocation indicator of RB \(n\). If \(x_{m,n}\) is equal to 1, CUE \(m\) is allocated RB \(n\), and 0 otherwise. The definition of \(x_{k,n}\) is similar to that of \(x_{m,n}\), \(P_{m,n}^{C}\) and \(P_{k}^{V}\) denote the transmit powers of CUE \(m\) on RB \(n\) and VUE \(k\), respectively. \(\sigma^{2}\) is the power of the received additive white Gaussian noise (AWGN).  
Similarly, the SINR of the VUE \(k\) on RB \(n\) can be defined as  
\[\gamma_{k,n}^{V}=\frac{x_{k,n}P_{k}^{V}a_{k,n}^{V}g_{k,n}^{V}}{\sigma^{2}+ \sum\limits_{k\in\mathcal{K}}x_{m,n}P_{m,n}^{C}a_{m,n}^{V}g_{m,k,n}^{V}} \tag{2}\]  
Since different VUEs may be in close distances to each other, we stipulate that the VUEs can only be assigned one RB and cannot occupy the same RBs.  
Due to the high vehicles mobility, the small-scale fading components of the channel power gain vary on a highly fast scale. Thus, the achievable data rate of the CUE \(m\) on RB \(n\) can be expressed as the ergodic capacity, which is  
\[\mathbb{E}\Big{\{}R_{m,n}^{C}\Big{\}}=\mathbb{E}\Big{\{}W\log(1+\gamma_{m,n} ^{C})\Big{\}} \tag{3}\]  
where \(W\) is the bandwidth of the single RB. Let \(\mathbb{E}\big{\{}R_{m}^{C}\big{\}}\) denote the total ergodic capacity of the CUE \(m\), which is \(\mathbb{E}\big{\{}R_{m}^{C}\big{\}}=\sum\limits_{n\in\mathcal{N}}\mathbb{E} \big{\{}R_{m,n}^{C}\big{\}}\).