Estimation of the radiative energy transfer phase function from simplified foliage structures

Foliage obstacles are one of the most dominant type of obstacle in rural propagation environments. The complex and random nature of these foliage obstacles provide a significant challenge in modeling their effects in the propagation of radio waves. The Radiative Energy Transfer (RET) based models have been shown in literature to provide accurate predictions of propagation effects in such foliage environments [1]. One of the parameters necessary for RET models is the phase function p(ŝ,ŝ´) which describes the directionality of the total scattered energy in the medium, where ŝ and ŝ´ represent the direction of the energy exiting and entering from each scatterer respectively. The phase function is typically modeled as a Gaussian function with an isotropic background [2] described by equation (1), where α is the ratio between the forward scattered power and the total scattered power, β is the beamwidth of the forward lobe, and γ is the angle between ŝ and ŝ´.