Diffraction of radio waves from arbitrary one-dimensional surface impedance discontinuities

Characterization of a propagation channel is essential in developing an optimum wireless system. Accurate prediction of field parameters, both stochastic and deterministic can greatly reduce the time and effort required to design and develop a progression of prototypes necessary to achieve the final system requirements. To accomplish this, a physics-based methodology must be considered. In this methodology, a series of scattering and diffraction models must be developed and integrated which accurately represent the effects of various terrain features on electromagnetic wave propagation. In this paper, diffraction of electromagnetic waves from a surface impedance discontinuity, which fan represent a river or trough is considered. In order to more accurately represent the transmitter antenna, dipole excitation is used as the wave source. The river or trough is modeled as a variable impedance insert in an infinite plane with one-dimensional (1-D) variation. An integral equation for an impedance surface is formulated in the Fourier domain, which is solved iteratively using a perturbation technique. An analytical solution is provided to any desired order in terms of multifold convolution integrals of the Fourier transform of the impedance function. The far-field integral is then evaluated using the stationary phase technique. Next, the formulation is extended to a short dipole with arbitrary orientation by expanding the dipole field in terms of a continuous spectrum of plane waves. Results are then shown for both plane wave and dipole excitation. Scattering results for an impedance insert are generated up to second order. These results are then compared to geometrical theory of diffraction (GTD) results. The effect of varying both the width and perturbation parameter of the insert are described. Results from plane wave incidence at various oblique angles are shown. Effects of varying the impedance transition shape are shown and compared. Scattering results for dipole excitation show E-field components in a planar grid at a given height above the scattering plane. It is shown that the (Z) over cap component of the diffracted field is maximized for either a vertical or horizontal dipole orientation. Effects generated by varying the receiver height are also discussed.