Application of the Spectral Acceleration Forward-Backward Method To Coverage Analysis Over Terrain Profiles

Abstract

The Forward-Backward (FB) method and its accelerated version (SA-FB, Spectral Accelerated Forward-Backward) were developed to compute the electromagnetic scattering from ocean-like rough surfaces. The FB algorithm provides very accurate scattering results and a very fast convergence, but its computational cost is still O(N²) per iteration, being N the number of unknowns used to discretize the surface. The Spectral Acceleration Algorithm proposed later reduces this cost to O(N). Nevertheless, the SA-FB can only be applied to quasi-planar structures or slightly rough surfaces (such as the sea surface), but it cannot be used to solve problems involving very undulating surfaces such as terrain profiles. In this paper the SA-FB method is modified to enhance its scope of application to considerable undulating surfaces. It will be seen that significant changes with respect to the original formulation as well as modifications of the integration path are necessary to get accurate results when dealing with terrain profiles. The proposed method is presented for vertical and horizontal polarizations and for PEC and non-PEC surfaces.