A Simplified Analytical Model to Predict the Specific Attenuation of a Tree Canopy

A simplified analytical model is presented to predict the specific attenuation for propagation through a tree canopy in a residential environment for frequencies of up to 2 GHz. In this approach, the canopy of a tree is modeled as an ensemble of leaves and branches all having prescribed location and orientation statistics. The Foldy-Lax discrete scattering theory is used to find the specific attenuation of a tree associated with the mean field. Explicit formulas are presented to calculate the specific attenuation of a tree canopy. It is shown that the specific attenuation of a tree canopy depends on the frequency, polarization, electrical and geometrical characteristics of branches and leaves, biophysical parameters of a tree, and statistical distribution of branches and leaves in reference to the angle of incidence of the plane wave. It is also shown that for deciduous trees, as opposed to coniferous trees, the inclination angle distribution of the branches is more vertical, producing a higher specific attenuation for the vertical-polarization incident wave than for the horizontal-polarization incident wave