Simulation of near-ground long-distance radiowave propagation over terrain using Nyström method with phase extraction technique and FMM-acceleration

Propagation of radiowaves over complex irregular terrain profiles at near-grazing angles is studied using an efficient numerical solver. In supporting signal coverage prediction for such specialized systems in which the transmitter and receiver are in extreme proximity to the ground, available studies have been limited to the dependence upon site-specific, empirical-based models. The usefulness of these models is restricted as they cannot be applied to general radio configurations and propagation environments. Propagation over irregular terrain surfaces remains to be a challenging open problem demanding ongoing analysis; the unique properties of near-earth propagation such as surface wave propagation, non-plane wave propagation, and higher order reflection and diffraction phenomena pose additional constraints that often beset the validity of classical analytical ray tracing and physical optics techniques and their heuristic extensions. As such, when improved solution accuracy is required, full-wave simulation routines, despite their computational inefficiency, are employed to assess near-earth propagation parameters. A new 2D surface integral equation-based Nystrom solver in which a phase extraction technique is utilized to reduce the number of surface unknowns is described. As forward scattering is the dominant mechanism at the near-ground region, the associated rapidly-varying phase components of the integral equation kernel and solution unknowns are deduced and isolated in advance and subsequently built into the solver. It is shown that by applying this method, as few as one to two average unknowns per wavelength is adequate in obtaining accurate solutions. This significantly reduces the memory storage and computational expense for the simulation of long-distance propagation effects. The efficiency of this method is further improved by incorporating it into the framework of the fast multipole method (FMM). The full details of the algorithm are discussed; solution- - convergence comparisons with the regular Nystrom solver for terrain surfaces are also presented.