# Quantification and Analysis of Carrier-to-Interference Ratio in High-Throughput Satellite Systems
## 1 Introduction
For example, it is mentioned in reference [7] that when the frequency reuse factor is 1, 2, 3, or 4, the CIR is about 0 dB, 8 dB, 25 dB, or 30 dB, respectively. In particular, the range is between 14 dB and 34 dB when the frequency reuse factor is 4. In references [8; 9], the CIR was set to 18 dB and 15 dB, respectively. In reference [10], the value of co-frequency co-polarization interference was set to 20 dB, while  
Figure 1: Different coverage modes in satellite systems: (**a**) single-beam coverage and (**b**) multi-beam coverage. the value of co-frequency cross-polarization interference and co-polarization interference of different frequencies were both set to 25 dB. In reference [11], the CIR was set to 16 dB for the reuse factor of 4. It is worth noting that these typical values are difficult to fully fit various real-world scenarios and are not persuasive due to a lack of theoretical support. In addition, some researchers take the actual measured values of the CIR as the input to conduct their research. For example, in reference [12], the authors obtained the CIR geographical maps in dB for the KaSat coverage and came to the conclusion that the CIR increases when the beamwidth is narrower. This method may facilitate the accuracy of the research, but it is hard to obtain the data and inconvenient for theoretical research and model demonstration. Furthermore, there are considerable efforts in the literature [13; 14] devoted to developing the interference model and frequency reuse solutions in HTS, and a relatively concise calculation method was proposed for the calculation of the CIR. That is, the equivalent isotropically radiated power (EIRP) or on-board antenna gain value of the useful signal relative to the target user divided by the sum of the EIRP or on-board antenna gain value of interference signals relative to the target user. The calculation of the CIR is closer to the definition but is not conducive to the actual calculation, and the uplink and downlink are also not fully discussed. Similar to references [13; 14], reference [15] provides an expression of co-channel interference power, which equals the sum of the power level of interference inside the target beam coming from all interfering beams of the target beam. However, this expression is conceptual and cannot indicate how we can derive the power level of interference. Reference [16] focused on the overall system design and introduced two software tools for system evaluation and analysis. In detail, the beam-drawing software developed by the University of Surrey can accomplish the gridding calculation of the CIR in the beam coverage area, and the calculation formula of the user link CIR is also known. However, the scenarios with multi-carriers in one beam related to the band plan and the influence of different frequency allocation schemes on the system CIR are not included in reference [16]. In summary, this has become a trend in CIR evaluation, from being computable to accurate and widely used. The difficulties lie in the in-depth analysis of the co-channel interference mechanism in multi-beam satellite systems and the derivation of closed-form expressions of the CIR that are compatible with various application scenarios. The application scenarios include not only geostationary orbit satellites but also non-geostationary orbit (NGSO) satellites, especially direct-to-satellite IoT (DtS-IoT) applications. In reference [17], the authors address massive MIMO in NGSO systems, which can substantially enhance spectral efficiency while bringing about inter-beam interference due to frequency reuse and the non-zero side lobes. In addition, the authors also emphasize the interference issue in waveform design, multiple access design, the co-existence of NGSO systems with other satellite systems and terrestrial networks, the emerging NGSO constellations, the inter-satellite links, and so on. Consequently, as the authors indicate, the interference quantification/management/cancellation should be paid more attention.