# Quantification and Analysis of Carrier-to-Interference Ratio in High-Throughput Satellite Systems
## 3 Quantification Method of CIR
### User Uplink  
The schematic diagram of co-channel interference in the user uplink is shown in Figure 5. The green continuous line represents the uplink of the useful signal, intended as the one from the actual user location to the satellite. The green dotted line represents the connection between the center of the cell that targets the user and the satellite. The red continuous line represents the uplink of the \(i\)-th interference signal; the red dotted line represents the connection between the center of the cell, where the \(i\)-th interfering user is located, and the satellite; \(P_{1}\) represents the terminal transmitting power of the target user; \(G_{T,1}\) represents the terminal antenna transmitting gain of the target user; \(L_{1}\) represents the path loss of the uplink of the useful signal; \(\theta_{1}\) represents the deviation angle of the uplink of the useful signal from its own cell center; \(G_{1}(\theta)\) represents the on-board antenna receiving gain function for the uplink of the useful signal; \(P_{i}\) represents the terminal transmitting power of the \(i\)-th interfering user; \(G_{T,i}\) represents the terminal antenna transmitting gain of the \(i\)-th interfering user; \(L_{i}\) represents the path loss of the uplink of the \(i\)-th interfering user; \(\theta_{i}\) represents the deviation angle of the uplink of the \(i\)-th interfering signal from its own cell center; \(G_{i}(\theta)\) represents the on-board antenna receiving gain function for the uplink of the \(i\)-th interfering signal; and \(\psi_{C,1,i}\) represents the deviation angle of the uplink of the \(i\)-th interfering signal from the center of the cell that targets the user.  
The CIR of the uplink for the target user is (without special instructions, the interference in the following section refers to the co-channel interference):  
\[\begin{array}{ll}(C/I)_{bu}&=\frac{(C)_{bu}}{\frac{1}{i}(L_{i})_{bu}}\\ &=\frac{P_{1}G_{T,1}G_{1}(\theta_{1})/L_{1}}{\frac{P_{1}}{i}P_{(}G_{T,i}G_{1}( \psi_{C,1,i})/L_{i}}\end{array} \tag{13}\]  
where \((I_{i})_{bu}\) is the power of the \(i\)-th interference signal received on the satellite and \((C)_{bu}\) is the power of the useful signal received on the satellite.  
Since uplink power control (UPC) is often adopted in HTS systems, the differences due to terminal transmitting power, terminal antenna gain, and path loss in different uplinks will be compensated. Finally, the signal powers received by the satellite from different terminals are uniform, namely:  
\[P_{i}G_{T,i}G_{i}(\theta_{i})/L_{i}=P_{1}G_{T,1}G_{1}(\theta_{1})/L_{1}. \tag{14}\]  
Figure 5: Schematic diagram of co-channel interference in the user uplink.  
Substituting Equation (14) into Equation (13), we can obtain:  
\[\begin{array}{ll}\left(C/I\right)_{bu}&=\frac{P_{\mathrm{G}}C_{\mathrm{T}}C_{ \mathrm{I}}(\theta_{\mathrm{I}})/L_{\mathrm{I}}}{\sum\limits_{i}P_{\mathrm{G}}C _{\mathrm{T}}C_{\mathrm{I}}(\theta_{\mathrm{I}})/L_{\mathrm{I}}}\\ &=\frac{P_{\mathrm{G}}P_{\mathrm{G}}G_{\mathrm{I}}(\theta_{\mathrm{I}})/L_{ \mathrm{I}}}{\sum\limits_{i}P_{\mathrm{G}}C_{\mathrm{I}}(\theta_{\mathrm{I}})/ L_{\mathrm{I}}}\\ &=1/\sum\limits_{i}\frac{G_{\mathrm{I}}(\varphi_{\mathrm{G}})}{G_{\mathrm{I}}( \theta_{\mathrm{I}})}\end{array} \tag{15}\]  
It can be seen that uplink interference occurs when the signal transmitted by the interfering user falls into the on-board receiving antenna for the target user. With the participation of the UPC, the CIR of the uplink is not related to the position of the target user but rather only to the positions of interfering users.