# Quantification and Analysis of Carrier-to-Interference Ratio in High-Throughput Satellite Systems
## 5 Analysis of the CIR under Different Frequency Plans
Taking beam 1 as an example (the other beams are similar), we compare and illustrate the influence of the two schemes on the cumulative distribution function of the CIR, as shown in Figure 11.  
A point on any line in Figure 11 has the following meaning. If the point coordinate is (x, y), it means that the number of CIR results lower than x in this 1000-times simulation  
Figure 11: CDF of the CIR in the user link of beam 1 for the two mapping schemes: (a) user uplink and (b) user downlink. is 1000 \(\times\) y. For two comparative lines, if point A is on line 1, point B is on line 2, the horizontal coordinates of A and B are both equal to x, and the horizontal coordinates of A and B are \(y_{1}\) and \(y_{2}\) and \(y_{1}\) < \(y_{2}\), respectively, we can easily derive that the number of CIR results lower than x in this 1000-times simulation is 1000 \(\times\) y\({}_{1}\) for line 1, while this value is 1000 \(\times\) y\({}_{2}\) for line 2. It is evident that line 1 corresponds to a better scheme in terms of the CIR level. Hence, we can conclude that the lower line is better for the result shown in Figure 11.  
It can be seen from Figure 11 that in 1000 simulation cases, for the user uplink of beam 1, the minimum CIR value under regular mapping is lower than 10 dB, while the minimum CIR value under irregular mapping is higher than 15 dB. Moreover, the corresponding maximum CIR values under the two schemes are similar. For the user downlink of beam 1, the minimum and maximum CIR values under regular mapping are lower than 11 dB and 24 dB, respectively, while the corresponding values under irregular mapping are higher than 15 dB and 28 dB. Specifically, with 20 dB as the reference value, the probability of meeting the reference value under regular mapping and irregular mapping is about 60% and 80%, respectively, regardless of the user uplink or downlink in beam 1. Therefore, irregular mapping is significantly better than regular mapping in terms of beam 1. In order to comprehensively consider all 19 beams, the CIR values satisfying the requirements of 100% coverage and 85% coverage are taken as the reference to compare the two schemes for all beams. The CIR of the user uplink and downlink are shown in Tables 1 and 2, respectively. In order to show the comparison effect more clearly, bar charts comparing the CIR of the user uplink and downlink for all beams with the 85% coverage requirement (the other coverage requirements are similar) are formed, as shown in Figure 12a,b, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Beam Number**} & **Regular Mapping** & **Irregular Mapping** & **Regular Mapping** & **Irregular Mapping** \\  & **(100\%)** & **(100\%)** & **(85\%)** & **(85\%)** \\ \hline
1 & 9.2606 & 14.9872 & 16.1319 & 18.8604 \\
2 & 10.1616 & 15.7991 & 18.9329 & 22.4388 \\
3 & 9.  
in bold. In addition, irregular mapping can make the CIR of the user uplink or downlink more balanced for all of the beams. Specifically, as shown in Figure 6, the variance in the user-uplink CIR in all beams obtained by regular mapping is 8.735, and the variance is 8.542 for user downlink. However, the variance in the user uplink CIR and user downlink CIR is only 1.393 and 1.805 under irregular mapping, respectively. From the above simulation cases, it is obvious that the frequency plan has a significant impact on the CIR. In general, the larger the minimum spacing between the beams at the same frequency (maximizing the minimum spacing at the same frequency), the better the system's CIR performance. Therefore, we can follow the above idea to explore the optimization scheme of the frequency plan based on the improvement of the CIR.