# 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 graphic interpretation of the angles referred to in Formula (20) is presented in \[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]2  
It should be noted that for distances at which the effect of the turbines may be significant, the far field criterion is usually not met, as in general [11]  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]3  
where \(L\) gives the tower length (m). In this case, the near-field scattering effects should be taken into account when considering the near-field tower height, \(L_{nf}\) [m] [11]:  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]4  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]5 Graphic interpretation of the angles occurring in the dependence (15). The inequality specified in Equation (21) may effectively be considered as the upper bound for the application (Please note this is merely a recommendation taking into account the specifics of the two Annexes and the conclusions from the measurements conducted by the authors of this paper. Formally. the Annex 2 model can be applied for far-field as well; however, it will be much less reliable in such a case compared to Annex 1.) of Annex 2. If this inequality is no longer true (for higher values of \(R_{Tx-WT1}\)), Annex 1 should be applied instead. The mean amplitude of each path can be determined as the ratio of the power of the reflected (unwanted) component to the direct (wanted) component [11]:  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]6  
Components for which the mean \(P_{i}\) amplitude is less than \(-45\) dB should be ignored (as insignificant). To compare the RCS formula for Annex 2 with the formula for Annex 1 (13), we can convert the Equation (20) to  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]7  
where  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]8  
and  
\[RCS_{A1}\Big{[}dBm^{2}\Big{]}=10\text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2} }\Big{)}+10\text{log}(f_{v}(\theta))+10\text{log}(f_{h}(\theta))+L_{mat}( \varepsilon_{r}) \tag{13}\]9  
Figure 4 shows the relationship between the RCS parameter (for both Annexes of [11]) and the distance between the wind turbine (137 m height) and the transmitter. For turbine 1, the equivalent area of wind turbine blades \(A=400\) m\({}^{2}\) and the mast radius \(r=3.2\) m were assumed. For turbine 2, \(A=700\) m\({}^{2}\), and \(r=4\) m were assumed. For Annex 1, RCS takes a constant value because it does not depend on distance. On the other hand, for Annex 2, substituting the relation (22) to the Formula (25), one can notice a change in the RCS value [21] depending on the distance between the turbine and  
\[RCS_{A1,MAX}\Big{[}dBm^{2}\Big{]}=\sigma_{A1,\ MAX}\Big{[}dBm^{2}\Big{]}=10 \text{log}\Big{(}\frac{4\pi A^{2}}{\lambda^{2}}\Big{)}+L_{mat}(\varepsilon_{r}). \tag{14}\]0 The dependence of the RCS parameter on the distance between the wind turbine and the transmitter. the transmitter.