On the Validity of an Analytical Solution for Characterizing Backscattering From Tree Trunks for FOPEN Sensing at $P$ -Band

A comprehensive set of simulations is performed to analyze the accuracy of an analytical solution for characterizing the backscattering responses of circular cylindrical tree trunks located above a dielectric ground. The formulation of interest here is from the volumetric current integration method, combined with a ray-based approach for the treatment of ground effects. Through comparisons with a reference solution provided by a full-wave solver, the region of validity of the closed-form approximate solution as a function of trunk length, trunk radius, incidence angle, and polarization is derived. Trunks with and without tapering along their lengths are considered. It is noted that, in general, the error behavior of the vv solution exhibits more complexity than that of the hh solution, due to the Brewster angle effects of the trunk and the ground; consequently, the hh solution is valid over a wider range of length and radius values. The backscattering signatures of the trunks are also examined in the imaging domain. It is found that the analytical solution can correctly predict the single ground-bounce returns but may not consistently capture other less prominent effects, such as scattering from the top of the trunk and higher order interactions.