Conformal mapping as a method for the numerical solution of the parabolic wave equation in the presence of small-angle terrain irregularities

Authors: Novikov A. V., Akulinichev Yu. P.

Annotation: Conformal mapping which allows remapping of terrain irregularities into equivalent refractive index of the troposphere has been found. Comparative results of the numerical calculation of the propagation factor height profile are given for two surface models using two methods. Comparison was made with the method of piecewise-linear approximation of the terrain profile. It is shown that the conformal mapping method is suitable only for terrain profiles well approximated by a truncated Fourier series. In the absence of exact solutions for the considered paths (the triangular and sinusoidal hills) it should be noted only that both methods give the propagation factor height the profiles which are qualitatively similar (the difference is not more than 2 dB in penumbra and the shadow region).

Keywords: refractive index, conformal mapping, rough ground surface, radio propagation, parabolic wave equation