## 3 Analytical Non-Stationary S2A Channel Model  
### Channel Impulse Response  
As mentioned above, three paths model is adopted in this paper, thus the CIR of the presented channel model can be given by Equation (10). \[h\left(t,\tau\right)=h_{\text{LOS}}\left(t,\tau\right)+h_{\text{SPE}}\left(t,\tau\right)+h_{\text{DIF}}\left(t,\tau\right) \tag{10}\]  
where \(h_{\text{LOS}}\left(t,\tau\right)\) is the impulse response of the LOS path with \(t\) as the observed moment, and \(\tau\) as the corresponding time delay, \(h_{\text{SPE}}\left(t,\tau\right)\) is the impulse response of the specular reflection path, and \(h_{\text{DIF}}\left(t,\tau\right)\) is the impulse response of the diffuse scattering path. Considering the large scale propagation attenuation, propagation delay and Doppler shift, the impulse response of the LOS path is denoted as Equation (11), where \(\alpha_{\text{LOS}}\left(t\right)=\lambda\frac{\sqrt{\frac{G_{\text{T}}^{ \text{LOS}}\left(t\right)G_{\text{R}}^{\text{LOS}}\left(t\right)}{4\pi l_{ \text{LOS}}\left(t\right)}}}{4\pi l_{\text{LOS}}\left(t\right)}\) is the path attenuation of the LOS path, with the assumption that the propagation loss attenuation factor equals to 2. \(\lambda\) is the wave length, and \(G_{\text{T}}^{\text{LOS}}\left(t\right)\) and \(G_{\text{R}}^{\text{LOS}}\left(t\right)\) are the antenna gains of the transmitter and the receiver at the moment \(t\) corresponding to concerned directions, \(\tau_{\text{LOS}}\left(t\right)=\frac{d_{\text{LOS}}\left(t\right)}{c}\) where \(d_{\text{LOS}}\left(t\right)\) is the length of the LOS path as Equation (1) at the moment \(t\). \[h_{\text{LOS}}\left(t,\tau\right)=\alpha_{\text{LOS}}\left(t\right)g_{\text{ LOS}}\left(t\right)\delta\left(\tau-\tau_{\text{LOS}}\left(t\right)\right) \tag{11}\]  
\(g_{\text{LOS}}\left(t\right)\) in Equation (11), is the term for phase shifts introduced by LOS transmitting and Doppler shift, and is calculated as in Equation (12), where \(k_{0}=2\pi/\lambda\), \(\mathbf{v_{\text{RT}}}\left(t\right)=\mathbf{v_{\text{R}}}\left(t\right)- \mathbf{v_{\text{T}}}\left(t\right)\), where \(\mathbf{v_{\text{T}}}\left(t\right)=\left({v_{\text{T}\_x}}\left(t\right),{v_ {\text{T}\_y}}\left(t\right),{v_{\text{T}\_z}}\left(t\right)\right)^{\text{T}}\) is the velocity of the transmitter, and \(\mathbf{v_{\text{R}}}\left(t\right)=\left({v_{\text{R}\_x}}\left(t\right),{v_ {\text{R}\_y}}\left(t\right),{v_{\text{R}\_z}}\left(t\right)\right)^{\text{T}}\) is the velocity of the receiver. The unity directional vector of the LOS path from the transmitter towards the receiver is \(\mathbf{n_{\text{RT}}}\left(t\right)=\left({n_{\text{RT}\_x}}\left(t\right),{n_{ \text{RT}\_y}}\left(t\right),{n_{\text{RT}\_z}}\left(t\right)\right)^{\text{T}}\). \[g_{\text{LOS}}\left(t\right)=\exp\left(jk_{0}d_{\text{LOS}}\left(t\right)+\text{j }\frac{2\pi}{\lambda}\int_{0}^{t}\mathbf{n_{\text{RT}}^{\text{T}}}\left(t\right) \cdot\mathbf{v_{\text{RT}}}\left(t\right)\text{d}t\right) \tag{12}\]The impulse response of the specular reflection path is given by Equation (13), where \(\tau_{\text{SPE}}=d_{\text{SPE}}\left(t\right)/c\). \(\alpha_{\text{SPE}}\left(t\right)\) and \(g_{\text{SPE}}\left(t\right)\) can be calculated by Equations (14) and (15).