# Study of the Ionospheric Scintillation Radio Propagation Characteristics with Cosmic Observations
## 1 Introduction
Many researchers use global positioning system (GPS) signals at low latitudes to reveal the propagation channel characteristics under scintillation [25; 26; 27]. It was assumed that GPS signals suffered amplitude attenuations and phase jitters due to scintillation, which caused different statistical propagation distributions compared with the known Rice and Rayleigh distribution. [PERSON] and [PERSON] first used the Nakagami-\(m\) model to describe the scintillation signal propagation features. The model was verified to most closely approximate the scintillation impacts on GPS signals in real experiments [1]. [PERSON] et al. investigated the probability distribution of ionospheric plasma intensities, revealing that the fluctuations of plasma intensities in the scintillation scale were far from the Gaussian distribution but similar to the Laplacian distribution. They also simulated the propagation of trans-ionosphere radio signals in ionospheric irregularities with two-dimensional phase screens under Gaussian and Laplacian assumptions. The relationship between non-Gaussian distributions and phase scintillation and delay time for signal propagation were discussed [28]. [PERSON] et al. further used real multifrequency GPS observables to study the dependency of scintillation on frequencies, with 150 nights of scintillation samples collected at the Sao Jose dos Campos site in Brazil [6]. They fitted the statistical features of GPS L1 signals under amplitude scintillation and tested the Nakagami-\(m\), Rician and \(\alpha\)-\(\mu\) distributions. The results show the superior fitting performance of the \(\alpha\)-\(\mu\) distribution over the other two models. This work indicates that the signal features can vary under different scintillation situations, which can be represented by different combinations of \(\alpha\) and \(\mu\) parameters. Further verification was conducted with long-term ground scintillation observations in Australia, showing that the values of \(\alpha\) and \(\mu\) are related to geophysical locations. The use of entropy evaluation proved the convincing region for \(\alpha\)-\(\mu\) and Nakagami-\(m\) distributions under different scintillation intensities [29]. Based on these results, the \(\kappa\)-\(\mu\) distribution was applied to describe the radio propagation channel under severe scintillation and compared with the \(\alpha\)-\(\mu\) distribution. It was noted that the \(\kappa\)-\(\mu\) distribution failed to achieve a better fitting accuracy in general situations but demonstrates better approximation to reality under extreme scintillation conditions. From theoretical aspects, the \(\alpha\)-\(\mu\), \(\kappa\)-\(\mu\) and \(\eta\)-\(\mu\) distributions were all proposed by [PERSON] [30; 31]. The \(\alpha\)-\(\mu\) distribution is considered a rewritten form of the general Gama distribution, while the \(\kappa\)-\(\mu\) distribution is a special form of the single lateral Gaussian distribution and \(\eta\)-\(\mu\) has potential applications for nonlinear cases. [PERSON]'s contributions break the traditional constraints for signal propagation modeling under complicated situations. Further investigations under different scintillation scenarios are warranted. Most studies on radio propagation under ionospheric scintillation have concentrated on ground-based receivers, in which the trans-ionospheric signals propagated in space-ground directions [32]. However, there is also another situation in which trans-ionospheric signals propagate from space to the receiver installed on low earth orbit (LEO) satellites, for instance, in the space-LEO directions [33; 34]. GNSS signals received by Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) satellites are in such a situation. When COSMIC satellites were first launched, researchers at the University Corporation for Atmospheric Research (UCAR) tried to investigate the signal propagation paths with simulation.