Greene Approximation Wide-Angle Parabolic Equation for Radio Propagation

This paper presents the Greene second-order parabolic equation (PE) solution to model radio propagation over irregular terrain. This solution is implemented by finite-difference and shift-map technique. The second-order finite-difference approach performs well for slopes up to about 15 degrees, and discontinuous slope changes up to about 30 degrees, which is better than can be achieved using the split-step/Fourier approach. The results prove that the Greene PE solution has greater propagation angles than does the Claerbout PE solution. Thus, the Greene second-order solution can certainly give better results for large angle propagation over complicated terrain boundaries. Besides, we treat the important problem of accuracy of the different approximations of the PE-based propagation models, and derive the general PE solutions with respect to the terrain slope for the different approximations. It is useful to have collected in one paper, the most important PE approximations for radio propagation.