# Challenges of Using the L-Band and S-Band for Direct-to-Cellular Satellite 5G-6G NTN Systems
## 4 Simulation Methodology
### Study Assumptions and Protection Criteria
Free-space propagation losses can be found using the following expression:  
\[L_{bfs}=32.4+20\log_{10}(f)+20\log_{10}(d) \tag{4}\]  
where \(L_{bfs}\) is the free-space basic propagation loss, \(f\) is the frequency in MHz, and \(d\) is the distance between the victim receiver and the interfering transmitter in km [21; 22]. Figure 7: Interference scenario in which the NTN satellite interferes with the incumbent system’s Earth station. All additional propagation losses formulas from Expression (2) can be found in ITU-R Recommendation 619 [23; 24]. To find the \(\varphi\) angle from the NTN satellite towards the victim receiver [25; 26], the following formula can be used; it should be noted that this formula can also be used to find the \(\varphi\) angle from the victim receiver towards the NTN satellite via substituting the appropriate formula values in reverse:  
\[ \begin{split}\varphi=arccos[\cos(\beta_{Tx-Rx})\cos(\beta_{\rm NTN })\cos(\alpha_{Tx-Rx}-\alpha_{\rm NTN})\\ +sin(\beta_{Tx-Rx})sin(\beta_{\rm NTN})]\end{split}  \tag{5}\]  
where \(\beta_{Tx-Rx}\) is the elevation angle of the NTN satellite towards the victim receiver, \(\alpha_{Tx-Rx}\) is the azimuth of the NTN satellite towards the victim receiver, \(\beta_{\rm NTN}\) is the elevation angle of the main lobe of the beam of the NTN satellite, and \(\alpha_{\rm NTN}\) is the azimuth of the main lobe of the beam of the NTN satellite. Given that the 5G NTN network will consist of a large number of satellites, aggregate interference should be considered. To calculate aggregate interference from numerous NTN satellites and beams, the following equation can be used [21]:  
\[I_{agg}=10\log_{10}(\sum_{i=satellites}\sum_{j=beams}\frac{I(i)}{10}\ ) \tag{6}\]  
The noise level at the input of the victim receiver can be expressed as follows:  
\[N=10\log_{10}(T)-228.6+10\log_{10}(B)(d) \tag{7}\]  
where \(N\) is the noise over the victim receiver bandwidth in dBW, \(T\) is the noise temperature of the victim receiver in K, \(B\) is the victim receiver bandwidth, and \(-228.6\) is the Boltzmann constant, expressed as \(\rm dBW/K/Hz\). The total system temperature will depend upon different external factors such as lighting discharges, emissions from atmospheric gases and hydrometeors, the ground or obstructions within the antenna beam, radiation from celestial sources, and human-made noise such as power transmission lines, electronic equipment, electrical machinery. Additionally, the amount of noise depends on the contribution from the equipment [21; 27]. Since the study calculates the \(C/(N+I)\) ratio of the incumbent satellite systems in the L-band and S-band, the desired signal must be calculated using the following expression:  
\[C=P_{wanted}+G_{wanted}(\varphi)+G_{victim}(\varphi)-L_{b} \tag{8}\]  
If the wanted and interfering signal levels are known, \(C/(N+I)\) can be expressed as follows:  
\[C/(N+1)=C-10\log_{10}\left[10\ \frac{I_{agg}}{10}\ +10\frac{N}{10}\right] \tag{9}\]  
where \(C\) represents the desired signal level of the victim satellite system in dBW, \(N\) represents the noise level of the victim receiver for a reference bandwidth in dBW, and \(I_{agg}\) represents the aggregate interference from all interfering satellites and beams [28; 29].