Two-way Fourier split step algorithm over variable terrain with narrow and wide angle propagators
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KünyeÖzgün, Ö., Apaydın, G., Kuzuoğlu, M., & Sevgi, L. (2010). Two-way Fourier split step algorithm over variable terrain with narrow and wide angle propagators. In 2010 IEEE Antennas and Propagation Society International Symposium (APSURSI) (pp. 1-4). Piscataway, NJ: IEEE. http://dx.doi.org/10.1109/APS.2010.5560904
Helmholtz's wave equation can be approximated by means of two differential equations, corresponding to forward and backward propagating waves each of which is in parabolic wave equation (PWE) form. The standard PWE is very suitable for marching-type numerical solutions. The one-way Fourier split-step parabolic equation algorithm (SSPE) is highly effective in modeling electromagnetic (EM) wave propagation above the Earth's irregular surface through inhomogeneous atmosphere [1-4]. The two drawbacks of the standard PWE are: (i) It handles only the forward-propagating waves, and cannot account for the backscattered ones. The forward waves are usually adequate for typical long-range propagation scenarios. However, the backward waves become significant in the presence of obstacles that redirect the incoming wave. Hence, this necessitates the accurate estimation of the multipath effects to model the tropospheric wave propagation over terrain. (ii) It is a narrow-angle approximation, which consequently restricts the accuracy to propagation angles up to 10°-15° from the paraxial direction. To handle propagation angles beyond these values, wide-angle propagators have been introduced [5-6].