Single Vegetative Obstruction Model
Encyclopedia
The ITU Single Vegetative Obstruction Model is a Radio propagation model
that quantitatively approximates the attenuation
due to the vegetation in the middle of a telecommunication link.
where,
A = The Attenuation
due to vegetation. Unit: decibel
(dB).
d = Depth of foliage. Unit: Meter (m).
= Specific attenuation for short vegetative paths. Unit: decibel per meter (dB/m).
Ri = The initial slope
of the attenuation curve.
Rf = The final slope
of the attenuation curve.
f = The frequency
of operations. Unit: gigahertz (GHz).
k = Empirical
constant
.
And the final slope as:
where,
a, b and c are empirical constants (given in the table below).
where,
k0 = Empirical constant (given in the table below).
Rf = Empirical constant for frequency dependent attenuation.
A0 = Empirical attenuation constant (given in the table below).
Ai = Illumination area.
Equation 1:
Equation 2:
where,
wT = Width of illuminated area as seen from the transmitter. Unit: meter (m)
wR = Width of illuminated area as seen from the receiver. Unit: meter (m)
w = Width of the vegetation. Unit: meter (m)
hT =Height of illuminated area as seen from the transmitter. Unit: meter (m)
hR = Height of illuminated area as seen from the receiver. Unit: meter (m)
h = Height of the vegetation. Unit: meter (m)
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(m)
dR = Distance of the vegetation from receiver. Unit: meter(m)
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.
Radio propagation model
A radio propagation model, also known as the Radio Wave Propagation Model or the Radio Frequency Propagation Model, is an empirical mathematical formulation for the characterization of radio wave propagation as a function of frequency, distance and other conditions...
that quantitatively approximates the attenuation
Attenuation
In physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
due to the vegetation in the middle of a telecommunication link.
Applicable to/under conditions
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.Mathematical formulations
The single vegetative obstruction model is formally expressed as,where,
A = The Attenuation
Attenuation
In physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
due to vegetation. Unit: decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
(dB).
d = Depth of foliage. Unit: Meter (m).
= Specific attenuation for short vegetative paths. Unit: decibel per meter (dB/m).Ri = The initial slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
of the attenuation curve.
Rf = The final slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
of the attenuation curve.
f = The frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
of operations. Unit: gigahertz (GHz).
k = Empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....
constant
Constant (mathematics)
In mathematics, a constant is a non-varying value, i.e. completely fixed or fixed in the context of use. The term usually occurs in opposition to variable In mathematics, a constant is a non-varying value, i.e. completely fixed or fixed in the context of use. The term usually occurs in opposition...
.
Calculation of slopes
Initial slope is calculated as:And the final slope as:
where,
a, b and c are empirical constants (given in the table below).
Calculation of k
k is computed as:where,
k0 = Empirical constant (given in the table below).
Rf = Empirical constant for frequency dependent attenuation.
A0 = Empirical attenuation constant (given in the table below).
Ai = Illumination area.
Calculation of Ai
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 (assumed horizontal) line joining the transmitter and receiver. The first three terms are measured vertically and the other thee are measured horizontally.Equation 1:
Equation 2:
where,
wT = Width of illuminated area as seen from the transmitter. Unit: meter (m)
wR = Width of illuminated area as seen from the receiver. Unit: meter (m)
w = Width of the vegetation. Unit: meter (m)
hT =Height of illuminated area as seen from the transmitter. Unit: meter (m)
hR = Height of illuminated area as seen from the receiver. Unit: meter (m)
h = Height of the vegetation. Unit: meter (m)
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(m)
dR = Distance of the vegetation from receiver. Unit: meter(m)
The empirical constants
Empirical constants a, b, c, k0, Rf and A0 are used as tabulated below.| Parameter | Inside Leaves | Out of Leaves |
|---|---|---|
| a | 0.20 | 0.16 |
| b | 1.27 | 2.59 |
| c | 0.63 | 0.85 |
| k0 | 6.57 | 12.6 |
| Rf | 0.0002 | 2.1 |
| A0 | 10 | 10 |
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.