# Towards 6G Satellite-Terrestrial Networks: Analysis of Air Mobility Operations
## 3 Link Budget Analysis
### Attenuations  
The communication system is expected to experience attenuation losses due to the various factors outlined below:  
* Free space path loss: An essential component of the link budget analysis, the free space path loss (FSPL) quantifies the reduction in signal strength as it travels through open space unimpeded by any obstacles or interference. The formula for calculating the free space loss (\(L_{FS}\)) is presented in Equation (4). \[20\log\left(\frac{4\pi d}{\lambda}\right)=20\log(d)+20\log(f)+20\log(4\pi/c)\] (4) where \(d\) represents the distance between the base station/satellite and the UAS.
* Doppler effect: Given that the UAS will be moving at some speed, the Doppler effect must be considered when determining the received power (\(P_{RX}\)). This consideration is incorporated into the formula as depicted in Equation (5), as all the variables in the equation are expressed in dB. \[P_{RX}=P_{TX}+G_{TX}-L_{TX}-L_{FS}-L_{M}+G_{RX}-L_{RX}\pm 10 log(f_{ds})\] (5) where \(f_{ds}\) is the shift in the Doppler effect given in Equation (6): \[f_{ds}=v_{rel}\frac{f}{c}\] (6)  
\(v_{rel}\) is the relative velocity of the UAV with respect to the base station/satellite. In the case of satellites, the relative velocity is considered to be the orbit velocity of the satellite. In Equation (5), the \(\pm\) symbol indicates the direction of travel of the UAV--whether it is moving towards or away from the base station. For this particular scenario, it is assumed that the UAV is departing from the base station; therefore, the '\(-\)' sign is applied.  
* Atmospheric attenuation: Atmospheric attenuation, mainly due to atmospheric gases, significantly influences the link budget of communication systems, particularly at higher frequencies. This type of attenuation adds to the total path loss and impacts the strength of the signal that is received. The attenuation, represented as \(\gamma\) (dB/km), is determined using the formula shown in Equation (7). \[\gamma=\gamma_{o}+\gamma_{w}\] (7) In this context, \(\gamma_{o}\) represents the specific attenuation due to dry air, and \(\gamma_{w}\) signifies the specific attenuation due to water vapor. The attenuation of the signal caused by the atmosphere is determined by multiplying the overall specific attenuation, \(\gamma\), by the distance, \(d\), that the signal travels through the gas. Therefore, the power loss from gas attenuation, denoted as \(L_{atm}\), can be computed using Equation (8). \[L_{atm}=\gamma d\] (8)
* \(R\) represents the rain rate in mm/h.
- \(k\) denotes the specific attenuation measured in dB/km.
- \(\alpha\) is the polarization constant, which can differ, based on the polarization orientation. \(k\) and \(\alpha\) are considered to be \(k_{V}\) and \(\alpha_{V}\) for vertical polarization. The scenario presented considers vertical polarisation only. The impact of this attenuation on signal losses due to rain can be calculated as shown in the next equation, where v is the vertical component of the distance from the UAV to the base station. \[L_{rain}=A_{rain}*\
u\] (10) In the case of satellite communications, the rain and atmospheric attenuations are limited to a certain altitude. The rain attenuation happens below the clouds, and the atmospheric attenuation significantly drops beyond the stratosphere. This can be visualized using Figure 2.  
Figure 2: Attenuation limits along the signal path.