## 3 Required Data Rate in V2V for Safe Overtaking
### Derivation of the Required Data Rate
This recognition method is a matching problem between scene and model points. Scene points are obtained from the output of the LiDAR sensor. On the other hand, model points are prepared in advance and have enough points to extract thefeature points of the target vehicle. The process of this recognition consists of calculating the feature points of the model and scene points and searching for the correspondence of the feature points between the model and scene points. If there are corresponding points, clustering with regard to the corresponding points is performed. We simplified two points about this model-based recognition process. The first point is using not the entire scene points, but the points clustered from the scene points. This extraction is performed in the first phase of ray tracing. The second point is the decision way of recognition. We defined a recognition score \(S\) as the ratio of the number of edge points shown in Equation (8). \(N_{\text{get}}\) and \(N_{\text{LOS}}\) are the number of edge points calculated from the two configurations, as shown in Figure 8.  
\[S=\frac{N_{\text{get}}}{N_{\text{LOS}}} \tag{8}\]  
The difference of these configurations is that the right configuration includes all objects, but the left configuration only includes the target vehicle, as shown in Figure 8. In the Figure 8a case, the sensing range of the LiDAR sensor for the ego vehicle is described by the green range. This environment enables the ego vehicle to sense the target vehicle with an LoS (Line-of-Sight). In the Figure 8b case, there are two LiDAR sensors. One is on the ego vehicle, but contrary to the former case, the blue vehicle blocks the sensing, as shown by the yellow range. The other is on the blue blocking vehicle, which senses with an LoS the same as the former case. The edge points obtained in the Figure 8a case are regarded as the maximum number of edge points of the target vehicle that the ego vehicle can obtain. On the other hand, the edge points in Figure 8b can be obtained in two ways, that is using cooperative perception or not. Using cooperative perception, the edge points calculation is based on the yellow and blue sensing range, while without cooperative perception, it is only based on the yellow sensing range. Figure 9a shows the entire edge points in the model points. Figure 9b shows two points. One is the white edge points obtained under the Figure 8a configuration, and the other is the red points obtained under the Figure 8b configuration using cooperative perception. Since the red points are also obtained from an LoS place, the red and white points' distribution is similar. Counting the number of edge points is different between the two configurations. \(N_{\text{LOS}}\) in Equation (8) is the number of LoS edge points obtained in the Figure 8a case. In detail, firstly, the LoS edge points of the model points are calculated by PCA edge extraction and voxelized. The resolution of the voxelization is based on the error range of a LiDAR sensor. Secondly, the edge points are moved and aligned with the target vehicle. Finally, the voxelized edge points that are in the LoS from the ego vehicle are extracted. On the other hand, the first process for \(N_{\text{get}}\) is the simulation of the LiDAR sensor data under the Figure 8b configuration. Since we focused on whether the scene points are on edges or not, we defined that the scene points have information about one feature point when a scene point is near the voxelized edge points of the model points. As a result, \(N_{\text{get}}\) is the total number of voxelized edge points obtained from the scene points. After the calculation of \(N_{\text{LOS}}\) and \(N_{\text{get}}\), the ratio and threshold were compared, and when the ratio was more than the threshold, we defined that the ego vehicle recognized the target vehicle. In the vehicle movement part, we derived the required distance \(d_{\text{req}}\) to avoid a collision.