## 4 Methodology of Simulations  
The study employed a hybrid approach, combining deterministic analysis and Monte Carlo simulations. The deterministic aspect involved calculating the orbital positions of the satellites based on Kepler's laws, while the Monte Carlo simulations were utilized to generate interfering transmitters from user equipment (UE). This process enabled us to estimate the cumulative interference caused by terrestrial UE on the NTN satellite receiver. For more precise results the simulations had a step size of 1 s. Due to the complex computations, they are performed in corresponding toolkits of Matlab at the same time, to understand the mathematics that lie behind these computations. Several of the most important expressions are provided to understand how the results were obtained.  
In the case of a space-to-space interference scenario, \(PL\) can be calculated using the free space propagation model, following Recommendation ITU-R P.525 [14].  
The interference level from the i-th interfering station can be calculated using the following expression:  
\[I=P_{interfer}+G_{interfer}(\varphi)+G_{victim}(\varphi)-PL\]  
where \(I\) represents the interference level caused by the the i-th interfering station. \(P_{interfer}\) denotes the output power of the interfering station, expressed in dBW. \(G_{interfer}\) stands for the gain of the transmitting antenna on the interferer satellite, directed to the victim receiver, and measured in dBi. \(G_{victim}\) represents the gain of the receiving antenna at the victim receiver station, oriented to the interfering station, and is also measured in dBi. \(PL\) stands for the propagation loss between the interfering transmitter and the victim receiver, measured in dB.  
To calculate the aggregate interference level from Starlink, the following expression can be used [14]:  
\[I_{agg}=10\log(\sum_{j=satellites}\sum_{j=beams}10^{\frac{(I)}{10}})\]  
The Carrier-to-Noise-and-Interference Ratio (C/(N + I)) for the transmission link between the satellite and UE can be derived from the Carrier-to-Noise Ratio (C/N) and Carrier-to-Interference Ratio (C/I), as indicated by the following equations [13;14]:  
\[C/(N+I)=-10\log\left(10^{-0.1C/N}+10^{-0.1C/I}\right)\]  
Figure 4: Antenna pattern approximations of NTN satellite and Starlink used in the simulations.  
The formula for C/N calculation is [15; 16]  
\[C/N=EIRP+G/T-k-PL-B\]  
where _EIRP_ stands for effective isotropic radiated power (EIRP), expressed in dBW, \(G/T\) is the antenna-gain-to-noise-temperature, measured in dB, \(k\) is the Boltzmann constant and equals to 228.6 \(\mathrm{dBW/K/Hz}\), \(PL\) is the free space pathloss, and \(B\) is channel bandwidth in dBHz.  
The antenna-gain-to-noise-temperature \(G/T\) can be derived by the following equation [16]:  
\[G/T=G_{R}+N_{f}-10\log\left(T_{0}+(T_{r}-T_{0})10^{-0.1N/f}\right)\]  
where \(G_{R}\) is the receiver antenna gain, \(N_{f}\) is the noise figure, \(T_{0}\) is the environment temperature, and \(T_{r}\) is the receiver.  
The pathloss between the interfering Starlink satellites and victim \(\mathrm{MSS/NTN}\) satellites can be calculated using the following traditional free space expression [17]:  
\[PL=32.4+20\log(f)+20\log(d)\]  
where \(f\) represents the frequency of the transmitter and \(d\) represents the distance between an interfering transmitter and a victim receiver.