Multibeam approach to pulse scattering from discrete random media

The problem of a pulsed aperture illuminating a two dimensional layer of discrete random medium over a flat, homogenous background is considered. The layer consists of sparsely distributed dielectric scatterers that are randomly oriented in space. The behavior of the backscattered signal from the medium is examined in the time domain for the case of a short pulse incidence. The excitation of the antenna is assumed to be arbitrary, and is represented as a discrete sum of shifted and tilted Gaussian beams by using Gabor expansion. The expansion is exact, and with the appropriate choice of beam parameters, the radiation pattern can be matched by considering only a few beams. The beams in the expansion represent the main and side lobes of the antenna, making it possible to examine the individual effects of each lobe on the backscattered signature.; The received power at the antenna is composed of a coherent and an incoherent part associated respectively with the mean and the fluctuating parts of the scattered fields from the medium. The coherent term is observed as a sharp peak, while the incoherent term builds up and decays more slowly. The incoherent response is dominated by three terms: direct, direct reflected and reflected. The direct term is associated with the volume scattering and arrives first at the antenna. The second term observed at the antenna is the direct reflected component, which results from a single interaction between the scatterer and the ground. Depending on the attenuation inside the medium, this term can be the strongest return at the antenna. The reflected term which involves a double bounce from the ground arrives last due to the relatively longer path it travels.; Using the multibeam representation, it is possible to examine individual returns from the side and main lobes of the antenna radiation pattern. The interference of the antenna lobes with each other can also be formulated via the multibeam representation. Strong responses from the side lobes can be observed when one of the side lobes of a tilted antenna is looking at nadir. In this case, significant returns are observed from the coherent and the direct reflected component of the incoherent terms. Individual and collective responses of the beams in the multibeam representation will be examined for various cases.