## 1 Introduction
### Motivation and Contributions of This Paper
\begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Definition** \\ \hline \(L\) & Number of the scatterers \\ \(\mathbf{n}_{\text{RT}}\)\((t)\) & The unity directional vector of the LOS path from the transmitter towards the receiver \\ \(\mathbf{n}_{\text{TO}}\) & The unit directional vector towards \(\mathbf{O}\) observed from \(\mathbf{T}\) \\ \(\mathbf{n}_{\text{RO}}\) & The unit directional vector towards \(\mathbf{O}\) observed from \(\mathbf{R}\) \\ \(\mathbf{n}_{\text{TD},i}\) & The unit directional vector towards the \(l\)th scatterer observed from the transmitter T \\ \(\mathbf{n}_{\text{RD},j}\) & The unit directional vector towards the \(l\)th scatterer observed from the receiver R \\ \(\mathbf{O}^{\prime}\) & The center of the earth \\ \(\mathbf{O}\) & The origin of the XOY plane, also the specular reflection point \\ \(r_{e}\) & The radius of the earth \\ R & The receiver (aircraft) \\ \(S\)\((t)\) & The time variant area of the scattering ellipse \\ \(t\) & Time \\ T & The transmitter (satellite) \\ \(\mathbf{v}_{\mathbf{R}}\)\((t)\) & Time variant velocity vector of the receiver \\ \(\mathbf{v}_{\mathbf{T}}\)\((t)\) & Time variant velocity vector of the transmitter \\ \(\mathbf{v}_{\mathbf{R}}\)\((t)\) & Norm of time variant velocity vector of the receiver \\ \(\mathbf{v}_{\mathbf{T}}\)\((t)\)\(,y_{\mathbf{T}}\)\((t)\)\(,z_{\mathbf{T}}\)\((t)\) & The time variant 3D coordinate of the transmitter \\ \(\left(x_{\mathbf{R}}\right)\)\(,y_{\mathbf{R}}\)\((t)\)\(,z_{\mathbf{R}}\)\((t)\) & The time variant 3D coordinate of the receiver \\ \(\left(x_{\mathbf{D}}\right)\)\((,y_{\mathbf{D}})\)\((\,t)\)\((0)\) & The time variant 3D coordinate of the scatterer \\ \(\left(x_{\mathbf{D}}\right)\)\((\,t)\)\(,y_{\mathbf{D}}\)\((\,t)\)\((0)\) & The time variant 3D coordinate of the \(l\)th scatterer \\ \(a_{\text{LOS}}\)\((t)\) & Path attenuation of the LOS path \\ \(a_{\text{SPE}}\)\((t)\) & Path attenuation of the specular reflection path \\ \(a_{\text{IDE}}\)\((t)\) & Path attenuation of the scattering path \\ \(a_{\text{IDE}j}\)\((t)\) & Path attenuation of the \(l\)th scattering path \\ \(\Delta t\) & Time interval \\ \(\Delta f\) & Frequency interval \\ \(\varepsilon_{r}^{\prime}\) & Relative dielectric permeittivity \\ \(\gamma_{1}\) & The angle between \(\text{OR}\) and \(Z\) axis \\ \(\gamma_{2}\) & The angle between \(\text{OT}\) and \(Z\) axis \\ \(\Gamma\)\((t)\) & Time variant reflection coefficient \\ \(\Gamma_{\perp}\)\((t)\) & Time variant reflection for vertical polarization \\ \(\Gamma_{//}\)\((t)\) & Time variant reflection coefficient for horizontal polarization \\ \(\gamma_{\text{MP}}\) & Normalized Doppler shift of the scattering path \\ \(\Phi\)\((t)\) & The geocentric angle between T (the satellite) and R (the aircraft) \\ \(\Phi_{l}\)\((t)\) & The geocentric angle between T (the satellite) and R (the aircraft) \\ \(\phi_{l}\) & Additional phase shift of the \(l\)th scattering path \\ \(\sigma\) & Radar cross section (RCS) \\ \(\tau\) & Delay \\ \(\tau_{\text{LOS}}\)\((t)\) & Time variant path delay of the LOS path at the moment \(t\) \\ \(\tau_{\text{SPE}}\)\((t)\) & Time variant path delay of the specular reflection path at the moment \(t\) \\ \(\tau_{\text{IDE}}\)\((t)\) & Time variant path delay of the scattering path at the moment \(t\) \\ \(\tau_{\text{TOF}j}\)\((t)\) & Time variant path delay of the \(l\)th scattering path at the moment \(t\) \\ \(\theta\) & Reflection angle \\ \(\theta\)\((t)\) & Time variant reflection angle \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cont. the common method of developing aeronautical channel models, such as presented in [2], three paths, including the LOS path, the reflection path, and the diffuse scattering path, are considered in this paper. Based on Figure 1, the lengths of the LOS path and the specular reflection path can be calculated by Equations (1) and (2).