## 1 Introduction
### Motivation and Contributions of This Paper
\[d_{\text{LOS}}\left(t\right)=\sqrt{\left[h_{\text{R}}^{\prime}\left(t\right)+r _{e}\right]^{2}+\left[h_{\text{T}}^{\prime}\left(t\right)+r_{e}\right]^{2}-2 \left[h_{\text{R}}^{\prime}\left(t\right)+r_{e}\right]\left[h_{\text{T}}^{ \prime}\left(t\right)+r_{e}\right]\cos\phi\left(t\right)} \tag{1}\]  
\[d_{\text{SPE}}\left(t\right) =d_{\text{TO}}\left(t\right)+d_{\text{OR}}\left(t\right) \tag{2}\] \[=\sqrt{\left[h_{\text{R}}^{\prime}\left(t\right)+r_{e}\right]^{2} +r_{e}^{2}-2\left[h_{\text{R}}^{\prime}\left(t\right)+r_{e}\right]r_{e}\cos \gamma_{1}\left(t\right)}\] \[+\sqrt{\left[h_{\text{T}}^{\prime}\left(t\right)+r_{e}\right]^{2 }+r_{e}^{2}-2\left[h_{\text{T}}^{\prime}\left(t\right)+r_{e}\right]r_{e}\cos \gamma_{2}\left(t\right)}\]  
As shown in Figure 1, in this paper, for simplifying the modeling, we assume that the scattering happens on a horizontal surface intersects with the earth surface at the specular reflection point O, thus the coordinates of the transmitter, the receiver, the scatterer are known as \(\mathbf{T}\left(x_{\text{T}}\left(t\right),y_{\text{T}}\left(t\right),z_{ \text{T}}\left(t\right)\right)\), \(\mathbf{R}\left(x_{\text{R}}\left(t\right),y_{\text{R}}\left(t\right),z_{ \text{R}}\left(t\right)\right)\), and \(\mathbf{D}\left(x_{\text{D}},y_{\text{D}},0\right)\), respectively, where \(x_{\text{T}}\left(t\right)=x_{\text{R}}\left(t\right)=0\), \(z_{\text{T}}\left(t\right)=h_{\text{T}}\left(t\right)\), and \(z_{\text{R}}\left(t\right)=h_{\text{R}}\left(t\right)\). Since the scattering path contains sub-paths, when we discuss the sub-paths, the coordinate of the \(l\)th scatterer is denoted as \(\left(x_{\text{D},l}\left(t\right),y_{\text{D},l}\left(t\right),0\right)\), thus the length of the scattering sub-path can be calculated as Equation (3). \[d_{\text{DEF},l}\left(t\right) =d_{\text{DR},l}\left(t\right)+d_{\text{TD},l}\left(t\right) \tag{3}\] \[=\sqrt{\left[x_{\text{T}}\left(t\right)-x_{\text{D},l}\left(t \right)\right]^{2}+\left[y_{\text{T}}\left(t\right)-y_{\text{D},l}\left(t \right)\right]^{2}+z_{\text{T}}^{2}\left(t\right)}\] \[+\sqrt{\left[x_{\text{R}}\left(t\right)-x_{\text{D},l}\left(t \right)\right]^{2}+\left[y_{\text{R}}\left(t\right)-y_{\text{D},l}\left(t \right)\right]^{2}+z_{\text{R}}^{2}\left(t\right)}\] \[=\sqrt{x_{\text{D},l}^{2}\left(t\right)+\left[y_{\text{T}}\left( t\right)-y_{\text{D},l}\left(t\right)\right]^{2}+z_{\text{T}}^{2}\left(t\right)}\] \[+\sqrt{x_{\text{D},l}^{2}\left(t\right)+\left[y_{\text{R}}\left( t\right)-y_{\text{D},l}\left(t\right)\right]^{2}+z_{\text{R}}^{2}\left(t\right)}\]  
In this paper, the scatterers are assumed to be distributed in an elliptical region determined by the maximum delay ellipsoid with \(\mathbf{T}\) and \(\mathbf{R}\) as its foci, and truncated by the XOY plane with the specular reflection point as the center, as shown in \[d_{\text{LOS}}\left(t\right)=\sqrt{\left[h_{\text{R}}^{\prime}\left(t\right)+r _{e}\right]^{2}+\left[h_{\text{T}}^{\prime}\left(t\right)+r_{e}\right]^{2}-2 \left[h_{\text{R}}^{\prime}\left(t\right)+r_{e}\right]\left[h_{\text{T}}^{ \prime}\left(t\right)+r_{e}\right]\cos\phi\left(t\right)} \tag{1}\]0 At the moment \(t\), the range of the scattering area is constrained by Equation (4),where \(\tau_{\text{max}}\) is the maximum path delay compared to the LOS path, and c is the speed of light. \[