## 2 Scenario Description
### Network Layout  
The scenario we adopted in this study is a typical hexagonal cell site divided in three sectors, each one covering a portion of 120 degrees in azimuth. Each sector is equipped with an antenna array, and the antenna parameters are the same for each sector. Figure 1 shows a representation of the cell site. The BS is placed at the center of the cell, represented as a hexagon of side or equivalently circumradius \(R=100\) m, and with height \(h_{BS}=10\) m.  
The bounded area \(\mathcal{A}\) of the hexagon can be computed as \(\mathcal{A}=\frac{3\sqrt{3}}{2}R^{2}\). The random placement of the users inside \(\mathcal{A}\) can be modelled as a spatial homogeneous Poisson point process. Denoting as \(M(\mathcal{A})\) the random variable corresponding to the amount of users of a point process present in the area \(\mathcal{A}\subset\mathbb{R}^{2}\), the probability of \(K\) users existing in \(\mathcal{A}\) can be expressed as:  
\[\Pr[M(\mathcal{A})=K]=\frac{(\mu\mathcal{A})^{K}}{K!}e^{-\mu\mathcal{A}} \tag{1}\]  
where \(\mu\) (users/km\({}^{2}\)) is the average user density per unit area. A homogeneous process implies constant \(\mu\), moreover \(\mu\) does not depend on the location. Given \(K\) users of the Poisson process in \(\mathcal{A}\), they are conditionally independent and uniformly distributed in the hexagon. Therefore, the positions of the randomly deployed \(K\) users can be determined by generating both the \(x\) and \(y\) coordinates. We denote with \(X\), the abscissa of a generic user in the hexagon, where \(X\) is the marginal random variable of a uniform 2-D distribution in the cell site. In order to find it, let us first define the two random variables \(X_{1}\) and \(X_{2}\):  
\[X_{1}\sim\mathcal{U}\left(-\frac{3}{4}R,\frac{3}{4}R\right) \tag{2}\]  
\[X_{2}\sim\mathcal{U}\left(-\frac{1}{4}R,\frac{1}{4}R\right) \tag{3}\]  
then we have:  
\[X=X_{1}+X_{2} \tag{4}\]  
where \(X\) is the sum of two uniform random variables with different bounds, the probability density function (_pdf_) of \(X\) is the convolution of the two uniform pdfs, resulting in a trapezoidal distribution. Once the abscissa is found, the conditional distribution of \(Y|X=x\), where \(Y\) is the ordinate of the user, is given by:  
Figure 1: Hexagonal cell site divided into three sectors.  
\[\begin{cases}\mathcal{U}\left(-\frac{\sqrt{3}}{2}R,\frac{\sqrt{3}}{2}R\right)&|x| \leq R/2\\ \mathcal{U}\left(-\sqrt{3}(R-|x|),\sqrt{3}(R-|x|)\right)&|x|>R/2\end{cases} \tag{5}\]  
As we are developing a 3-D channel model, the height of the UTs must be determined subsequently. For outdoor users, the height is fixed at 1.5 m. For indoor users, first of all we need to generate the number of floors of the building in which the user is placed. According to the TR 38.873 [40], we can generate it as follows  
\[floor_{\max}\sim\mathcal{U}\{4,8\} \tag{6}\]  
where \(floor_{\max}\) denotes the number of floors of the building and \(\mathcal{U}\{\cdot\}\) is the discrete uniform distribution. Therefore, we can generate the actual floor \(UT_{floor}\) of the user according to a discrete uniform distribution  
\[UT_{floor}\sim\mathcal{U}\{1,floor_{max}\} \tag{7}\]  
and finally we can calculate the height of the user according to [40] through the formula  
\[h_{UT}=1.5+3 UT_{floor}. \tag{8}\]  
Hence, this step consists in setting the number of users to take into account, fixing their position, and generating their height. Once we know that, we can evaluate the angles of the potential _LOS_ path: \(\phi_{LOS,AOD}\) and \(\theta_{LOS,ZOD}\), the azimuth and zenith of departure, respectively, and their counterpart in the arrival point of view \(\phi_{LOS,AOA}\) and \(\theta_{LOS,ZOA}\). Finally, we can set the carrier frequency \(f_{c}\) and the system bandwidth \(B\).