# 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  
The effective reflecting surface is known as the Radar Cross Section (RCS) as this concept is derived from radar technology. The RCS parameter describes the ability of an object to reflect radio (radar) or sound waves. It is expressed as the area (in [m\({}^{2}\)]) situated in a plane perpendicular to the direction of the incident wave, which, in the case of ideal, isotropic reflection of all the energy incident on it, would produce the same equivalent isotopically radiated power as the power generated by the real object. Factors that influence the RCS value include the following [13]:  
* The size of the cross-sectional area of the object;
* The shape of the object;
* Material the object is made of or covered with;
* Frequency of the signal reflected from the object;
* Angle of incidence of the signal;
* Signal reflection angle;
* Polarization of the transmitted and received signal in relation to the target. Objects with a larger effective reflection surface will reflect waves better, i.e., give a stronger echo. They can, therefore, be detected from a greater distance. In electromagnetic analysis, the formula for the RCS parameter (most often denoted by the \(\sigma\)) can be presented as follows [14]:  
\[\sigma=\lim_{r\rightarrow\infty}4\pi r^{2}\frac{|E_{s}|^{2}}{|E_{i}|^{2}}. \tag{12}\]  
\(E_{i}\)--the intensity of the electric field incident the object;  
\(E_{s}\)--the intensity of the electric field scattered on the object. Depending on the distance of a transmitter from the wind turbine, an appropriate mathematical formula is used to calculate the RCS parameter value. If the far-field criterion is met, the mathematical formulas for Annex 1 are used to calculate the RCS parameter [14; 15; 16] (since the Annex 1 is more suitable for large distances between the transmitter and turbine). In this case, the reflection of the signal from the wind turbine rotors is taken into account, where the calculation should primarily take into account the equivalent area of the blades of the wind turbine. However, if the far-field criterion is not met, the formulas in Annex 2 are used for calculations, where mainly reflection from the wind turbine mast, characterized by its radius, is taken into account. In general, the effective reflecting surface for Annex 1 can be described by the following formula:  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]  
where lower index \({}_{A1}\) indicates the formula is true for Annex 1 of [11]. \(A\)--equivalent of the total area of the blades [m\({}^{2}\)];  
\(\lambda\)--wavelength [m];  
\(S\)--mean width of the wind blade [m];  
\(f_{h}(\theta)\)--rotor's equivalent antenna pattern (The wind turbine is treated as a \"radio transmitter\" generating interference, while the functions \(f_{v}(\theta)\) and \(f_{h}(\theta)\) indicate the directional characteristics of the \"transmitting antenna\") in the horizontal plane;  
\(f_{v}(\theta)\)--rotor's equivalent antenna pattern in the vertical plane;  
\(f(\theta)=g(\theta)^{2}\);  
\(g(\theta)=sinc^{2}\Big{[}\frac{S}{\lambda}(\cos\theta-\cos\theta_{0})\Big{]} \text{sin}\,\theta\), where: \(sinc(x)=\frac{sin(\pi x)}{(\pi x)}\);  
\(L_{mat}(\varepsilon_{r})\)--losses related to the relative permeability of the turbine blade material. The graphic interpretation of the angles referred to in Formula (13) is presented in Figure 2[11]. To compare the RCS parameters for both anneves, the losses resulting from the material and the antenna angles were temporarily omitted. Ultimately, the following formula was reached for Annex 1:  
\[RCS_{A1,MAX}\Big{[}dBm^{2}\Big{]}=\sigma_{A1,\ MAX}\Big{[}dBm^{2}\Big{]}=10 \text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2}}\Big{)}+L_{mat}(\varepsilon_{r}). \tag{14}\]  
To discuss the influence of the material the blades of the wind turbine are made from on the signal reflection, the \(L_{mat}\) coefficient will be introduced.