## 3 A Hybrid Propagation Channel Model  
### The Proposed 3 DFPHPCM  
The proposed 3 DFPHPCM is used to model the environment first, and the three-dimensional PE derived from the waveguide equation is used to combine the absorption boundary and impedance boundary conditions of the actual rough ground with the initial field. Moreover, the step-by-step Fourier transform algorithm is adopted to obtain the magnetic field \(H_{y},E_{x},E_{y},E_{z},H_{x},H_{z}\) as described in Section 2.1. As there is almost no restriction on the applicable conditions of three-dimensional RT, the initial field \(E_{total},H_{total}\) of three-dimensional RT can be obtained directly. According to the relationships among \(\overset{\rightarrow}{k},\overset{\rightarrow}{E}\), and \(\overset{\rightarrow}{H}\) in Equation (25), the propagation direction of the ray in the three-dimensional RT can be obtained. \[\overset{\rightarrow}{H}=\hat{k}\times\overset{\rightarrow}{E}/\eta \tag{25}\]  
Thereafter, the propagation mechanism of the rays and the building is determined (i.e., direct, reflected, and diffracted rays). Finally, the scattering effect is considered in the three-dimensional RT, several scattered rays are taken, and the direction of scattered rays is determined via sampling to enable us to propose the presented 3 DFPHPCM. The steps used in the proposed 3 DFPHPCM to calculate the different polarizations (HH, VV, VH, and HV) are given below. 1. Preparatory work: The first step involves reading the file of the environment data, including the vertex coordinate, the sides, and the outer normal vector of the triangular surface. The second step involves initializing the information on various electromagnetic parameters, including the height of the transmitting and receiving antennas, operating frequency, transmitting power, wavelength, dielectric constant, and dielectric conductivity;
2. Computation of the initial field information for three-dimensional RT: Firstly, the environment is modeled. Secondly, the three-dimensional PE derived from the waveguide equation is used to combine the absorbing boundary and impedance boundary conditions of the actual rough ground with the initial field, and the step-by-step Fourier transform algorithm is adopted to obtain the field component information at the boundary of the region. Finally, the field component information at the boundary of the region is used as the initial field information of the three-dimensional RT;
3. Determination of whether the ray is a direct ray: We determine whether the connecting line of the receiving antenna and transmitting antenna contain an intersection point in the triangular surface. If there is no intersection, there is no obstruction between the transmitting antenna and the receiving antenna. Thereafter, we record the relevant information;
4. Determination of single scattered rays: We determine which rays are single scattered rays from the transmitting to the receiving antenna;
5. Determination of double scattered rays: We determine which rays are double scattered rays from the transmitting to the receiving antenna;
6. Calculation: We calculate the path loss for different polarizations (HH, VV, VH, and HV) at each receiving point based on the ray path. The pseudocode for the proposed 3 DFPHPCM is shown in Algorithm 1. ```
1:proceduretotalpathLossL
2:Hy
3:Ex, Ey, Ez, Hx, Hz
4:k
5:cc
6:for(each ray)do
7:ifthe ray is a direct ray
8:record the ray
9:elseif the ray is single scattered ray
10:record the ray
11:elseif the ray is double scattered ray
12:record the ray
13:endif
14:endfor
15:L \(\leftarrow\) Calculate the total Path LossL
16:returnL
17:endprocedure
```  
**Algorithm 1** Calculate the total Path Loss **L**  
Based on the above steps, the detailed pseudocode of the serial algorithm for three-dimensional RT is developed as shown in Algorithm 2. The implementation of the proposed 3 DFPHPCM involves the sampling of scattered rays, as shown in Section 3.2.