## 3 Required Data Rate in V2V for Safe Overtaking
### Derivation of the Required Data Rate
Furthermore, from the recognition process, we can judge that the ego vehicle recognizes the target vehicle at a given distance. Therefore, the combination of the required distance \(d_{\text{req}}\) in Equation (5) and the recognition process derives the required sensor data rate \(R_{\text{req}}\) to avoid a collision as follows. \[\{\overline{r_{\phi}},\,\overline{r_{\theta}}\}=\operatorname*{arg\,min}_{\{r_ {\phi},\,r_{\theta}\}}S(r_{\phi},\,r_{\theta}\mid d_{\text{req}},\,d_{\text{ pe}})>0.9 \tag{9}\]  
\[R_{\text{req}}=\left(\left\lfloor\frac{A_{\phi}}{\overline{r_{\phi}}}\right \rfloor+1\right)\times\left(\left\lfloor\frac{A_{\phi}}{\overline{r_{\theta}}} \right\rfloor+1\right)\times F_{\text{scan}}\times D_{\text{symbol}} \tag{10}\]  
where \(S\) is the recognition score in Equation (8), \(A_{\phi}\) and \(A_{\theta}\) are the scanning range in the azimuth and elevation angle, \(F_{\text{scan}}\) is scan frequency (Hz) of the LiDAR sensor, and \(D_{\text{symbol}}\) is the amount of information per one laser point (bit). Note that the required sensor data rate depends on the velocity \(v\) of the ego vehicle and the distance \(d_{\text{be}}\). Finally, we can derive the realized maximum overtaking velocity by obtaining the minimum outage capacity that exceeds the required sensor data rate, which will be introduced in the simulation section. Figure 10 shows the required sensor data rate with the two options such as cooperative perception and driving path. The solid (dotted) line with square markers shows the minimum required sensor data rate to overtake with (not) using cooperative perception and not considering the driving path. The solid (dotted) line with circle markers considers the driving path with (without) cooperative perception. From the figure, firstly, we can see that all required sensor data rates rapidly increased. This rapid increase was due to  
Figure 8: The two configurations for the recognition score. Figure 9: Examples of the point cloud used in the recognition process. the laser density, or the resolution of the LiDAR sensor, which became rapidly sparse at a far place. In the case of no cooperative perception, since the blocking vehicle interrupted the sensing, a much higher resolution was required so that the required sensor data rate increased rapidly. Secondly, there was a difference between considering the driving path or not. This reflects the result of the 5 s driving overtaking shown in Figure 7 so that no difference was seen at more than 60 km/h. Figure 11 shows the required sensor data rate with \(d_{\text{be}}=5,\,10,\,15\) m and 5 s overtaking. In the case of using cooperative perception, as \(d_{\text{be}}\) becomes larger, the required sensor data rate becomes smaller. When \(d_{\text{be}}\) is large, the blocking vehicle gets near to the oncoming vehicle. This allows the blocking vehicle to recognize the oncoming vehicle with a low-resolution LiDAR sensor. On the other hand, the required sensor data rate in no cooperative perception depends on two factors, which leads to a complicated result. One is the distance \(d_{\text{oe}}\). When \(d_{\text{oe}}\) is large with the presence of the blocking vehicle, it is easy for a high-resolution LiDAR sensor on the ego vehicle to see the shape of the whole oncoming vehicle in a small sensing range, which obviously has a limit for the recognition. The other is distance \(d_{\text{be}}\). As the blocking vehicle gets near to the ego vehicle, the blocking vehicle blocks a large part of the range that sees the oncoming vehicle except for a very near location. Since the LiDAR sensor is on the roof, a large part of the blocking vehicle does not block the sensing in the case of a very near location.