# Quantification and Analysis of Carrier-to-Interference Ratio in High-Throughput Satellite Systems
## 2 System Model  
The HTS communication system consists of a space segment that includes the satellite constellation, a ground segment including gateway (GW) stations and large ground facilities for control, network operations, and backhauling, and a user segment with the user terminals deployed on fixed and mobile platforms (e.g., airplanes and ships) [25], as shown in Figure 2.  
The space segment adopts the bent-pipe repeater, and the repeater is divided into the forward link and the return link. The forward link is from the ground gateway to the satellite and then to the ground users. The return link is just the opposite. According to the targeted object, the repeater can also be divided into the user link and the feeder link. The user link refers to the link between the satellite and the ground users, which can be further divided into the user uplink and user downlink. The feeder link refers to the link between the satellite and the ground gateway, which can be further divided into the feeder uplink and feeder downlink. The system utilizes the Ka band or the Q/V band as the communication frequency of feeder links and the Ka or Ku band for user links. The common model for frequency reuse in high-throughput satellite systems is as follows [26]. The allocated bandwidth to a satellite, \(B_{w}\), is first sliced into sub-bands, typically two or three. A guard band is necessary between the adjacent sub-bands. Then, right-hand or both right- and left-hand polarization are used with the sub-bands. Each sub-band and polarization type constitutes a color (see Figure 3). Then, each color is assigned to a spot beam, and Figure 4 shows the four-color reuse scheme among all the beams. Furthermore, as long as the colors do not overlap, they can be reused in separate spot beams as many times as needed/possible (subject to various constraints including the antenna size, power limitation, pointing accuracy, and the system CIR discussed in this paper). Based on the frequency reuse scheme, the total bandwidth in the system can be calculated as follows:  
\[B_{total}=(\frac{N_{p}N_{b}}{N_{c}})B_{w}(1-\eta_{guard}), \tag{1}\]  
where \(N_{p}\) is the number of polarization (1 or 2), \(N_{c}\) is the number of colors, \(N_{b}\) is the number of beams, and \(\eta_{guard}\) is the guard band relative to the bandwidth of a single channel (typically 5% to 10%). For example, a 2.5 GHz allocated bandwidth can translate into 112.5 GHz total bandwidth for the satellite when allocated to 4 colors with 2 polarizations and 100 spot beams (\(\eta_{guard}=0.1\) for a 10% guard scheme). Figure 3: Examples of 3, 4, and 6 colors for frequency reuse. Figure 2: Architecture diagram of high-throughput satellite systems. The common model for the link budget in such systems is as follows. The propagation distance in free space can be obtained by:  
\[d=\sqrt{R^{2}+\left(R+H\right)^{2}-2R(R+H)\cos(\theta_{1}-\theta_{2})\cos(\varphi _{1}-\varphi_{2})}, \tag{2}\]  
where \(d\) is the propagation distance in free space specified in meters; \(R\) is the earth radius specified in meters; \(H\) is the minimum distance between the satellite and the Earth's surface and the unit is also in meters; \(\theta_{1}\) and \(\theta_{2}\) are the longitudes of the satellite and the Earth station, respectively, in degrees; and \(\varphi_{1}\), \(\varphi_{2}\) are the latitudes of the satellite and the Earth station, respectively, in degrees. The propagation loss can be calculated by:  
\[L=10\lg\left(\frac{4\pi d}{\lambda}\right)^{2}, \tag{3}\]  
where \(L\) is the propagation loss in free space specified in decibels and \(\lambda\) is the working wavelength specified in meters. The effective isotropic radiated power of transmitting antennas can be calculated by:  
\[EIRP=P-L_{t}+G_{t}, \tag{4}\]  
where \(EIRP\) is the effective isotropic radiated power specified in dBW, \(P\) is the transmitting power specified in dBW, \(L_{t}\) is the feeder loss at the transmitter and the unit is in decibels, and \(G_{t}\) is the gain of the transmitting antenna specified in dBi.