Physics:Weissberger's model

Weissberger’s modified exponential decay model, or simply, Weissberger’s model, is a radio wave propagation model that estimates the path loss due to the presence of one or more trees in a point-to-point telecommunication link. This model belongs to the category Foliage or Vegetation models.

Applicable to/under conditions

• This model is applicable to the cases of line of sight propagation. Example is microwave transmission.
• This model is only applicable when there is an obstruction made by some foliage in the link. i.e. In between the transmitter and receiver.
• This model is ideal for application in the situation where the LOS path is blocked by dense, dry and leafy trees.

Coverage

Frequency: 230 MHz to 95 GHz

Depth of foliage: up to 400 m

History

Formulated in 1982, this model is a development of the ITU Model for Exponential Decay (MED).

Mathematical formulation

Weissberger’s model is formally expressed as

[math]\displaystyle{ L = \begin{cases} 1.33 \, f^{0.284} \, d^{0.588} \,\mbox{, if } 14 \lt d \le 400 \\ 0.45 \, f^{0.284} \, d \, \, \, \, \, \, \, \, \, \, \mbox{, if } 0 \lt d \le 14 \end{cases} }[/math]

where,

L = The loss due to foliage. Unit: decibels (dB)

f = The transmission frequency. Unit: gigahertz (GHz)

d = The depth of foliage ‘’’along’’’ the path. Unit: meters (m)

Points to note

• The equation is scaled for frequency specified in GHz range.
• Depth of foliage must be specified in meters (m).

Limitations

• This model is significant for frequency range 230 MHz to 95 GHz only, as pointed out by Blaunstein.
• This model does not define the operation if the depth of vegetation is more than 400 m.
• This model predicts the loss due to foliage. The path loss must be calculated with inclusion of the free space loss.

See also

• Fresnel zone
• Radio propagation model

Further reading

• Introduction to RF Propagation, John S. Seybold, 2005, John Wiley and Sons.
• Radio Propagation in Cellular Networks, N. Blaunstein, 2000, Artech House
• The Mobile Radio Propagation Channel, J. D. Parsons, 2000, Wiley
• Mark A. Weissberger (1982) (PDF). An initial critical summary of models for predicting the attenuation of radio waves by trees. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA118343. Retrieved 2012-02-01.