Pade Second-Order Parabolic Equation Modeling for Propagation Over Irregular Terrain

The Pade second-order parabolic equation (PE) method is developed to predict radio propagation over irregular terrain. This solution is solved by the finite-difference method, which produces a stable pentadiagonal difference scheme. It allows propagation angles up to about 55° from the paraxial direction, which is able to give better results than the Fourier split-step method. This solution can be extended to an arbitrary general terrain profile by the boundary shift approach. We investigate the important problems about propagation angles of the different approximations of the PE models. It is found that Pade second-order PE model has the greater propagation angles, and thus can provide more accurate prediction of radio propagation. The calculated results are compared with the measurements in a fir forest environment, and a good agreement is obtained.