# Radio Channel Modelling for VHF System Operating in the Offshore Wind Farms Propagation Environment
## 2 Methods
### Itu-R BT.1893-1 Model
#### 2.1.3 Effective Reflecting Surface
For a broader analysis of this issue, the concept of the wave reflection coefficient should be presented, i.e., the ratio of the intensity of the reflected wave to the intensity of the incident wave. An electromagnetic wave falling on the boundary surface of two media with given refractive indices is refracted and partially reflected. In general terms, the wave reflection coefficient can be described by the following formula [17]:  
\[L_{mat}[dB]=20\text{log}(|\gamma|), \tag{15}\]  
where  
\[\gamma=\frac{Z-Z_{0}}{Z+Z_{0}}. \tag{16}\]  
\(Z\) is the wave impedance of the electromagnetic wave, which in the case of an ideal dielectric (where the conductivity is close to 0) can be described as  
\[Z=\sqrt{\frac{\mu}{\varepsilon}} \tag{17}\]  
where \(\mu\) is the magnetic permeability and \(\varepsilon\) is the electrical permittivity. \(Z_{0}\) in the Formula (16) denotes the wave impedance in free space and is expressed by  
\[Z_{0}=\sqrt{\frac{\mu_{0}}{\varepsilon_{0}}}\approx 120\pi\Omega\approx 376.7\Omega. \tag{18}\]  
Using the above formulas, it is possible to determine the value of the reflection wave coefficient applicable to the analyzed case. Modern wind turbine blades are usually made of glass fibers or glass-fiber-reinforced plastics (GFRP) (e.g., [18]). In order to calculate the value of the reflection wave coefficient, information was found that the relative permittivity of the GFRP material takes values \(\varepsilon_{r}=3.3\div 4.2\)[19]. In an isotropic, homogeneous dielectric with negligible magnetic properties, \(\mu=\mu_{0}=4\pi\times 10^{-7}\) H/m and \(\varepsilon=\varepsilon_{r}\times 8.854\times 10^{-12}\) F/m. This means that the value of the wave impedance (in a  
Figure 2: Graphic interpretation of the angles occurring in the dependence (8). isotropic and homogeneous dielectric with negligible magnetic properties) can be calculated from a simplified formula:  
\[Z=\sqrt{\frac{\mu}{\varepsilon}}=\sqrt{\frac{\mu_{0}}{\varepsilon_{0}\varepsilon_ {r}}}=\frac{Z_{0}}{\sqrt{\varepsilon_{r}}}=\frac{377}{\sqrt{\varepsilon_{r}}} \Omega, \tag{19}\]  
For GFRP we can assume \(\mu=\mu_{0}\)[20], and the range of the reflection wave coefficient is  
\[L_{mat_{r}=3,3}[dB]=20\text{log}(|\gamma|)=20\text{log}\left|\frac{Z-Z_{0}}{Z+ Z_{0}}\right|=20\text{log}\left|\frac{\frac{377}{\sqrt{2}}-Z_{0}}{\frac{377}{ \sqrt{2}}+Z_{0}}\right|=-10.97,\]  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]0  
Modern turbine blades are often made of GFRP material with \(\varepsilon_{r}=4.2\), for which the reflectance is approx. 9 dB. In the performed calculations, it was assumed that the theoretical reflection would be reduced by 9 dB. The parameter \(\sigma_{A2}\) (RCS of the turbine mast towards the receiving antenna) for Annex 2 can be calculated from the following equation [11]:  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]1  
lower index A2 indicates the formula is true for Annex 2 of [11],  
\(k=\frac{2\pi}{\lambda}\) (1/m). \(r\)--tower radius (m);  
\(\phi_{r}\)--receive antenna angular position in the horizontal plane measured at the wind turbine under consideration in an anti-clockwise direction from the direction of the transmit antenna;  
\(\theta_{t}\)--transmit antenna angular position in the vertical plane.