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

Abstract

Abstract-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 can 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 theẑ 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.

Efficient calculation of the fields of a dipole radiating above an impedance surface

“…The characteristic impedance of free space and of the impedance plane are defined as and , respectively. The total fields above the impedance plane propagate with propagation constant and can be decomposed into a direct wave and diffracted wave given by (1) where is the distance to the observation point and is the distance to the source location. Also in (1), superscripts , , and are indicative of the total, direct, and diffracted fields, respectively; the diffracted fields being the perturbation in the total fields caused by the impedance half-space.…”

“…These effects can be decomposed into the effects of the homogeneous surface and the effect caused by some impedance transition in the surface such as a river, sea/land interface, or swamp/dry land transition. The effect of the impedance transition was addressed by Sarabandi and Casciato [1] in an analytic fashion for a transition with a general one-dimensional (1-D) impedance variation and small dipole excitation. The effect of the homogeneous surface, which is the classic Sommerfeld problem of an infinitesimal electric dipole radiating above a lossy half-space, is the focus of this work.…”

Radio wave propagation in the presence of a coastline

“…The resulting expressions are analytic and valid for any general one‐dimensional impedance transition for which the Fourier transform exists. The limits of the method are the radius of convergence of the perturbation series, and of course the limit of the first‐order impedance boundary condition applied [ Sarabandi and Casciato , 1999; Senior and Volakis , 1995]. Asymptotic techniques are then used to solve the field integrals and the resulting expressions are algebraic to first order in the perturbation series.…”

“…The method provides a solution for calculating the diffraction from a surface impedance transition of arbitrary profile, such as a river, shoreline, or trough, when excited by a small dipole of arbitrary orientation. This technique is an extension of a twodimensional (2-D) model presented by Sarabandi [1990] for a resistive sheet when excited by a plane wave. It was shown by Sarabandi [1990] that the method could be extended to that of an impedance sheet simply by replacing the resistivity with the complex impedance divided by a factor of two.…”

“…This technique is an extension of a twodimensional (2-D) model presented by Sarabandi [1990] for a resistive sheet when excited by a plane wave. It was shown by Sarabandi [1990] that the method could be extended to that of an impedance sheet simply by replacing the resistivity with the complex impedance divided by a factor of two. The technique was extended to include the case of oblique incidence and dipole excitation by Sarabandi and Casciato [1999], and this is the formulation applied here.…”