Simulation of Long Distance Wave Propagation in 2-D Sparse Random Media: A Statistical S-Matrix Approach in Spectral Domain

The problem of long distance wave propagation in a sparse random medium is considered in this paper. A mathematical technique for modeling the behavior of electromagnetic wave propagation as a function of distance in a 2-D sparse random media at millimeter wave (MMW) regime is presented. The proposed model is a field method based on Maxwell's equation and, thus, the phase and magnitude of the field in the random medium can be tracked accurately. The random media is characterized by low volume fraction but electrically large scatterers having relatively high dielectric constant. The technique relies on discretizing the random media into thin slabs and relating the forward and backward scattered plane wave spectra from the individual slabs by an equivalent spectral bistatic scattering matrix. By cascading the scattering matrices of the individual slabs, the statistics of the overall scattered wave in both forward and backward directions are obtained. This technique will be referred to as statistical S-matrix approach in spectral domain, or SSWaP-SD. Using this method, it is shown that after propagation to a critical range inside the random media, the incoherent component of the forward propagating wave overcomes the mean-field component resulting in a dual-slope attenuation curve as a function of distance. The accuracy of the model is examined against a full wave Monte Carlo simulation and a very good agreement is observed. Finally, based on the proposed model, analytical expressions for predicting the forward path-loss as well as the back scattered power from a sparse, translational invariant discrete random media are derived. The analytical expressions are tested against Monte Carlo simulation for a very long random medium and very good agreements are demonstrated.