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^[1]

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

L={\begin{cases}1.33\,f^{{0.284}}\,d^{{0.588}}\,{\mbox{, if }}14<d\leq 400\\0.45\,f^{{0.284}}\,d\,\,\,\,\,\,\,\,\,\,{\mbox{, if }}0<d\leq 14\end{cases}}

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.^[2]

References

↑ Radio propagation in cellular networks, N. Blaunstein
↑ Introduction to RF propagation, John S. Seybold