# Radio Channel Modelling for VHF System Operating in the Offshore Wind Farms Propagation Environment
## 2 Methods
### Modelling of the Radio Channel Based on Selected Parameters  
Signal propagation in a radio channel is influenced by many factors. It depends primarily on the properties of the wave itself, i.e., its length and polarization, as well as on the conditions of the environment in which the wave propagates. By \"environmental conditions\" we mean topography and the type of coverage--radio waves propagate differently in areas near water, in forests, in urban or open areas. In the area covered by this article, communications with sea-going vessels are mainly based on the VHF band systems. Ultra-high frequency waves propagate in the form of a ground-level spatial wave. In practice, at most a quasi-horizontal range of about 30 national miles (Nm) can be achieved. It should be emphasized that in the maritime radio channel the terrain does not affect wave propagation; however, reflections from the sea surface must be taken into account, as well as the possibility of the first Fresnel zone being obscured by the water surface, which is also affected by the curvature of the Earth. This causes multipath propagation, as a result of which one or more reflected waves reach the receiver. In turn, multipath is a source of interference and transmission quality degradation. The propagation of the signal in the VHF marine radio channel is also influenced by tropospheric refraction, which may increase the range due to the formation of tropospheric ducts [22]. Multipath propagation causes the signal--through diffraction, refraction, scattering, and reflection--to reach the receiver as a sum of component signals with different delays, phases, and amplitudes. The main parameters that describe a multipath propagation radio channel are as follows:  
* Power Delay Profile (PDP)--determines how the strength of the signal reaching the receiver input changes over time. In general, it is the impulse response of the channel to an excitation with a very short pulse, defined as a series of components with different power levels and different delays (Figure 5); the delay of the \(k\)-th component is denoted as \(\tau_{k}\). Figure 5: Example of a power delay profile in a radio channel. To describe such a profile, we usually use the following parameters [23]: \[\text{average delay}:\ \overline{\tau}=\frac{\sum_{k}P(\tau_{k})\tau_{k}}{\sum_{k}P( \tau_{k})},\] (28) \[\text{standard deviation}:\ \sigma_{k}=\sqrt{\overline{\tau^{2}-(\overline{ \tau})}^{2}}.\] (29)
* Coherence bandwidth (\(B_{c}\))--means the frequency range in which the channel can be considered invariant. In this range, the channel amplitude response is constant and the phase response is linear. This means that the channel will similarly affect two sinusoidal signals separated by less than \(B_{c}\) [Hz] (that are inside the coherence bandwidth), while two signals spaced apart by a bandwidth greater than \(B_{c}\) will be affected differently. The \(B_{c}\) band is often defined as the frequency range where the frequency correlation is greater than 0.5. In this case [23; 24], \[B_{c}\approx\frac{1}{5\sigma_{\tau}}\] (30) where \(\sigma_{\tau}\) it is the maximum spread of the delay. * Doppler Spread (or Doppler band--\(B_{D}\))--determines the extent to which the band has expanded as a result of one of the radio system components (transmitter or receiver) being in motion. As it is known, during the movement of the mobile station relative to the base station, the frequency of the received signal will differ from the frequency of the transmitted signal. The frequency deviation depends on the speed and the angle of the electromagnetic wave. The Doppler band is defined as the maximum Doppler shift, i.e., \[f_{d\ max}=\frac{v}{\lambda}\] (31) where \(v\) is the speed of the terminal and \(\lambda\) represents the electromagnetic wavelength. If the baseband of the signal is much greater than \(B_{D}\), the Doppler effect can be ignored.