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This paper presents a closed-form expression for multiple forward diffraction by rows of tree canopies and buildings applicable to the propagation predictions at centimeter and millimeter wavelengths for local multipoint distribution service (LMDS). The expression is derived from the uniform geometrical theory of diffraction and physical optics, as well as from some existing models for vegetation and buildings. When the transmitter antennas are sufficiently high, the attenuation of the buildings varies around the value of free space and the building effect is negligible, because a line-of-sight (LOS) propagation path between transmitter and over building-rooftop receiver antennas exists and plays a major role. The tree canopies which extend above the building rooftop heights block the LOS propagation path and cause additional signal attenuation. An existing study of the LMDS radio channel based on measurements came to the same conclusion. The attenuation effect of the buildings is significant if the transmitter antennas are not high enough.

Formulation of multiple diffraction by trees and buildings for radio propagation predictions for local multipoint distribution service