# UAV Dynamic Non-Terrestrial Transmission Channel Analysis Based on SSCM-RT Model
## 2 Theoretical Background
### Channel Fading Model Parameters  
Radio waves can be classified according to the fading type as large-scale fading and small-scale fading, depending on the interval at which the received signal field strength changes. Signals will encounter large-scale and small-scale fading throughout the real scene propagation processes. Large-scale fading typically impacts the wireless system's ability to provide network coverage, while small-scale fading impacts the communication system's quality [16; 17; 18]. Path loss and shadow fading are used to characterize the properties of large-scale fading. Large-scale average path loss is used to assess the average fading of the signal between the transmitter and receiver and is defined as the difference between the effective transmit power and the average received power. For shadow fading, when radio signals are transmitted in channels at mesoscale distances, obstructions such as terrain undulations or tall building groups can cause the formation of a shadow area behind the obstruction, leading to erratic changes in the average power of the received signal. It fades in a manner that roughly corresponds to a lognormal distribution [19]. When a radio signal rapidly changes in amplitude, phase, or multipath delay over a short period of time or space (a few wavelengths), it is referred to as small-scale fading. It is caused by the same transmission signal traveling along different paths, and the signals arriving at the receiver at different moments (or phases) are superimposed on each other. The signals that travel along these various paths include direct path and multipath signals produced by scatterers, such as reflection, diffraction, and scattering. Small-scale channel modeling primarily takes the modeling of temporal dispersion parameters, frequency dispersion parameters, and spatial dispersion characteristics into account [20]. The symbols and descriptions of channel parameters are shown in Appendix A. According to the table in Appendix A, the omnidirectional received power can be described as  
\[P_{r-ommi}=\sum_{i,j}\sum_{k,m}P_{r}(AZ_{TX,i},EL_{TX,j},AZ_{RX,k},EL_{RX,m}) \cdot d_{T-R}, \tag{1}\]  
where \(i,j,k,m\) denote unique pointing directions indices in azimuth and elevation at the TX and RX, respectively. \(AZ_{TX,i},EL_{TX,j},AZ_{RX,k},EL_{RX,m}\) represent the TX azimuth and elevation angles, and the RX azimuth and elevation angles, respectively [21]. Path loss can be described as  
\[PL[\text{dB}]=FSPL[\text{dB}]+10 lg(\
icefrac{{d}}{{d_{0}}})+AT[\text{dB}]+X_{ \sigma}[\text{dB}], \tag{2}\]  
where \(FSPL\) implies free space path loss, \(AT\) is related to the attenuation factor which includes the collective attenuation effects of dry air (including oxygen), water vapor, rain, and haze. \(X_{\sigma}\) is a zero\(-\)mean Gaussian random variable with a standard deviation \(\sigma\) in dB. \(d_{0}\) signifies the free space reference distance, and should not exceed 5 m to guarantee free space propagation [22]. According to the Friis transmission equation, free space path loss can be described as  
\[FSPL[\text{dB}]=-32.44-20 lgd_{T-R}-20 lgf, \tag{3}\]  
the unit of \(d_{T-R}\) is km, the unit of \(f\) is MHz [23]. From another point of view, the directional path loss can be written as  
\[PL=P_{TX}+G_{TX}+G_{RX}-P_{r}. \tag{4}\]  
In addition, the relationship between time delay and T\(-\)R separation distance for Line of Sight (LOS) can be described as  
\[\tau=\frac{d_{T-R}}{c}, \tag{5}\]  
where \(c\) represents the electromagnetic wave propagation speed. Therefore, in the presence of multipath components, each multipath component has a slightly larger time delay than the direct path. The open-source millimeter wave channel modeling software simulator (NYUSIM Version 3.1) is used in this study to obtain the SSCM channel parameters [24]. At a T\(-\)R separation of 2000 m, Figure 2 depicts the frequency dependence of path loss using the statistical channel model.