The idea here is to decompose the field into plane waves along the horizontal direction and to use the appropriate plane wave boundary condition for each plane wave component in the spectral domain. No approximations are made beyond the original parabolic approximation, which neglects backscatter. The spectral parameter s corresponds to a horizontal plane wave component with grazing angle . A Fourier split-step implementation is much more desirable in terms of efficiency. This technique is actually quite slow because it involves solving an integral equation at each step, and it can also run into stability problems.
Computational overheads depend on the shape of the convolution kernel w .
Results are in good agreement for moderate wind speeds, as shown in Figure 3. The source here is a 10 GHz vertically polarized antenna located at 25 m above mean sea level. Figure 3 shows path loss against range at 25 m amsl. Comparison of local and non-local models for 10 GHz antenna in strong surface duct. Comparisons for stronger wind speeds are underway.