Propagation of Waves in Randomly Distributed Cylinders Using Three-Dimensional Vector Cylindrical Wave Expansions in Foldy–Lax Equations

In this article, we develop a hybrid method to calculate the propagation of microwaves in randomly distributed dielectric cylinders. The hybrid method combines off-the-shelf techniques for single object and our developed techniques of Foldy-Lax (FL) method that include extracting the T-matrix for single object, vector translation addition theorem, and solving FL multiple scattering equations. For cylindrical scatterers such as tree trunks, the T-matrix in vector three-dimensional cylindrical waves are extracted from infinite cylinder approximation (ICA). In solving FL to calculate statistical moments, we iterate one order of multiple scattering at a time, with averaging over realizations performed after each order. This physically based iterative method of calculating statistical moments converges faster than the traditional iterative method of calculating the exact solution for each realization. The main purpose is to simulate tall tree trunks at the L-band and ICA is of sufficient accuracies. Numerical results are illustrated for a large number of cylinders of up to 196 and cylinder lengths of up to 94 wavelengths, which are typical of forests at the L-band. Results of the simulations of the hybrid method show that the transmission coefficients of waves are several times larger than that of the commonly used models of the radiative transfer equation and distorted Born approximation.