# Quantification and Analysis of Carrier-to-Interference Ratio in High-Throughput Satellite Systems
## 5 Analysis of the CIR under Different Frequency Plans  
The adjustment of the frequency plan will directly affect the degree of interference between the co-channel beams. The variation in the interference degree will cause the variation in the CIR (and hence the carrier to interference and noise ratio, CINR), which will affect the system's capacity. This section takes 19 beams with 4-color reuse (single polarization) as an example. Assuming two different beam-to-color mapping schemes, namely, regular mapping and irregular mapping, are adopted, we analyze the user-link CIR of each beam under them, respectively, by using the quantization method described in Section 3 and the statistical method described in Section 4. Furthermore, it can provide an idea for our future exploration, namely, frequency planning optimization based on CIR optimization. The two mapping schemes, regular mapping and irregular mapping, are shown in Figure 10a,b, respectively. For regular mapping, the cell-center points of beams with the same color (except beam 1) always form a rectangular shape. Meanwhile, for irregular mapping, these points may form a parallelogram or a hexagon, not like in regular mapping with a rectangular shape. In addition, an important difference between these two mapping schemes is that the minimum spacing between beams with the same color for regular mapping is smaller than that for the irregular one. Each color corresponds to a certain frequency band, that is, the beams with the same color shall share the same uplink/downlink frequency band, and the interferences will appear among them consequently. In this simulation, we assume a Ka-band HTS for illustrative purposes and the simulation conclusion is also applicable to the satellite systems using other frequency bands, such as Ku. Specifically, the red color represents the uplink frequency of 27,500-28,125 MHz and the downlink frequency of 17,700-18,325 MHz, as shown on beams 4/7/9/11/15/17 in Figure 10a and beams 1/9/11/13/15/17/19 in Figure 10b. The yellow color represents the uplink frequency of 28125-28750 MHz and the downlink frequency of 18,325-18,950 MHz, as shown on beams 2/6/12/14 in Figure 10a and beams 2/5/12/18 in Figure 10b, respectively. The green color represents the uplink frequency of 28,750-29,375 MHz and the downlink frequency of 18,950-19,575 MHz, as shown on beams 3/5/8/18 in Figure 10a and beams 3/6/8/14 in Figure 10b, respectively. The orange color represents the uplink frequency of 29,375-30,000 MHz and the downlink frequency of 19,575-20,200 MHz, as shown on beams 1/10/13/16/19 in Figure 10a and beams 4/7/10/16 in Figure 10b, respectively. It is worth noting that these frequency values are taken only as an example and can be replaced by other values according to the actual situation. Figure 10: Two mapping schemes of 19 beams with 4 colors: (**a**) regular mapping and (**b**) irregular mapping. The \(-3\) dB beamwidths of the 19 beams are all assumed to be \(0.25^{\circ}\). UPC is considered for the uplink of each beam, and the output power of the downlink travelling wave tube (TWT) is 100 W. Moreover, the sub-satellite point (i.e., the intersection points of the line segment, from the satellite to the Earth's core, and the Earth's surface) is in beam 1. The gain function of the onboard user antenna is as follows [13]:  
\[g(\delta)=51.5-12\times(\delta/\theta_{\text{-3 dB}})^{2}. \tag{24}\]  
where \(\delta\) refers to the deviation angle between the user link and antenna center, \(0<\delta\leq 2\theta_{\text{-3 dB}}\), and \(\delta\) is specified in degrees. \(g(\delta)\), specified in dBi, is the antenna gain value when the deviation angle is \(\delta\). Finally, 51.5 is the peak gain in dBi, and \(\theta_{\text{-3 dB}}\) is the \(-3\) dB width of the beam in degree. In the simulation, the locations of the target user and interfering users in their respective areas are randomly generated and repeated 1000 times to obtain the cumulative distribution function of user-link CIR in 19 beams under different schemes.