Mark D. Casciato

Efficient Calculation of the Fields of a Dipole Radiating Above an Impedance Surface

The classic problem of field computation for an infinitesimal dipole radiating above an impedance half-space is revisited. The expressions for the traditional solution consist of integrals of the Sommerfeld type that cannot be evaluated in closed form and due to their highly oscillatory nature are difficult to evaluate numerically. The exact image theory, which has previously been applied to vertical electric and magnetic dipoles, is used to derive explicit expressions for dipoles of arbitrary orientation above impedance surfaces. Starting from the spectral representation of the field, the reflection coefficients are cast in the form of exact Laplace transforms and then by changing the order of integrations field expressions in terms of rapidly converging integrals are obtained. These expressions are exact, and valid for any arbitrary source alignment or observation position. It is shown that the formulation for a horizontal dipole contains an image in the conjugate complex plane resulting in a diverging exponential term not previously addressed in the literature. It is shown through further mathematical manipulations, that the diverging term is a contribution of the mirror image which can be extracted. Comparison of numerical results from exact image theory and the original Somm~rfeld-type expressions shows good agreement as well as a speedup in computation time of many orders of magnitude, which depends on the distance between the transmitter and the receiver. This formulation can effectively replace the approximate asymptotic expressions used for predicting wave propagation over a smooth planar ground (having different regions of validity). The exact image formulation is also of practical use in evaluation of the Greens function for various applications in scattering problems where approximate solutions are not sufficient.

Demonstration of time reversal methods in a multi-path environment

Time reversal methods (TRM) offer a unique opportunity for solving the problem of electromagnetic (EM) wave propagation and focusing in a spatially varying (inhomogeneous) medium. While the concept of time reversal is new to the field of EM wave propagation, it has been applied in the area of acoustics and ultrasonics for several years (Fink, M. and Prada, C., Inverse Problems, vol.17, p.R1-38, 2001). In any finite size array that occupies a limited spatial area, the system is diffraction limited; however in acoustics, it has been shown that, in an inhomogeneous medium, a time reversal array is not always diffraction limited and can achieve super-resolution. Basically, scatterers near the transmitting array and/or focal point act as an extension of the array in the focusing process. The paper shows that the same phenomenon exists for EM waves. While the feasibility of applying TRM to EM problems has been demonstrated, many issues must be investigated and resolved before TRM can be implemented practically in a communications or radar imaging system.

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. The 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 the z/spl circ/ 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.

A measurement system for ultrawide-band communication channel characterization

In this paper a novel wide-band propagation channel measurement system with high dynamic range and sensitivity is introduced. The system enables the user to characterize signal propagation through a medium over a very wide frequency band with fine spectral resolution (as low as 3 Hz) by measuring the attenuation and phase characteristics of the medium. This system also allows for the study of temporal, spectral and spatial decorrelation. The high fidelity data gathered with this system can also be utilized to develop empirical models or used as a validation tool for physics based propagation models which simulate the behavior of radio waves in different environments such as forests, urban areas or indoor environments. The mobility and flexibility of the system allows for site specific measurements in various propagation scenarios.

Scattering from a land/sea transition

In order to completely characterize the fields of an infinitesimal dipole above a lossy Earth, the effects of any impedance transition or inhomogeneity, such as caused by a river or land/sea interface must be accounted for. In general, geometrical theory of diffraction (GTD) methods have been applied to solve this type of problem, however they are valid only for abrupt transitions. In this paper the perturbation technique is applied to study the effects of a land/sea transition on the total fields of a dipole above an impedance surface. It is shown that the effects of the transition on the total fields is significant for observation distances far from the transition and independent of the gradient of the transition when both source and observation are near the impedance surface.

Radio wave diffraction from impedance surfaces with one dimensional general impedance variation

The problem of plane wave diffraction from shorelines in planar land-sea boundaries, using the Wiener-Hopf technique, was addressed by Bazer et al. (1962). Geometrical theory of diffraction (GTD) methods, while accurate at high frequencies, have only been applied to problems where abrupt variations in a surface are present. An analytical formulation is developed to predict the diffraction from a surface impedance discontinuity, of an arbitrary profile, such as rivers, shorelines, or troughs, when excited by a small dipole of arbitrary orientation. Basically the river is modeled as an impedance change in an infinite impedance plane, representing the ground plane. An integral equation is developed in the Fourier domain for ease of analysis and then solved analytically using a perturbation technique, assuming a one dimensional impedance variation. Recursive expressions for the induced current of any order, for arbitrary impedance variations, are shown. Using these currents, the far field expressions for plane wave excitation are evaluated using the stationary phase technique. The derivation is then extended to small dipole excitation represented by a continuous spectrum of plane waves, again using the stationary phase to calculate the diffracted fields. Results for both plane wave and dipole excitation are shown.

Wave propagation in the near vicinity of a coastline

The problem of a radio transmitter, radiating near or along a coastline is one of considerable interest. A common situation is one in which the transmitting antenna sits atop a cliff or bluff overlooking the shoreline and the effects of both the cliff and the shoreline on the radio signal must be taken into account, including their mutual interaction. By application of a perturbation technique, the problem of diffraction from a shoreline or lanusea transition was addressed by Casciato and Sarabandi [l], [2]. In this paper this model is extended to include the effects of a cliff or bluff in close proximity to the shoreline by using standard UniformTheory of Diffraction (KJTD) techniques [3]. Note that throughout this work the term coast or coastline describes the combination of the cliff and landsea transition, while shoreline or seashore describes the effects of the lanusea only. Also the diffracted fields are defined as fields generated by the shoreline or cliff edge. while scattered fields are defined as the combined effects of the shorelindcliff diffraction as well as fields reflected from flat impedance surfaces. There are currently no asymptotic solutions for the general case of an obliquely incident wave on an impedance wedge of arbitrary wedge angle. Because of this, and for the purpose of this analysis a 2-D UTD solution for an impedance wedge will be applied, and it will be assumed that the source is distant (including secondary sources) from the transition and cliff so that plane wave excitation is assumed. In the next section the UTD solution for an impedance wedge will be applied and integrated with the perturbation solution previously cited and results calculated. The case of a receiver mounted on an aerial vehicle (helicopter, UAV, etc.) flying from the sea, up and over the cliff and land will be examined.

Fields of an infinitesimal dipole radiating near an impedance half-space by application of exact image theory

In this paper exact image theory is applied to the problem of an electric dipole, of arbitrary orientation, radiating above an impedance plane and the subtlety regarding the derivation of the explicit expressions of horizontal dipoles are discussed. First the Sommerfeld formulation for the diffracted electric fields is given followed by a discussion of the application of exact image theory to transform the Sommerfeld integrals into a form more conducive to numerical evaluation. Then explicit expressions for all electric field quantities, in terms of the exact image formulation, is shown. The field expressions for a horizontal dipole show a diverging exponential term not discussed by Lindell and Alanen. Also, it is shown that the expressions for the exact image can be rearranged to separate the space waves (direct+geometrical optics (GO)) from the surface wave and hence the behavior of the surface waves can be analyzed independent of the distance between source and observation points, and for very low values of impedance, where the saddle point is near the pole. Finally a comparison is made between the time required to evaluate the electric fields using the Sommerfeld formulation and using the exact image expressions.

Modeling surface currents on electrically large impedance cylinders-2D, TM case

Scattering and diffraction from terrain obstacles have a major effect on radio wave propagation in a natural environment. Mountains, ridge lines and hills can exhibit the properties of a long, slowly curving feature essentially infinite in one dimension. The local radius of curvature of these obstacles is large compared to wavelength and therefore diffraction from convex surfaces as opposed to wedge diffraction is the more applicable approach. No GTD field solutions for diffraction from convex surfaces are valid in all regions around the object. The calculation of surface currents will generate the exact fields in all regions through the radiation integrals. If the exact surface current is formulated in terms of a physical optics (PO) term and correction or diffraction term the diffraction current is highly localized to the shadow boundary for a surface with large, slowly varying, radius of curvature. The diffraction current for a circular cross section is therefore applicable to any convex surface where the local radius of curvature is known. Surface diffraction currents can be generated by applying Fock theory, however the formulations are mathematically complex, and in the lit region near the shadow boundary numerical integration must be performed. In Casciato and Sarabandi a heuristic approach was used to develop a macromodel which simply and accurately predicts the asymptotic behavior of the Fock currents for a PEC circular cylinder illuminated by a plane wave at oblique incidence. In this paper a method is developed to extend this method for the TM case, normal incidence, to that of an impedance cylinder which more accurately represents a natural terrain feature.

A novel approach to high frequency diffraction from curved, perfectly conducting cylinders

Discusses diffraction from singly curved surfaces. Diffracted fields can be defined as a correction to those generated by physical optics (PO). These diffracted fields are generated by events local to the shadow boundary of the curved surface therefore knowledge of local radius of curvature at the shadow boundary will give accurate diffracted fields for any arbitrarily shaped curved surface. Knowledge of surface currents allows for the prediction of fields everywhere outside of the curved body. Once the diffraction currents, exact surface current minus PO current, are known total fields can be generated for any arbitrarily shaped, singly curved surface by adding simple PO currents to the diffracted current. To predict these currents a macromodel of the surface diffraction currents, due to plane wave excitation, for the perfect electric conducting (PEC) case is developed. These diffraction currents are from the exact eigensolution for circular cylinders at oblique incidence. Approximate algebraic, expressions, based on the high frequency behavior of the surface fields, are generated by a curve fit to match the exact diffraction current. Expressions are macromodeled for both the TE and TM case and the formulations were split into two regions: (1) 1/spl lambda/</spl alpha/<20/spl lambda/, and 2) 15/spl lambda/</spl alpha/. The curve fit was performed for cylinders up to /spl alpha/=200/spl lambda/, where /spl alpha/ is the cylinder radius, and the macromodeled current was validated up to /spl alpha/=400/spl lambda/ by a comparison with the eigensolution distributions.