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The asymptotic solution of the single and multiple diffraction problems


V.V. Akhiyarov

Simple and efficient methods exist for the field strength prediction over terrain profile. These methods are based on the approximation of the real obstacles with the wedges. Those wedge’s surface impedance must correspond to the real surface impedance. Another example is the prediction of radio wave propagation in urban environments. In this case vertical edges of the buildings can be considered as impedance wedges. The uniform theory of diffraction can be used in both those cases. Known formulas for the calculation of diffraction field near the boundary between the shadow zone and illuminated area is quite acceptable. However, in a wide range of incidence and scattering angles, these formulas must be elaborated in order to achieve better agreement with Malyuzhinets’ solution. Using uniform theory of diffraction, the wave propagation problem for multiple obstacles can be solved. As an example, in this paper the solution for two absorbing half-planes is presented. The main issue in solving this problem is to determine the parameters L and LS, which are used for calculation of the amplitude and slope diffraction coefficients. For the determination of these parameters, continuity equations are used. These equations are derived from the fact that the transition from the illuminated area to the shadow zone must not be accompanied by a discontinuity of the diffraction field. The results of field strength calculations for two absorbing half-planes and a comparison with calculations based on a parabolic equation are shown in this paper.

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