The model is applicable to scenarios where no end of the link is completely inside foliage, but a single plant or tree stands in the middle of the link.
The single vegetative obstruction model is formally expressed as, where, A = The Attenuation due to vegetation. Unit: decibel. d = Depth of foliage. Unit: Meter. = Specific attenuation for short vegetative paths. Unit: decibel per meter. Ri = The initial slope of the attenuation curve. Rf = The final slope of the attenuation curve. f = The frequency of operations. Unit: gigahertz. k = Empirical constant.
Calculation of slopes
Initial slope is calculated as: And the final slope as: where, a, b and c are empirical constants.
Calculation of ''k''
k is computed as: where, k0 = Empiricalconstant. Rf = Empirical constant for frequency dependent attenuation. A0 = Empirical attenuation constant. Ai = Illumination area.
Calculation of ''A''i
Ai is calculated in using any of the equations below. A point to note is that, the terms h, hT, hR, w, wT and wR are defined perpendicular to the line joining the transmitter and receiver. The first three terms are measured vertically and the other there are measured horizontally. Equation 1: Equation 2: where, wT = Width of illuminated area as seen from the transmitter. Unit: meter wR = Width of illuminated area as seen from the receiver. Unit: meter w = Width of the vegetation. Unit: meter hT =Height of illuminated area as seen from the transmitter. Unit: meter hR = Height of illuminated area as seen from the receiver. Unit: meter h = Height of the vegetation. Unit: meter aT = Azimuth beamwidth of the transmitter. Unit: degree or radian aR = Azimuth beamwidth of the receiver. Unit: degree or radian eT = Elevation beamwidth of the transmitter. Unit: degree or radian eR = Elevation beamwidth of the receiver. Unit: degree or radian dT = Distance of the vegetation from transmitter. Unit: meter dR = Distance of the vegetation from receiver. Unit: meter
The empirical constants
Empirical constants a, b, c, k0, Rf and A0 are used as tabulated below.
Limitations
The model predicts the explicit path loss due to the existence of vegetation along the link. The total path loss includes other factors like free space loss which is not included in this model. Over 5 GHz, the equations suddenly become extremely complex in consideration of the equations for below 3 GHz. Also, this model does not work for frequency between 3 GHz and 5 GHz.
