# Radio Channel Modelling for VHF System Operating in the Offshore Wind Farms Propagation Environment
## 3 Results and Discussion
### The Measurement Results
#### 3.1.2 Measurements of the Doppler Power Spectra Density  
The measurements of the Doppler power spectra density were performed within three measurement scenarios, in three different locations--two in the north part of the Jasna wind farm (Figure 7a) and one in its south part (Figure 7b). Wind conditions varied from day to day, both in terms of strength and direction; Table 8 summarizes the rotational speeds of the turbine rotors and the corresponding Doppler frequencies. In addition, a channel coherence time (Tc) was determined and shown in the table where the channel is invariant as a function of time (i.e., the time where the channel impulse response is approximately constant). The channel coherence time is (approximately) inversely proportional to the Doppler bandwidth, so if the symbols are shifted by more than Tc with respect to one another their time correlation will be below 0.5 (see formula 32 and [23]). According to the methodology of determining the Doppler spectrum presented in recommendation ITU-R BT.1893-1 [11], three variants of power spectral density are defined depending on the degree of variability in time, the rotational speed of the rotors, and their spatial orientation (called low, medium, and high variability). They differ from each other in the shape of the spectrum and the level of its concentration around the carrier frequency. According to the model:  
\"High variability\"--covers the range from \(-0.9\cdot f_{B\ max}\) to \(0.9\cdot f_{B\ max}\);  
\"Medium variability\"--covers the range from \(-0.7\cdot f_{B\ max}\) to \(0.6\cdot f_{B\ max}\);  
\"Low variability\"--covers the range from \(-0.3\cdot f_{B\ max}\) to \(0.3\cdot f_{B\ max}\). Table 9 presents these frequency limits for all three discussed variants and three sets of measurement scenarios. Figure 8 shows the theoretical calculations of the Doppler spectrum (for high, medium, and low variability variants from recommendation [11]) and measured for scenario 1. Tables 10-12 contain numerical values of the Doppler power spectrum determined computationally and measured for each scenarios. The presented results have been normalized so that they can be directly compared. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Location** & \begin{tabular}{c} **Rotational Speed of the Rotor** \\ **of the Nearest Turbine** \\ **during the Measurements** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum Doppler** \\ **Frequency [Hz]** \\ \end{tabular} &
\begin{tabular}{c} **Channel Coherence** \\ **Time [ms]** \\ \end{tabular} \\ \hline Scenario 1 & \(53^{\circ}59^{\prime}38.329^{\prime\prime}\) N & 10.9 rpm & 75.99 & 5.567 \\  & \(19^{\circ}20^{\prime}56.212^{\prime\prime}\) E & 12.7 rpm & 88.53 & 4.778 \\ \hline Scenario 2 & \(53^{\circ}59^{\prime}27.717^{\prime\prime}\) N & 12.7 rpm & 88.53 & 4.778 \\  & \(19^{\circ}20^{\prime}53.273^{\prime\prime}\) E & 7.6 rpm & 52.98 & 7.984 \\ \hline Scenario 3 & \(53^{\circ}51^{\prime}25.342^{\prime\prime}\) N & 7.6 rpm & 52.98 & 7.984 \\  & \(19^{\circ}20^{\prime}18.622^{\prime\prime}\) E & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Rotational speeds of rotors and Doppler frequencies on individual measurement scenarios. By analyzing the measurement results and comparing them with theoretical calculations, a similar shape of the Doppler spectrum can be observed. Moreover, in the range of approx. \(+/-10\) Hz, the plots with the measurement data coincide with the theoretical plots for low variability, which are the widest around the carrier frequency of all theoretical plots. In the measurement campaign carried out at the wind farm, it was not possible to separate individual paths representing each of the wind turbines when measuring the Doppler  
Figure 8: Doppler power spectral density measured on scenario 1 and calculated for the conditions prevailing on that day.