Propagation and scattering in a ducting maritime environment from a fast method of moments

International audienceIn coastal and maritime regions the microwave propagation is affected by the highvariability of the meteorological parameters in space and time. This variability leads torespective changes in the tropospheric refractive index, namely ducting effect, whichimplies that the Radar wave is trapped near the surface and can propagate over a longdistance. The ducting is present for a small percent of time but it significantly influencesthe radar and communications systems working in the microwave range. Then, thepresence of a duct strongly affects the propagation, but also jointly, the scattering fromthe sea surface.For a longtime, The Parabolic Wave Equation (PWE) method combined with SSF (Split-Step Fourier), has been widely used to model radiowave propagation in a cone centeredon the paraxial direction over highly-conducting irregular surfaces in an inhomogeneousatmosphere. For a complete review of this method, see the textbook of Levy (2000, IET,London) and the references therein. The great advantage of the PWE-SSF method is thatit can deal with most real-life inhomogeneous environments and is that it fast (based onthe calculation of successions of FFTs). Its main drawback is the underlying paraxialapproximation leading to an approximation of the propagator (that is, the Green'sfunction) and the boundary conditions are determined from a heuristic way, for instancefrom the Ament reflection coefficient (Ament, IRE, 1953).The well-known Method of Moments (MoM) is a way of solving rigorously thescattering problem by converting the Boundary Integral Equation (BIE) into a linearsystem, in which the impedance matrix must be inverted to determine the surface currents.Then, the scattered field is computed by radiating the surface currents. For a ductingenvironment, the main drawback of the MoM is that the Green's function (propagator) isknown only for a small class of refractive index profiles. That is why, when the BIEmethod is applied, the propagator is usually derived under the PWE approximation. Theduct effect is significant over a long distance, which means that the size (related to thesurface length) of the linear system to solve is huge for practical applications.Combining three techniques, i.e., Subdomain Decomposition Iterative Method (SDIM),Adaptive Cross Approximation (ACA) and Forward-Backward Spectral acceleration(FBSA), a fast MoM is presented to efficiency calculate the propagation and scattering inducting maritime environments. The resulting method is named ``SDIM+FBSA+ACA''.The SDIM allows us to split up the surface into sub-surfaces, the ACA allows us toaccelerate the coupling steps between the sub-surfaces and FBSA allows us to acceleratethe calculation of the local interactions on the sea sub-surfaces. The resulting complexityand memory requirement are then nearly proportional to N, the number of surfaceunknowns, whereas from a brute force of MoM, they are N3 and N2, respectively