A Percolation Model for the Wave Propagation in Non-Uniform Random Media

The statistical characterization of the electromagnetic propagation in urban radio channels is investigated. Towards this end, the propagation medium is modeled with a semi-infinite percolating lattice of lossless scatterers whose density varies in space according to a known one-dimensional distribution. The scenario is illuminated by a monochromatic plane wave that propagates according to the geometrical optics laws. By applying the random processes’ theory, a closed form analytical formula is provided, which allows a statistical estimation of the penetration capability of the electromagnetic wave into the medium. The analytical result has been validated through an exhaustive numerical assessment that demonstrates the effectiveness of the proposed model for a wide range of incidence conditions and scatterers’ density distribution.