# Study of the Ionospheric Scintillation Radio Propagation Characteristics with Cosmic Observations
## 3 Experimental Results
### Statistical Analysis for SNR  
Figure 4 shows the probability density function of the normalized SNR when the normalized S4 values are 0.5, 0.7 and 0.9. In statistical analysis, the Parzen window method is used to fit the measured curve. Here, the fitting result is called the evaluated curve, which is applied to calculate the Nakagami-\(m\), \(\alpha\)-\(\mu\) and \(\kappa\)-\(\mu\) distribution models. All the data from solar maximum year 2014 and solar minimum year 2019 are selected for analyses. When S4 is 0.5, with moderate scintillation, the fitting curves of the Nakagami-\(m\) distribution and \(\kappa\)-\(\mu\) distribution are nearly the same. On the other hand, the \(\alpha\)-\(\mu\) distribution better approximates the measured SNR in 2019, when the solar activity is in the low phase. When S4 is 0.7, the fitting curves of the Nakagami-\(m\) distribution and \(\kappa\)-\(\mu\) distribution begin to diverge, and the \(\alpha\)-\(\mu\) distribution still outperforms the other two distributions in approximating the measured SNR in both 2014 and 2019. When S4 is 0.9,  
Figure 3: The yearly occurrences of ionospheric scintillation at different latitudes from 2010 to 2019.  
Figure 2: The probability histogram of the ionospheric amplitude scintillation with different intensities in the E and F layers from 2010 to 2019. The results are based on the data from all levels.  
the fitting performances of these three distributions are the most similar in 2014, with the \(\alpha\)-\(\mu\) distribution achieving the best fitting performance. For 2019, the \(\alpha\)-\(\mu\) distribution loses efficiency, and the \(\kappa\)-\(\mu\) distribution outperforms the Nakagami-\(m\) distribution.  
Figure 4 shows that the distribution of the normalized SNR demonstrated non-Gaussian distribution features [35]. The protruding part shows another peak of the distribution curve. With the increase in normalized S4, the protrusion decreases gradually. When the normalized S4 reaches approximately 0.7, the protrusion becomes mild.  
The ten-year COSMIC occultation data are studied, and the corresponding SNR distributions are shown in Figure 5. The Nakagami-\(m\) and \(\kappa\)-\(\mu\) distribution curves are quite close to each other when S4 ranges from 0.4 to 0.6, showing \"high and thin\" shapes. The \(\alpha\)-\(\mu\) distribution fits the measured SNR better when \(S4\geq 0.6\). With increasing scintillation intensity, the fitting performance of the Nakagami-\(m\) and \(\kappa\)-\(\mu\) distributions starts to diverge. When 54 is 0.9, the fitting performances of the Nakagami-\(m\) and \(\alpha\)-\(\mu\) distributions are very similar, and when 54 is 1.0, the Nakagami-\(m\) distribution outperforms the other two distributions. It is preliminarily considered that the fitting performance of the \(\alpha\)-\(\mu\) distribution curve is the best when \(S4\geq 0.6\), which is consistent with the results from ground-based observations [29].  
Table 2 shows the calculated values of the parameters \(\alpha\) and \(\mu\) under different scintillation intensities assuming \(\beta\) = 3. As shown by [PERSON] et al., the relationship of \(\alpha\) and S4 can be estimated [41]. By analyzing the \(\alpha\) parameters in the table, it is noticed that the \(\alpha\) parameter decreases with the increase in S4. This phenomenon also occurs in the variation of the \(\alpha\) parameter calculated in ground-based observations. When the normalized amplitude scintillation index is equal to 0.9, \(\alpha\) is 1.9489, close to 2. When \(\alpha\) = 2, the Nakagami-\(m\) distribution function and \(\alpha\)-\(\mu\) distribution function are equal. Therefore, the fitting performance of these two standard probability density distribution curves should be close [43].  
Figure 4: The normalized signal-to-noise probability density curve when S4 = 0.5, S4 = 0.7, S4 = 0.9 in 2014 and 2019 are considered.