Radiowave Propagation Analysis With a Bidirectional 3-D Vector Parabolic Equation Method

A 3-D bidirectional solution to the parabolic approximation of the wave equation is investigated by using a vector field representation. The backward propagating wave is integrated to the classical parabolic equation approach, which represents the forward propagating wave. Propagation over flat terrain in the presence of knife-edges is considered as well as over irregular terrain consisting of hills modeled by the succession of knife-edges. At each knife-edge, appropriate boundary conditions are enforced, and the wave is partly reflected in the backward direction. The wave is marched in both directions by using the split-step algorithm. Different tests are conducted in order to analyze and validate the results obtained by the proposed algorithm. Comparisons with results from both, 2-D parabolic equation-based algorithm, and 3-D finite-difference time domain-based algorithm, are presented in this paper.