Time-domain analysis of multiple scattering effects on the radar cross section (RCS) of objects in a random medium

Abstract

This dissertation presents a theory of the time-domain radar cross section (RCS) of large conducting objects in discrete random media. The time-domain formula is obtained by applying the inverse Fourier transform of the two-frequency mutual coherence function (MCF) which is derived from both the 2nd order Rytov approximation and the strong fluctuation theory. The general formulation contains the 4th order moment which includes the correlation between the forward and the backward waves. The 4th order moment can be reduced to the summation of the 2nd order moments by assuming the fields are circular complex Gaussian random variables. The stochastic Green’s function is simplified using the parabolic equation (PE) approximation, and the sizes of the conducting objects are large in terms of wavelength; therefore, the Kirchhoff approximation is applicable for calculating the surface fields. This theory includes both the backscattering enhancement and the time-domain shower curtain effect that are not normally considered in the conventional theory. Numerical examples of the time-domain RCS of a conducting square plate in a discrete random medium characterized by the Gaussian phase function are shown to highlight the random media effects on the time-domain waveforms including time delay and pulse broadening in terms of optical depth and random medium location. Numerical results show that both pulse arrival time and pulse broadening increase significantly when the random media is placed far away from the object. This degradation of the image quality, known as the shower curtain effect, can be explained by the characteristics of the incoherent component.