# A Power Control and Intervention Algorithm for Co-Existing IMT Base Stations and Satellite Services
## 2 System Model
### Aggregate Interference Calculations  
In order to evaluate the aggregated interference caused by multiple IMT macro-base stations to FSS spatial receivers, the interference from each BS sector is first calculated as follows:  
\[I_{i}^{DL}=P_{t}+G_{t}(\theta_{t})+G_{r}(\theta_{r})-PL-OL, \tag{11}\]  
where \(I_{i}\) denotes the single incoming interference power from the base station \(i\) in dBm/MHz. \(P_{t}\) is the signal power density of one base station in dBm/MHz. \(G_{t}\) (\(\theta_{t}\)) is the base station antenna gain in the direction of the FSS spatial receiver after viewing the beamforming antenna direction map in dBi. \(G_{r}\) (\(\theta_{r}\)) is the gain of the FSS space receiver antenna in the direction of the base station after considering the off-axis angle, in dBi. \(PL\) is the propagation loss, including polarisation discrimination, clutter loss, free-space path loss and atmospheric gas attenuation, in dB. \(OL\) is the transmitter station array ohmic loss in dB. The overall interference level caused by all IMT-2020 base stations after considering TDD is:  
\[I_{\text{total}}=10\log\left(0.75*\sum_{i=1}^{i=N_{DL}}10^{i_{i}^{DL}/10} \right), \tag{12}\]  
The thermal noise power density of the FSS spatial receiver can be calculated as  
\[N_{0}=10*\log(k*T*1000*B)=-110.61\quad(\text{dBm / MHz}), \tag{13}\]  
Finally, \(I/N\) can be expressed as \(I_{i}otal-N_{0}\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{
\begin{tabular}{c} **Elevation** \\ **Angle** \\ \end{tabular} } & \(\sigma_{SF}^{2}\) **in the** & \(\sigma_{SF}^{2}\) **in the** & \(CL\) **in the** & \(\sigma_{SF}^{2}\) **in the** & \(\sigma_{SF}^{2}\) **in the** & \(CL\) **in the** \\  & **S-Band LOS** & **S-Band NLOS** & **S-Band NLOS** & **Ka-Band LOS** & **Ka-Band NLOS** & **Ka-Band NLOS** \\  & **Scenario** & **Scenario** & **Scenario** & **Scenario** & **Scenario** & **Scenario** \\ \hline
10 & 1.79 & 8.93 & 19.52 & 1.9 & 10.7 & 29.5 \\
20 & 1.14 & 9.08 & 18.17 & 1.6 & 10.0 & 24.6 \\
30 & 1.14 & 8.78 & 18.42 & 1.9 & 11.2 & 21.9 \\
40 & 0.92 & 10.25 & 18.28 & 1.3 & 11.6 & 20.0 \\
50 & 1.42 & 10.56 & 18.63 & 2.7 & 11.8 & 18.7 \\
60 & 1.56 & 10.74 & 17.68 & 2.1 & 10.8 & 17.8 \\
70 & 0.85 & 10.17 & 16.50 & 3.0 & 10.8 & 17.2 \\
80 & 0.72 & 11.52 & 16.30 & 3.6 & 10.8 & 16.9 \\
90 & 0.72 & 11.52 & 16.30 & 0.4 & 10.8 & 16.8 \\ \hline \end{tabular}
\end{table}
Table 4: Shadow fading and clutter loss in suburban environments.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{
\begin{tabular}{c} **Elevation** \\ **Angle** \\ \end{tabular} } & \(\sigma_{SF}^{2}\) **in the** & \(\sigma_{SF}^{2}\) **in the** & \(CL\) **in the** & \(\sigma_{SF}^{2}\) **in the** & \(\sigma_{SF}^{2}\) **in the** & \(CL\) **in the** \\  & **S-Band LOS** & **S-Band NLOS** & **S-Band NLOS** & **Ka-Band LOS** & **Ka-Band NLOS** & **Ka-Band NLOS** \\  & **Scenario** & **Scenario** & **Scenario** & **Scenario** & **Scenario** \\ \hline
10 & 4 & 6 & 34.3 & 4 & 6 & 44.3 \\
20 & 4 & 6 & 30.9 & 4 & 6 & 39.9 \\
30 & 4 & 6 & 29.0 & 4 & 6 & 37.5 \\
40 & 4 & 6 & 27.7 & 4 & 6 & 35.8 \\
50 & 4 & 6 & 26.8 & 4 & 6 & 34.6 \\
60 & 4 & 6 & 26.2 & 4 & 6 & 33.8 \\
70 & 4 & 6 & 25.8 & 4 & 6 & 33.3 \\
80 & 4 & 6 & 25.5 & 4 & 6 & 33.0 \\
90 & 4 & 6 & 25.5 & 4 & 6 & 32.9 \\ \hline \end{tabular}
\end{table}
Table 3: Shadow fading and clutter loss in urban environments.