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The [[ITU]] '''single vegetative obstruction model''' is a [[radio propagation]] model that quantitatively estimates [[attenuation]] due to a single plant or tree standing in the middle of a telecommunication link.<ref>{{cite web |title=Rec. ITU-R P.833-2 1 RECOMMENDATION ITU-R P.833-2 ATTENUATION IN VEGETATION (Question ITU-R 202/3) |url=https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.833-2-199910-S!!PDF-E.pdf |website=www.itu.int |publisher=The ITU Radiocommunication Assembly |access-date=26 April 2024}}</ref>

==Coverage==

[[Frequency]] = Below 3 GHz and over 5 GHz 
Depth = Not specified

==Mathematical formulations==

The single vegetative obstruction model is formally expressed as,

<math>A = \begin{cases}d \gamma \mbox{ , frequency} < 3 GHz \\ R_fd \;+\;k[1-e^{(R_f - R_i)\frac{d}{k}}] \mbox{ , frequency} > 5 GHz \end{cases}</math>

where,
''A'' = The [[Attenuation]] due to vegetation. Unit: [[decibel]](dB).

''d'' = Depth of foliage. Unit: Meter (m).

<math>\gamma</math> = [[Specific attenuation]] for short vegetative paths. Unit: decibel per meter (dB/m).

''R''i = The initial [[slope]] of the attenuation curve

''R''f = The final [[slope]] of the attenuation curve

''f'' = The [[frequency]] of operations. Unit: [[gigahertz]] (GHz).

''k'' = [[Empirical]] [[Constant (mathematics)|constant]]

===Calculation of slopes===

Initial slope is calculated as:

<math>R_i\;=\;af</math>

And the final slope as:

<math>R_f\;=\;bf^c</math>

where,

''a'', ''b'' and ''c'' are empirical constants (given in the table below).

===Calculation of ''k''===

''k'' is computed as:

<math>k = k_0\;-\;10\;\log {[A_0\;(1\;-\;e^{\frac{-A^i}{A_0}})(1-e^{R_ff})]}</math>

where,

''k''0 = Empirical constant (given in the table below)

''R''f = Empirical constant for frequency dependent attenuation

''A''0 = Empirical attenuation constant (given in the table below)

''A''i = Illumination area

===Calculation of ''A''i===

''A''i is calculated in using any of the equations below. A point to note is that, the terms ''h'', ''h''T, ''h''R, ''w'', ''w''T and ''w''R are defined perpendicular to the (assumed horizontal) line joining the transmitter and receiver. The first three terms are measured vertically and the other there are measured horizontally.

Equation 1: <math>A_i\;=\;min(w_T, w_R, w)\;x\;min(h_T, h_R, h)</math>

Equation 2: <math>A_i\;=\;min(2d_T\;\tan {\frac{a_T}{2}}, 2d_R \tan{\frac{a_R}{2}}, w)\;x\;min(2d_T \tan {\frac{e_T}{2}}, 2d_R \tan{\frac{e_R}{2}}, h)</math>

where,

''w''T = Width of illuminated area as seen from the transmitter. Unit: meter (m).

''w''R = Width of illuminated area as seen from the receiver. Unit: meter (m).

''w'' = Width of the vegetation. Unit: meter (m).

''h''T =Height of illuminated area as seen from the transmitter. Unit: meter (m).

''h''R = Height of illuminated area as seen from the receiver. Unit: meter (m).

''h'' = Height of the vegetation. Unit: meter (m).

''a''T = Azimuth beamwidth of the transmitter. Unit: degree or radian.

''a''R = Azimuth beamwidth of the receiver. Unit: degree or radian.

''e''T = Elevation beamwidth of the transmitter. Unit: degree or radian.

''e''R = Elevation beamwidth of the receiver. Unit: degree or radian.

''d''T = Distance of the vegetation from transmitter. Unit: meter (m).

''d''R = 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.

{| border="1"
! Parameter !! Inside leaves !! Out of leaves
|-
| ''a'' || 0.20 || 0.16
|-
| ''b'' || 1.27 || 2.59
|-
| ''c'' || 0.63 || 0.85
|-
| ''k''0|| 6.57 || 12.6
|-
| ''R''f || 0.0002 || 2.1
|-
| ''A''0 || 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.

==See also==

* [[Radio propagation model]]
* [[Weissberger's model]]
* [[Early ITU model]]

==Further reading==

* Introduction to RF propagation, John S. Seybold, 2005, Wiley.

==References==
{{reflist}}

{{Radio frequency propagation models}}

[[Category:Radio frequency propagation model]]

Single vegetative obstruction model - Revision history

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