## 2 System Model
### Channel Model  
Geometric angles used for radio channel modeling include the zenith angle \(\theta\) and the azimuth angle \(\phi\) in a Cartesian coordinate system, where \(\theta=0^{\circ}\) points to the zenith and \(\theta=90^{\circ}\) points to the horizon.  
First, a ray tracing channel model is used to compute the parameters of each ray, including path loss, delay, and angles. To identify the properties of each ray, the shooting and bouncing rays (SBR) method, which supports up to eight reflections, is considered. The SBR method is widely used in practical propagation modeling [42]. To presume a realistic model, the effect of materials is considered by assuming that all buildings are made of bricks, with permittivity and conductivity as in [43]. In addition, weather impairments are added to the propagation model.  
While ray tracing finds individual rays between the AP and SN, the CDL channel models ray clusters. Therefore, the information retrieved for each ray configures the cluster average values of the CDL channel. The path losses obtained from ray tracing are considered the average path gains of the CDL. The elevation angles returned by ray tracing are converted to zenith angles that are used by the CDL, as follows:  
\[\theta=90^{\circ}-\gamma, \tag{1}\]  
where \(\theta\) is the zenith angle (in degrees), and \(\gamma\) is the elevation angle (in degrees) at either the transmitter or receiver. Finally, it is worth noting that CDL introduces small-scale fading because it models SN movement as compared with ray tracing, which is used for static analysis.  
To model multiple interactions with the scattering media in the downlink, departure angles are considered for the first scatterers interacted with from the transmitting side, and arrival angles are for the last bounce scatterers. For an uplink, the arrival and departure parameters can be swapped. In addition to the geometry parameters, small-scale parameters, such as cluster delays and power, need to be considered. Cluster delays are normalized by subtracting the minimum delay and sorted in ascending order, as follows [34]:  
\[\tau_{n}=\text{sort}\big{(}\tau_{n}^{\prime}-min\big{(}\tau_{n}^{\prime}\big{)} \big{)} \tag{2}\]  
where \(\tau_{n}^{\prime}\) is the absolute delay (in seconds) for cluster \(n\). For a LoS condition, additional scaling of delays is made as follows [34]:  
\[\tau_{n}^{LOS}=\frac{\tau_{n}}{0.7705-0.0433K+0.0002K^{2}+0.000017K^{3}}, \tag{3}\]  
where \(\tau_{n}\) is the normalized delay, and \(K\) is the Ricean \(K\)-factor (in dB). Cluster powers are normalized such that the sum of all cluster powers is equal to one, as in [34]:  
\[P_{n}=\frac{P_{n}^{\prime}}{\sum_{n=1}^{N}P_{n}^{\prime}}, \tag{4}\]  
where \(P_{n}^{\prime}\) is the absolute power in the linear scale for cluster \(n\) and \(N\) is the number of clusters. For a LoS condition, an additional specular component is added to the first cluster, and the cluster powers are normalized as follows:  
\[P_{n}=\frac{1}{K_{R}+1}\frac{P_{n}^{\prime}}{\sum_{n=1}^{N}P_{n}^{\prime}}+ \delta(n-1)\frac{K_{R}}{K_{R}+1}, \tag{5}\]  
where \(\delta(.)\) is Dirac's delta function and \(K_{R}\) is the Ricean \(K\)-factor in linear scale. Therefore, for LoS cases, the CDL model splits the first path into two components: one being LoS and the other having a Rayleigh fading characteristic. This results in a combined Ricean fading characteristic.  
Instead of using the generic profiles available in the standards, such an approach can provide a customized CDL channel profile that represents the intended environment by considering its geometry.