## 2 Materials and Methods
It is calculated using the specific attenuations for vapors \(\gamma_{w}\) and oxygen \(\gamma_{o}\), as:  
\[L_{g}[dB]=(\gamma_{o}+\gamma_{w})d \tag{6}\]  
The fog/cloud attenuation is a function of distance, signal frequency, fog/cloud temperature, and fog/cloud water density, as shown in [17]. The information about clouds is contained in the specific attenuation, defined as:  
\[\gamma_{c}[dB/km]=K(f)M \tag{7}\]  
where \(K(f)\) is a specific attenuation coefficient which depends on frequency and \(M\) is the liquid water density. The determination of the total attenuation for a signal transmitted on a path is based on (8), where \(r\) is the path distance:  
\[L_{c}[dB]=\gamma_{c}r \tag{8}\]  
The total atmospheric losses \(L_{atm}\) is defined as the sum of the aforementioned losses. Additionally, these important losses, there may be various other additional losses that are taken into account at the reception, such as: polarization loss \(L_{pol}\), antenna mispointing loss \(L_{mis}\) or interference loss \(L_{interf}\). Among these, polarization loss could be the strongest and occurs when the polarization of the transmitted signal does not perfectly match that of the receiving antenna. Polarization loss is derived from the polarization mismatch angle \(Pol_{mis}\) and can be defined as:  
\[EIRP[dBW]=P_{TxHPA}[dBW]-OBO_{TxHPA}[dB]-L_{TxFeder}[dB]-L_{TxOther}[dB]+G_{Tx}[ dBi]-L_{Radome}[dB] \tag{1}\]0  
When the signal reaches the satellite, one of the fundamental parameters is given by the Received Isotropic Power (RIP), calculated by subtracting the total propagation losses from the transmitted EIRP [18], as shown in Equation (10). \[EIRP[dBW]=P_{TxHPA}[dBW]-OBO_{TxHPA}[dB]-L_{TxFeder}[dB]-L_{TxOther}[dB]+G_{Tx}[ dBi]-L_{Radome}[dB] \tag{1}\]1  
Once at the reception, the signal must be qualitatively analyzed so that the received information can be verified. For this, an essential indicator of link quality is given by \(\frac{C}{N_{o}}\) ratio (Carrier-to-Noise Density Ratio), which represents the ratio of carrier power to spectral noise density [19]. In general, it can be defined as in Equation (11):  
\[EIRP[dBW]=P_{TxHPA}[dBW]-OBO_{TxHPA}[dB]-L_{TxFeder}[dB]-L_{TxOther}[dB]+G_{Tx}[ dBi]-L_{Radome}[dB] \tag{1}\]2  
where \(P_{r}\) is the power of the received signal (carrier), \(k\) is [PERSON]'s constant and \(T\) is the temperature of the system. Customizing the equation for the previously defined notions, this ratio can also be written as a function of the received isotropic power \(RIP\), the reception gain related to the system temperature \(\left(G/T\right)_{Rx}\), the Boltzmann's constant, the feeder loss \(L_{Rxfinder}\) and other losses \(L_{RxOther}\):  
\[EIRP[dBW]=P_{TxHPA}[dBW]-OBO_{TxHPA}[dB]-L_{TxFeder}[dB]-L_{TxOther}[dB]+G_{Tx}[ dBi]-L_{Radome}[dB] \tag{1}\]3  
When we want to evaluate this information over a certain bandwidth \(B\), we get the \(\frac{C}{N}\) ratio (Carrier-to-Noise Ratio), defined as:  
\[EIRP[dBW]=P_{TxHPA}[dBW]-OBO_{TxHPA}[dB]-L_{TxFeder}[dB]-L_{TxOther}[dB]+G_{Tx}[ dBi]-L_{Radome}[dB] \tag{1}\]4  
Another key parameter in determining link performance, reflecting the ability of the system to maintain a certain bit error rate at a given noise level is the received \(\frac{E_{b}}{N_{o}}\) ratio (Energy per Bit to Noise Power Density Ratio) [20], defined in Equation (14) and expressed in \(dB\) in Equation (15):  
\[EIRP[dBW]=P_{TxHPA}[dBW]-OBO_{TxHPA}[dB]-L_{TxFeder}[dB]-L_{TxOther}[dB]+G_{Tx}[ dBi]-L_{Radome}[dB] \tag{1}\]5  
\[EIRP[dBW]=P_{TxHPA}[dBW]-OBO_{TxHPA}[dB]-L_{TxFeder}[dB]-L_{TxOther}[dB]+G_{Tx}[ dBi]-L_{Radome}[dB] \tag{1}\]6  
where \(B_{r}\) is the bit rate or information transmission rate expressed in bits per second (bps). In this situation, we can determine the margin, a parameter that indicates the extra power or spare capacity available above the minimum necessary to ensure an acceptable quality of communication under normal operating conditions.