## 4 Performance Evaluation of Millimeter-Wave V2V
### Millimeter-Wave V2V Communications with Antenna Height Diversity
As a result, it was shown that the two-ray ground reflection model was suited for the V2V channel. Therefore, we adopted the two-ray ground reflection model as a large-scale path loss model in the simulation, as shown in Figure 13. The additional characteristics of this model are that vibrating of both the transmitter and receiver due to vehicle movement has an effect on small-scale fading [33]. To avoid the fading in the driving environment, in [34], it was shown that, when one vehicle with multiple receivers is chasing the other vehicle with a transmitter, diversity gain is maximized by a vertically displaced antenna rather than a horizontally displaced antenna. In [35], the authors analyzed the outage capacity under the 60 GHz two-ray ground reflection model that follows the Rayleigh and the Rice distribution. They derived theoretically that height diversity provides large improvements rather than horizontal space diversity. In [36], the author derived that the antenna space for height diversity should be more than 10 cm. In our analysis, we assumed height diversity at the receiver and discussed how much height diversity improved the outage capacity. Since 99.99% reliability is required in cooperative perception, we estimated the improvement by a 0.01% outage capacity [8]. Moreover, we derived the best antenna space that improved the outage capacity among 5, 30, and 60 GHz. Firstly, we analyzed the basic characteristics of this channel model. As described above, this channel model can be separated into the effect of two-ray ground reflection and antenna vibration. The received power \(P_{\rm r}\) under the two-ray ground reflection is formulated as follows. \[P_{\rm r}=\frac{P_{\rm t}}{L(r_{\rm d})}\bigg{|}\sqrt{G_{\rm d}}\bigg{(}\frac{ \lambda}{4\pi r_{\rm d}}\bigg{)}+\sqrt{G_{\rm r}}\bigg{(}\frac{\lambda}{4\pi r _{\rm r}}\bigg{)}\Gamma\mathrm{e}^{-\mathrm{j}\{k(r_{\rm d}-r_{\rm r})\}} \bigg{|}^{2} \tag{11}\]  
where \(P_{\rm t}\) is the transmission power, \(G_{\rm d}\) and \(G_{\rm r}\) are the antenna gains for direct and reflected waves, \(r_{\rm d}\) and \(r_{\rm r}\) are the optical path length for direct and reflected waves, \(L(r_{\rm d})\) is the absorption factor at 60 GHz by oxygen as 15 dB/km, \(\lambda\) is the wavelength, \(k\) is \(2\pi/\lambda\), and \(\Gamma\) is the complex reflection coefficient. When the antenna vibration caused by the motor on the vehicle is adopted in this channel model, it changes \(r_{\rm d}\) and \(r_{\rm r}\). In [33], the authors modeled this antenna vibration by a Gaussian distribution \(\mathcal{N}_{\rm r}(0,\,\sigma_{0}^{2})\) where \(\sigma_{0}\) is 0.0319 m. This vibration causes a shift of all fading points, and all receiving places have the possibility to encounter strong fading. To avoid strong fading, height diversity was adopted. In this case, the receivers vibrated by the same motor so that they followed the same distribution as Equations (12) and (13). Figure 13: V2V two-ray ground reflection channel model. \[h_{\rm{tv}} =h_{\rm{t}}+\delta_{\rm{t}}\quad\text{where}\quad\delta_{\rm{t}} \sim\mathcal{N}_{\rm{t}}\Big{(}0,\;\sigma_{0}^{2}\Big{)} \tag{12}\] \[h_{\rm{rv1}} =h_{\rm{r1}}+\delta_{\rm{r}}\quad\text{where}\quad\delta_{\rm{r}} \sim\mathcal{N}_{\rm{r}}\Big{(}0,\;\sigma_{0}^{2}\Big{)} \tag{13}\]  
Finally, the 0.01% outage capacity \(C_{\rm{out}}\) was calculated under the height diversity. \[P(c<C_{\rm{out}})=0.01\% \tag{14}\]  
Figure 14 shows the above discussion in the case of 60 GHz. The black solid line shows the basic characteristic of the two-ray ground reflection model. The blue dotted and dashed lines show the moment of vibrating to \(3\sigma\) and \(-3\sigma\). We can see that the strong fading points are shifted to the left and right. The red dotted line shows the 0.01% outage capacity under no height diversity. We can see that the fading occurred at an arbitrary V2V distance.