Radio-Wave-Propagation Modeling in the Presence of Multiple Knife Edges by the Bidirectional Parabolic-Equation Method

Fast full-wave computation of fields is the main reason for a radio system planner to apply the parabolic-equation method (PEM) for radio-coverage prediction. In this paper, the capability of PEM for the determination of backward electromagnetic-field scattering by single and multiple knife edges is investigated. For the wave equation, a suitable solution is considered. Contrary to the available formulations for the PEM, the proposed method includes a backward-propagating term. For both the forward and backward terms, the split-step algorithm is employed. Similar to the terrain-masking method, the effect of edges is exerted by the Fresnel-Kirchhof approximation into the forward-propagating wave. For the backward field, a similar algorithm is derived. Then, an iterative marching algorithm is developed for modeling radio wave propagation over multiple knife edges. Numerical results are compared with those of Uniform Theory of Diffraction (UTD) and finite-difference time-domain methods for the single-knife-edge problem. In addition, the effect of the backward-propagating field on radio wave propagation is investigated. The effect of edge locations and heights on the backward scattered field and number of computational iterations is studied. It is seen that, for the single knife edge, the backward scattered field depends on the height and location of the edge. The intensity of the backscattered field is a monotonic increasing function of the edge height. In addition, by increasing the edge height, the beam width of the backward scattered field increases. In ranges far from the knife edge in front of it, the field spreads, and its amplitude decreases. For multiple knife edges, it is seen that, in addition to the single backward scattered field, radio-wave-propagation modeling requires multiple forward-backward terms between successive edges. The geometry of the problem determines the required number of terms for sufficient accuracy