# Quantification and Analysis of Carrier-to-Interference Ratio in High-Throughput Satellite Systems
## 2 System Model
The receiver's figure of merit can be obtained by:  
\[G/T=G_{r}-10\lg\left(T_{A}+\left(10^{L_{t}/10}-1\right)T_{p}+10^{L_{r}/10}T_{ r}\right), \tag{5}\]  
where \(G/T\) is the receiver's figure of merit specified in dB/K, \(G_{r}\) is the gain of the receiving antenna specified in dBi, \(T_{A}\) is the output noise temperature of the antenna specified in K, \(L_{r}\) is the feeder loss at the receiver and the unit is in decibels, \(T_{p}\) is the feeder temperature specified in K, and \(T_{r}\) is the effective input noise temperature of the receiver specified in K.  
The carrier-to-noise ratio (CNR) of the uplink and downlink can be then obtained, respectively:  
\[\left[C/N\right]_{u}=\left[EIRP\right]_{e}-L_{u}-\Delta L_{u}+\left[G/T\right] _{s}-10\lg(kB), \tag{6}\]  
\[\left[C/N\right]_{d}=\left[EIRP\right]_{s}-L_{d}-\Delta L_{d}+\left[G/T\right] _{e}-10\lg(kB), \tag{7}\]  
where \(\left[C/N\right]_{u}\) and \(\left[C/N\right]_{d}\) are the CNRs of the uplink and downlink, respectively, specified in decibels; \(\left[EIRP\right]_{e}\) and \(\left[EIRP\right]_{s}\) are the effective isotropic radiated power of the earth  
\[B_{total}=(\frac{N_{p}N_{b}}{N_{c}})B_{w}(1-\eta_{guard}), \tag{1}\]0 Four-color reuse scheme among all of the beams. station (or the terminal) and the satellite, respectively, specified in dBW; \(L_{u}\) and \(L_{d}\) are the propagation losses in the free space of the uplink and downlink, respectively, specified in decibels; \(\Delta L_{u}\) and \(\Delta L_{d}\) are the additional losses (including atmospheric absorption, pointing error, and polarization loss) of the uplink and downlink, respectively, specified in decibels; \(\left[G/T\right]_{s}\) and \(\left[G/T\right]_{e}\) are the figures of merit of the satellite and the Earth station (or the terminal), respectively, specified in dB/K; \(k\) is the Boltzmann's constant; and \(B\) is the receiver's bandwidth specified in Hz. Based on the CNR of the uplink and downlink, \(\left[C/N\right]_{u}\) and \(\left[C/N\right]_{d}\), the total CNR of the entire link, \(C/N\), for a conventional frequency translation satellite, can be approached as follows [13]. \(\left[C/N\right]_{u}\), \(\left[C/N\right]_{d}\), and \(C/N\) are all specified in decibels. \[B_{total}=(\frac{N_{p}N_{b}}{N_{c}})B_{w}(1-\eta_{guard}), \tag{1}\]1  
By combining the total CNR, \(C/N\), and the system CIR, \(C/I\), which is just our research focus in this paper, we can obtain the carrier-to-interference-plus-noise ratio \(C/\left(I+N\right)\)[13]:  
\[B_{total}=(\frac{N_{p}N_{b}}{N_{c}})B_{w}(1-\eta_{guard}), \tag{1}\]2  
followed by the ratio of the signal power per bit to noise power spectrum \(E_{b}/N_{0}\):  
\[B_{total}=(\frac{N_{p}N_{b}}{N_{c}})B_{w}(1-\eta_{guard}), \tag{1}\]3  
where \(R_{b}\) is the information transmission rate specified in bps. Based on \(E_{b}/N_{0}\), we can derive the available highest-level modulation coding mode and then the system capacity. Through the whole derivation process, we can conclude the importance of \(C/I\) for the system capacity budget.