# V2X Communication over Cellular Networks: Capabilities and Challenges
## 5 5G Capacity Analysis for V2X Communications  
In this section, we evaluate the spectrum needed to support the V2X UCs of Table 1. Our analysis adopts the framework provided by 5 GAA in [20]; however, it also provides a complete picture for the advanced UCs discussed in Section 2 for three distinct scenarios that assume different vehicles' density in the considered area. To analyze the capacity requirements, we have considered the Urban Grid Environment [43], as shown in Figure 3.  
The urban grid size is 1299 m \(\times\) 750 m with lanes of 3.5 m. The vehicles in the urban grid are assumed to be stationary (red light) in the vertical lanes, or could be moving (green light) in the horizontal streets and in the perimeter lanes. For calculating the number of stationary vehicles, we have considered an average vehicle length of 4.5 m and a bumper-to-bumper separation of 1.5 m. This means that there is one car at every \(1.5+4.5=6\) m per lane in the stationary direction of the grid. Across a total of 24 lanes, the total number of stationary vehicles is \([(433-14)\times 24]/6=1676\). Regarding the number of moving vehicles, three cases are considered for different vehicle speeds, as shown in Table 12. The assumed inter-vehicle spacing is given as the sum of the typical vehicle length (4.5 m) and a bumper-to-bumper separation of 20.8, 10.4, and 3.5 m for vehicle speeds of 30, 15, and 5 km/h, respectively, which corresponds to a time to collision of 2.5 s. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vehicle Speed** & **30 km/h** & **15 km/h** & **5 km/h** \\ \hline Inter-vehicle spacing & 20.8 + 4.5 = 25.3 m & 10.4 + 4.5 = 14.9 m & 3.5 + 4.5 = 8 m \\ \hline Number of moving vehicles & \([(750\times 12)+(1299\times 4)]/25.3\) & \([(750\times 12)+(1299\times 4)]/14.9\) & \([(750\times 12)+(1299\times 4)]/8=\) \\ \(=562\) & \(=953\) & 1775 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Number of moving vehicles in the urban grid road environment for multiple speeds. Figure 3: 3 GPP’s road configuration for Urban Grid. We have assumed that stationary vehicles are in a state that does not require services, so we only take into consideration the moving vehicles for the spectrum analysis. We also assume that this area is covered by two gNBs, each of which has three sector antennas. The Inter Site Distance (ISD) between the gNBs is 500 m and the size of each sector is \(\text{A}=\frac{1}{2\sqrt{3}}\text{ISD}^{2}=0.072\text{km}^{2}\). In the following analysis, we have also evaluated the cases where this geographic area is to be covered by 3 or 4 gNBs. Following the analysis in [20], the succeeding categories have been distinguished. The bandwidth B needed for repetitive V2V services that require the transmission of broadcast/multicast/unicast messages is given by  
\[\text{B}=\ \frac{\text{M}\ \times\ \text{T}\ \times\ \text{a}}{\text{e}\ \times\ \text{u}}, \tag{9}\]  
where M is the number of vehicles actively participating in a V2X UC; T is the throughput of the V2X service; a is the activity factor, e is the spectral efficiency, assumed to be 1.2 for the UL 4 for the DL and 0.6 for the sidelink; and \(u\) is the channel utilization factor equal to 0.336 for all UCs. This formula is applied to all UCs apart from UCs 2, 3, and 5, as reported in Table 1. For the activity factor, we have assumed a value of 1 for all UCs (as they are considered to be in a fully communicating state), apart from \"Platooning\" and \"Lane Merging\" (0.1) and \"Collective Information Sharing\" (0.8), as also assumed in [20]. The spectrum needs for V2N UCs are given by  
\[\text{B}=\ \frac{\text{T}\ \times\ \text{M}_{\text{D}}\times\ \text{A}}{\text{e}}, \tag{10}\]  
where T is the required data rate per link in bit/s, M\({}_{\text{D}}\) is the density of (transmitting or receiving) vehicles served per unit area in km\({}^{-2}\), e is the sector spectral efficiency in bits/s/Hz, and A is the area of the serving sector.