## 3 Communication and Channel Modeling
### Channel Modeling
#### 3.1.3 MIMO Beamforming  
By deploying massive mMIMO BSs in future 6G networks [44] stronger signals can be propagated for IoVs, see Figure 5. In multiple antennas, the precoding (weighting) vector corresponding to the unit power signal is equal to the unit response vector of the linear antenna arrays to maximize the SNR. Therefore, based on Remark 6, the channel gain of the cascaded LoS path BS-RIS-IoV is obtained as  
\[\mathcal{G}^{BSRIV}_{CLoS}\approx\widehat{\mathcal{G}^{BSRIU}\left(\varphi^{ BSRU},\,\xi^{BSRU}\right)}\times\widehat{\left(\mathfrak{a}^{RIS\dagger}_{ inc}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)\right)}\times\widehat{\mathcal{G}^{ RIS}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)} \tag{16}\]  
where \(N\) is the number of antennas in the mMIMO BS; superscripts \"\(BSRU\)\" and \"\(RUIV\)\" denote the BS-RISeUAV (RU) link (i.e., corresponding to the incident (_inc_) signal with respect to the RIS) and RU-IV link (i.e., corresponding to the reflection (_ref_) signal with respect to the IV), respectively. \(\mathcal{G}^{BSRIU}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)\in\mathbb{C}\) denotes the channel gain of the BS-RU path given as follows:  
\[\mathcal{G}^{BSRIU}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)=\sqrt{G_{BS}} \mathrm{a}^{BS}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)\times\Gamma^{BS} \left(\varphi^{BSRU},\,\xi^{BSRU}\right)\times\mathcal{G}^{BSRU}_{Ploss}, \tag{17}\]  
where \(\mathrm{a}^{BS}\left(\varphi^{BSRU},\,\zeta^{BSRU}\right)\in\mathbb{C}^{N}\) denotes the array response (wave) vector of the mMIMO BS with respect to the RU position given as follows:  
\[\mathrm{a}^{BS}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)=\left[e^{-j\varphi^{ BSRU}_{(n-1)}},\ldots,e^{-j\varphi^{BSRU}_{n}},\ldots,e^{-j\varphi^{BSRU}_{N}} \right]^{\top}, \tag{18}\]  
\[\text{with }\phi^{BSRU}_{n}=\frac{2\pi}{\lambda}\mathrm{w}^{r\top}\left(\varphi^{ BSRU},\,\xi^{BSRU}\right)\left(p^{BS}_{n}-p^{BS}\right)\]  
\[\text{and }\mathrm{w}^{r}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)= \begin{bmatrix} \sin\left(\xi^{BSRU}\right)\cos\left(\varphi^{BSRU}\right)\\ \sin\left(\xi^{BSRU}\right)\sin\left(\varphi^{BSRU}\right)\\ \sin\left(\xi^{BSRU}\right)\end{bmatrix} ,\]  
\(p^{BS}_{n}=\left[x^{BS}_{n}\quad y^{BS}_{n}\quad z^{BS}_{n}\right]^{\top}\in \mathbb{R}^{3}\) denotes the Cartesian coordinates of the \(n^{th}\) antenna of the mMIMO BS, which can be obtained based on the BS position and its spacing among its elements, see Figure 5 and Appendix C. \(\Gamma^{BS}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)\in\mathbb{C}^{N}\) denotes the BS phase array  
\[\Gamma^{BS}\left(\varphi^{BSRU},\,\xi^{BSRU}\right)=\frac{1}{\sqrt{N}}\left[e^ {-j\gamma^{BSRU}_{(n-1)}},\ldots,e^{-j\gamma^{BSRU}_{n}},\ldots,e^{-j\gamma^ {BSRU}_{N}}\right]^{\top}, \tag{19}\]  
\(\mathcal{G}^{BSRIU}_{Ploss}\in\mathbb{C}\) denotes the path loss of the BS-RIS path:  
\[\mathcal{G}^{BSRIU}_{Ploss}=\frac{\lambda}{4\pi}\underbrace{\frac{e^{-j\varphi ^{BSRU}}}{\left\|p^{RU}-p^{BS}\right\|_{2}}}_{d^{BSRU}},\]  
where  
\[\varphi^{BSRU}=\frac{2\pi}{\lambda}\mathrm{w}^{\top}\left(\varphi^{BSRU},\, \xi^{BSRU}\right)\left(p^{RU}-p^{BS}\right);\]The array response vectors of the RIS for incident and reflected paths are obtained as presented earlier in (12)-(15).