# Radio Channel Modelling for VHF System Operating in the Offshore Wind Farms Propagation Environment
## 2 Methods
### Itu-R BT.1893-1 Model
#### 2.1.2 Wind Turbine Impact Studies on Radiocommunication Systems--Model ITU-R BT.1893-1 Annex 2  
The model presented in the Annex 2 of the recommendation [11] describes the radio channel in the presence of a wind farm in the form of the so-called Tapped-Delay Line, in which individual paths are characterized by the following:  
* Corresponding delays;
* Mean amplitudes;
* Doppler spectrum associated to each path to account for the variability caused by the rotation of the blades. The above parameters closely depend, among others, on the specific location of the transmitter and receiver with respect to the specific wind turbine. The key parameters of the Annex 2 model are presented further in this section. As a first approximation, the total number of model paths equals the number of turbines on the wind farm plus the direct path representing the signal from the transmitter. Depending on the values of delays and amplitudes determined in the further modeling procedure, this number can be ultimately reduced. Relative delays of the path  
For a given wind turbine, the relative delay \(\tau_{i}\)(s) of the scattered signal is determined as a function of the distance between the direct path (transceiver) and the scattered signal path (transmitter-\(>\) turbine-\(>\) receiver) [11]:  
\[\tau_{i}=\frac{\left(R_{Tx-WT_{i}}+R_{WT_{i}-Rx}-R_{Tx-Rx}\right)}{c}. \tag{6}\]  
\(R_{Tx-WT_{i}}\)--transmit antenna to i-th wind turbine distance [m];  
\(R_{WT-Rx}\)--i-th wind turbine to receive antenna distance [m];  
\(R_{Tx-Rx}\)--transmit antenna to receive antenna distance [m];  
\(c\)--speed of light \(\approx\) 300,000,000 m/s. Mean amplitude of the paths  
The direct path power from the transmitting antenna at the receiver location, \(P_{Tx-Rx}\), can be determined from the following relationship [11]:  
\[P_{Tx-Rx}=\frac{P_{t}G_{Tx-Rx}G_{Rx-Tx}\lambda^{2}L_{prop}}{\left(4\pi\right)^ {2}R_{Tx-Rx}^{2}}. \tag{7}\]  
\(P_{t}\)--maximum transmitter power [W];  
\(G_{Tx-Rx}\)--transmit antenna gain in the direction of the receive antenna (dimensionless);  
\(G_{Rx-Tx}\)--maximum gain of the receive antenna (dimensionless);  
\(L_{prop}\)--propagation losses (dimensionless);  
\(R_{Tx-Rx}\)--transmitter to receiver distance [m];  
\(\lambda\)--wavelength [m]. It is worth noting that the power described by the Formula (7) corresponds to the Annex 1 parameter, FSR (Wanted Field Strength). In turn, the power at the receiver of the scattered (reflected) signal from a given turbine, \(P_{TX-WTI-Rx}\), can be calculated in the following way [11]:  
\[P_{TX-WTI-Rx}=\frac{P_{t}G_{TX-WTI}G_{Rx-WTI}\lambda^{2}\sigma_{i}}{(4\pi)^{3}R_{ TX-WTI}^{2}R_{WTI-Rx}^{2}}. \tag{8}\]  
\(G_{TX-WTI}\)--transmit antenna gain in the direction toward the wind turbine \(i\) (dimensionless); \(G_{Rx-WTI}\)--receive antenna gain in the direction toward the wind turbine \(i\) (dimensionless); \(\sigma_{i}\)--bistatic radar cross section (RCS) of the mast in the receive antenna direction [m\({}^{2}\)]; \(R_{Tx-WTI}\)--transmit antenna to \(i\)-th wind turbine distance [m]; \(R_{WTI-Rx}\)--\(i\)-th wind turbine to receive antenna distance [m]. It is noteworthy that the power of the spread signal described by formula (8) corresponds to the Annex 1 parameter, UFSR (Unwanted Field Strength). Doppler Spectra  
In order to take into account the characteristics of the Doppler spectra, the authors of the ITU-R model [11] defined three representative, empirical cases of the Power Spectral Density (PSD), valid for the scenarios of high-, medium-, and low-degree time variability, which correspond to the rotational speed of the rotors and their spatial orientation. The maximum Doppler frequency,\(f_{Bmax}\) (Hz), is defined by the recommendation as follows [11]:  
\[f_{Bmax}=\frac{2\omega_{\max}l}{\lambda}\text{cos}\bigg{(}\frac{\phi_{r}}{2} \bigg{)}. \tag{9}\]  
\(\omega_{max}\)--the maximum rotation frequency of the wind turbine [rad/s]; \(l\)--blade length [m].