## 2 System Model
A biasing value of 0 indicates that a V-N may be linked with the MBS, a UAV with LOS visibility, or a UAV with NLOS visibility; however, a biasing factor traversing infinity indicates that a V-N will connect with a neighboring V-N. The channel-dependent fading linked with the V-N reflects Rayleigh fading, with the fading gain \(g_{V}\sim\exp(1)\). UAVs, \(U\), are modeled using a 3D PPP, \(\Phi_{U}\). The UAVs' density is \(\lambda_{U}\), and their height is \(h_{U}\). The \(i\)-th LAP may be depicted in a 3D space using \((x_{i},y_{i},h_{U})\), wherein \(i\in\{1,2,\ldots,u\}\) and the number of UAVs is \(u\). Furthermore, \(U\in\{L,N\}\), where \(L\) indicates LOS-LAPs and \(N\) indicates NLOS-LAPs. The LAP's power is \(P_{U}\). The path loss exponents for \(L\) and \(N\) are \(\alpha_{L}\) and \(\alpha_{N}\), respectively. The extra path loss for \(L\) and \(N\) is \(\eta_{L}\) and \(\eta_{N}\), respectively. The LAP's channel-dependent fading adopts Nakagami-\(m\) fading with a stochastic distribution \(g_{U}(t)=\dfrac{m_{U}^{m_{U}}t^{m_{U}-1}\exp(-m_{U}t)}{\Gamma(. )}\) throughout the equipment and the LAP channel, wherein \(m_{U}\in\{L,N\}\) indicates fading and \(\Gamma(. )\) represents the Gamma distribution [29]. The LAP's fading gain is \(t=x^{2}\), with \(t\sim\Gamma(m_{U},1/m_{U})\), wherein \(x\) is a Nakagami-\(m_{U}\). The LAP's LOS probability is calculated as follows:  
\[\mathbf{p}_{L}(z_{L})=\left(1+\mathcal{A}.e^{-\dfrac{180}{\pi}B\phi+\mathcal{ A}.\mathcal{B}}\right)^{-1}, \tag{1}\]  
where \(\mathcal{A}\) and \(\mathcal{B}\) are determined by the environment. \(\theta=\arctan(h_{U}/D_{L})\), where \(D_{L}\) represents the V-N and \(L\) distances. Taking the complement of \(\mathbf{p}_{L}(z_{L})\) yields \(\mathbf{p}_{N}\), the NLOS-LAP probability. Figure 1: V2X communications assisted by base stations and UAVs. This paper modeled the antenna pattern of the UAV by considering a uniform square array antenna of \(N\times N\) elements. Beamforming assumes high-gain antennas with directional capabilities installed on UAVs to compensate for significant millimeter-wave frequency transmission losses, especially for long-distance and high-bandwidth backhaul communications. Beamforming antenna structures that are small, light, affordable, and appropriate for UAVs with constrained payload capacity are considered for the UAV-assisted C-V2X communications. The UAVs used an identical square antenna arrangement with \(N\times N\) elements that evenly distribute themselves throughout the x-axis and y-axis directions to provide robust beamforming even when fluctuations are caused by mobility. Beamforming also assumed identical antenna arrays' power; such an assumption makes it easier to analyze an ideal array dimension, which improves transmission rate without taking the system layout and UAV instabilities into consideration. In real-world settings, accomplishing an ideal alignment of the beam is an extreme challenge because of the excessive ambient wind, atmospheric pressure, mechanical noise, and controlling-motor imperfections of the UAVs, which influence angle, \(\theta\), and phase, \(\phi\), of the 3D beam width. \(\sigma_{x}\) and \(\sigma_{y}\) represent the antenna's x-z and y-z vibration orientations, respectively. The angle and phase affiliated with the oscillating 3D beam width are specified as follows: \(\theta=\tan^{-1}\Bigl{(}\sqrt{\tan(\sigma_{x})^{2}+\tan(\sigma_{y})^{2}}\Bigr{)}\) and \(\phi=\arctan\Bigl{(}\dfrac{\tan(\sigma_{y})}{\tan(\sigma_{x})}\Bigr{)}\), respectively. The number of transmitting and receiving antennas linked to the device (i.e., LOS-LAP, NLOS-LAP, MBS, or V-N) is provided by \(N_{t}\times N_{r}\). The transmitting and receiving antennas are represented by \(t\) and \(r\), correspondingly, with \(t,r\in L,N,M,V\). The square array antenna's transmitting and receiving gains are calculated as \(\mathcal{G}_{W}=\mathcal{G}_{W}^{o}\times\mathcal{G}_{W}^{E}\times\mathcal{G} _{W}^{A}\), wherein \(W\in t,r\).