# Weissberger's model

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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

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

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

1. ^ Radio propagation in cellular networks, N. Blaunstein
2. ^ Introduction to RF propagation, John S. Seybold