## 2 Scenario Description
### Antenna Parameters
#### 2.2.1 BS Antenna and Array Model  
We assume that the BS is equipped by a single-panel Uniform Planar Array (UPA) per each of the three sectors. Each UPA of the BS has \(N_{tz}\) antennas along the \(z\)-axis and \(N_{ty}\) along the \(y\)-axis, i.e., \(N_{t}=N_{tz}\times N_{ty}\) total antenna elements. Moreover, \(N_{t}\) also indicates the number of antennas with the same polarization. Antenna elements are uniformly spaced in both dimensions, with distances \(d_{H}\) and \(d_{V}\) in horizontal and vertical direction, respectively. We set the spacing \(d_{H}=d_{V}=\lambda/2\) where \(\lambda=c/f_{c}\) is the wavelength and \(c\) the speed of light. Dual polarization has been taken into account with the parameter \(P\), so each array can be single polarized (\(P=1\)) or dual polarized (\(P=2\)), as shown in Figure 2. We denote with \(s=(0,1,2)\) the sector index, the UPA with \(s=0\) lies on the \(yz\)-plane (broadside to \(\theta=90^{\circ}\), \(\phi=0^{\circ}\)), the UPAs with \(s=1\) and \(s=2\) are broadside to (\(\theta=90^{\circ}\), \(\phi=120^{\circ}\)) and (\(\theta=90^{\circ}\), \(\phi=240^{\circ}\)), respectively. Figure 2: Uniform Planar Array with cross-polarized antenna elements. \(N_{ty}=4\), \(N_{tz}=2\). Given a Zenith of Departure (_ZOD_) \(\theta\) and an Azimuth of Departure (_AOD_) \(\phi\) in the GCS (Global coordinate system), we need first to convert them into LCS (Local coordinate system) through the mapping:  
\[\theta^{\prime} =\theta\] \[\phi^{\prime} =\phi-s120^{\circ} \tag{9}\]  
where \(\theta^{\prime}\) and \(\phi^{\prime}\) are the _ZOD_ and _AOD_ in LCS, respectively. We can first write the \(N_{tz}\times 1\) steering vector (SV) of the Uniform Linear Array (ULA) on \(z\)-axis \(\mathbf{a}_{z}(\theta^{\prime})\):  
\[\mathbf{a}_{z}(\theta^{\prime})=\left[1,e^{j\pi\cos\theta^{\prime}},\dots,e^{ j\pi(N_{tz}-1)\cos\theta^{\prime}}\right]^{T} \tag{10}\]  
while we denote with \(\mathbf{a}_{y,s}(\theta^{\prime},\phi^{\prime})\) the \(N_{ty}\times 1\) SV of the generic ULA that lies on the \(y\)-axis for \(s=0\):  
\[\mathbf{a}^{y,s}(\theta^{\prime},\phi^{\prime})= \begin{bmatrix}1\\ e^{j\pi\sin\theta^{\prime}\sin\phi^{\prime}}\\ \vdots\\ e^{j\pi(N_{ty}-1)\sin\theta^{\prime}\sin\phi^{\prime}}\end{bmatrix}  \tag{11}\]  
for \(s\
eq 0\), \(\mathbf{a}_{y,s}(\theta^{\prime},\phi^{\prime})\) is rotated of \(\pm 120^{\circ}\). Finally, we can express the \(N_{t}\times 1\) SV for each UPA at the BS as the Kronecker product of the 2 SV's along each axis:  
\[\mathbf{a}_{tz,s}(\theta^{\prime},\phi^{\prime})=\mathbf{a}_{z}(\theta^{\prime })\otimes\mathbf{a}_{y,s}(\theta^{\prime},\phi^{\prime}). \tag{12}\]  
The 3-D radiation power pattern of each antenna element \(A(\theta^{\prime},\phi^{\prime})\) (adopted for the antenna elements of each array of the BS) is evaluated in LCS (Table 7.3-1 of [21]). It can be expressed in terms of the vertical cut \(A^{\prime}_{dB}(\theta^{\prime},\phi^{\prime}=0^{\circ})\) and horizontal cut \(A^{\prime}_{dB}(\theta^{\prime}=90^{\circ},\phi^{\prime})\), as follows:  
\[A^{\prime}_{dB}(\theta^{\prime},\phi^{\prime})=-\text{min}\{-(A^{\prime}_{dB} (\theta^{\prime},\phi^{\prime}=0^{\circ})+A^{\prime}_{dB}(\theta^{\prime}=90^ {\circ},\phi^{\prime})),\,A_{max}\} \tag{13}\]  
where \(A_{max}=30\) dB is the maximum attenuation. The vertical cut is obtained by fixing \(\phi^{\prime}\) to \(0^{\circ}\):  
\[A^{\prime}_{dB}(\theta^{\prime},\phi^{\prime}=0^{\circ})=-\text{min}\{12\bigg{(} \frac{\theta^{\prime}-90^{\circ}}{\theta_{3 dB}}\bigg{)}^{2},\,SLA_{V}\}\quad[ \text{dB}] \tag{14}\]  
with \(\theta_{3 dB}=65^{\circ}\), \(\theta^{\prime}\in[0^{\circ},180^{\circ}]\) and \(SLA_{V}=30\) dB is the side-lobe attenuation in the vertical direction.