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Showing papers in "IEEE Transactions on Antennas and Propagation in 1989"


Journal ArticleDOI
TL;DR: In this article, a ray-shooting approach is presented for calculating the interior radar cross section (RCS) from a partially open cavity, where a dense grid of rays is launched into the cavity through the opening.
Abstract: A ray-shooting approach is presented for calculating the interior radar cross section (RCS) from a partially open cavity. In the problem considered, a dense grid of rays is launched into the cavity through the opening. The rays bounce from the cavity walls based on the laws of geometrical optics and eventually exit the cavity via the aperture. The ray-bouncing method is based on tracking a large number of rays launched into the cavity through the opening and determining the geometrical optics field associated with each ray by taking into consideration: (1) the geometrical divergence factor, (2) polarization, and (3) material loading of the cavity walls. A physical optics scheme is then applied to compute the backscattered field from the exit rays. This method is so simple in concept that there is virtually no restriction on the shape or material loading of the cavity. Numerical results obtained by this method are compared with those for the modal analysis for a circular cylinder terminated by a PEC plate. RCS results for an S-bend circular cylinder generated on the Cray X-MP supercomputer show significant RCS reduction. Some of the limitations and possible extensions of this technique are discussed. >

831 citations


Journal ArticleDOI
TL;DR: In this article, a generalized pencil-of-function (GPOF) method is developed for extracting the poles of an electromagnetic system from its transient response, which needs the solution of a generalized eigenvalue problem to find the poles.
Abstract: A generalized pencil-of-function (GPOF) method is developed for extracting the poles of an electromagnetic system from its transient response. The GPOF method needs the solution of a generalized eigenvalue problem to find the poles. Subspace decomposition is also used to optimize the performance of the GPOF method. The GPOF method has advantages over the Prony method in both computation and noise sensitivity, and approaches the Cramer-Rao bound when the signal-to-noise ratio (SNR) is above threshold. An application of the GPOF method to a thin-wire target is presented. >

693 citations


Journal ArticleDOI
TL;DR: In this article, the Nyquist number was shown to be practically equal to the effective (spatial) bandwidth of the scattered field and to the extension of the observation domain, and it was shown that the field representation can be made in terms of field values and simple sampling functions.
Abstract: Starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities, the degrees of freedom of the scattered field are introduced and then computed. The degrees of freedom are shown to be practically equal to the Nyquist number appropriate to the effective (spatial) bandwidth of the scattered field and to the extension of the observation domain. Accordingly, a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error. It is also shown that the field representation can be made in terms of field values and simple sampling functions, provided that a marginal increase in the approximation error is tolerated. The results not only completely justify the use of sampling interpolation for representing scattering fields, but also demonstrate that such representation is practically an optimal one. An algorithm for the reconstruction of scattered fields, given the maximum allowed error, is then produced. >

487 citations


Journal ArticleDOI
TL;DR: In this paper, a wideband multipath measurements at 1300 MHz were made in five factory buildings in Indiana and the average factory path loss was found to be a function of distance to the 2.2 power.
Abstract: Wideband multipath measurements at 1300 MHz were made in five factory buildings in Indiana. Root-mean-square delay spread ( sigma ) values were found to range between 30 and 300 ns. Median sigma values were 96 ns for line-of-sight paths along aisleways and 105 ns for obstructed paths across aisles. Worst-case sigma or 300 ns was measured in a modern open-plan metal-working factory. Delay spreads were not correlated with transmitter-receiver separation or factory topography but were affected by factory inventory, building construction materials, and wall locations. Wideband path loss measurements consistently agreed with continuous-wave measurements made at identical locations. It is shown that such empirical data suggest independent and identical uniform distributions on the phases of resolvable multipath signal components. Average factory path loss was found to be a function of distance to the 2.2 power. >

429 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed broadband impedance matching as a natural way to increase the bandwidth of conventional microstrip patch antennas and found that by using an optimally designed impedance-matching network, the bandwidth can be increased by a factor of at least 3.9, the exact value depending on the degree of matching required.
Abstract: The nature of the inherent narrow bandwidth of conventional microstrip patch antennas is considered. It is observed that, except for single-feed circularly polarized elements, their bandwidth is limited only by the resonant behavior of the input impedance and not by radiation pattern or gain variations, which usually are negligible over a moderate 10 to 20% bandwidth. Therefore, broadband impedance matching is proposed as a natural to increase the bandwidth. The maximum obtainable bandwidth is calculated using Fano's broadband matching theory. It is found that by using an optimally designed impedance-matching network, the bandwidth can be increased by a factor of at least 3.9, the exact value depending on the degree of matching required. A transmission-line prototype for a proper matching network is developed. The translation of this prototype network into a practical structure (e.g. a microstrip or stripline circuit) is considered. Practical design examples and experimental results which clearly show the validity of the technique are given. >

388 citations


Journal ArticleDOI
TL;DR: In this paper, a surface current approach is applied in which the electrical currents in the feed lines are modeled as in ideal transmission lines, and the free-space radiation and the surface-wave excitation of typical segments in printed feed networks are studied.
Abstract: The radiation and losses in microstrip antennas with a corporate feed network are studied. A surface current approach is applied in which the electrical currents in the feed lines are modeled as in ideal transmission lines. The free-space radiation and the surface-wave excitation of typical segments in printed feed networks are studied. A four-element array antenna with its printed feed network is analyzed and predicted radiation patterns, directivity, and gain are presented and compared with experimental results. The gain and directivity of large arrays of 16, 64, 256 and 1024 elements are calculated and measurements in the frequency range of 10 to 35 GHz are reported. >

324 citations


Journal ArticleDOI
TL;DR: In this paper, a set of measurements of patch antennas on substrates of varying thickness and permittivity, using three types of feeds, is presented, and the measurements show that erratic results may be obtained for substrates thicker than about 0.02 lambda/sub 0/, where lambda /sub 0/ is the free-space wavelength at the resonant frequency.
Abstract: A set of measurements of patch antennas on substrates of varying thickness and permittivity, using three types of feeds, is presented. Resonant frequency and resonant resistance are compared with calculated values from the representative theories. The measurements show that erratic results may be obtained for substrates thicker than about 0.02 lambda /sub 0/, where lambda /sub 0/ is the free-space wavelength at the resonant frequency. These problems may be related to coax-to-microstripline transitions, but their cause is not yet definitely known. The theoretical models that are compared give reasonably good results for resonant frequency, but none give impedance results that are consistently reliable. It thus appears that further work is needed to develop analytical models that can adequately predict the impedance performance of microstrip antennas on thick and/or high dielectric constant substrates. >

256 citations


Journal ArticleDOI
TL;DR: In this article, the feasibility of using a periodic dielectric layer composed of alternating bars having dielectrics constants epsilon/sub 1/ and epsil/sub 2/ as a dichroic surface at millimeter-wave frequencies is examined for oblique incidence.
Abstract: The feasibility of using a periodic dielectric layer, composed of alternating bars having dielectric constants epsilon /sub 1/ and epsilon /sub 2/, as a dichroic surface at millimeter-wave frequencies is examined For oblique incidence, it is found that total transmission and total reflection can be obtained at different frequencies for proper choices of epsilon /sub 1/ and epsilon /sub 2/ and the geometric parameters The frequencies of total reflection and transmission can be estimated from wave phenomena occurring in a layer of uniform dielectric constant equal to the average value in the periodic layers For some of the frequencies of total transmission, the bandwidth for 90% transmission is found to be 40% The bandwidth for 90% reflection is always found to be much narrower, the greatest value obtained being 25% >

242 citations


Journal ArticleDOI
TL;DR: In this article, a technique which utilized the inherent mutual coupling in an array to both calibrate and predict the radiation patterns of a phased-array antenna is investigated, where the only restriction of the technique is that the ability to transmit and receive with pairs of the array elements is required.
Abstract: A technique which utilized the inherent mutual coupling in an array to both calibrate and predict the radiation patterns of a phased-array antenna is investigated. The only restriction of the technique is that the ability to transmit and receive with pairs of the array elements is required. The theory associated with array mutual coupling and its relationship to both array calibration and array patterns is discussed. The design of a test bed phased-array antenna is covered. The mutual coupling technique (MCT) is used experimentally to calibrate the test array as well as to predict the array radiation patterns. It is shown that the results obtained by MCT are in good agreement with conventional far-field measurements. >

205 citations


Journal ArticleDOI
TL;DR: In this paper, the authors extended the wedge diffraction coefficients for computing propagation path loss over finitely conducting earth to include slope diffraction, with the assumption that propagation of energy through the wedge is negligible.
Abstract: Heuristic wedge diffraction coefficients for computing propagation path loss over finitely conducting earth are extended to include slope diffraction, with the assumption that propagation of energy through the wedge is negligible. The slope diffraction terms for the lossy wedge are obtained in an analogous manner as for the perfectly conducting case, except that special care must be taken with the factor multiplying the incident field for grazing incidence. Results given show that the slope diffraction term produces continuous results that behave reasonably when compared with results for perfectly conducting wedges. >

176 citations


Journal ArticleDOI
TL;DR: In this paper, the propagation properties of suspended water and ice particles which make up atmospheric haze, fog, and clouds were examined for microwave and millimeter-wave frequencies, and the rates of attenuation alpha (dB/km) and delay tau (ps/km), derived from a complex refractivity based on the Rayleigh absorption approximation of Mie's scattering theory, were derived.
Abstract: Propagation properties of suspended water and ice particles which make up atmospheric haze, fog, and clouds were examined for microwave and millimeter-wave frequencies. Rates of attenuation alpha (dB/km) and delay tau (ps/km) are derived from a complex refractivity based on the Rayleigh absorption approximation of Mie's scattering theory. Key variables are particle mass content and permittivity, which depends on frequency and temperature both for liquid and ice states. Water droplet attenuation can be estimated within a restricted (10+or-10 degrees C) temperature range using a simple two-coefficient approximation. Experimental data on signal loss and phase delay caused by fog at four frequencies (50, 82, 141, and 246 GHz) over a 0.81-km line-of-sight path were found to be consistent with the model. >

Journal ArticleDOI
TL;DR: In this paper, a numerical scheme to obtain radar cross section (RCS) of three-dimensional bodies of resonant size (BRS) with arbitrary geometry and material composition is described.
Abstract: A numerical scheme to obtain radar cross section (RCS) of three-dimensional bodies of resonant size (BRS) with arbitrary geometry and material composition is described. The RCS is obtained by solving the electric-field integral equation (EFIE) using the conjugate gradient-fast Fourier transform method (CG-FFT). The choice of a suitable set of basis and testing functions to discretize the EFIE leads to a very accurate and computationaly efficient CG-FFT procedure. This accuracy is checked by comparison with RCS measurements or predictions by other methods. As compared to the moment method, this CG-FFT scheme avoids the storage of large matrices and reduces the computer time by orders of magnitude. >

Journal ArticleDOI
TL;DR: In this paper, an analysis of a thin cylindrical-rectangular microstrip patch antenna is presented, where the electric field under the curved patch and the resonant frequencies using the cavity model are obtained by considering the equivalent magnetic current radiating in the presence of a cylinrical surface.
Abstract: An analysis is presented of a thin cylindrical-rectangular microstrip patch antenna. After obtaining the electric field under the curved patch and the resonant frequencies using the cavity model, the far-field is found by considering the equivalent magnetic current radiating in the presence of a cylindrical surface. The input impedance and the total Q-factor are then calculated. Numerical and graphical results are presented to illustrate the effect of curvature on the characteristics of the TM/sub 10/ and TM/sub 01/ modes. >

Journal ArticleDOI
TL;DR: In this paper, the study of microstrip patch antennas is directly treated in the time domain, using a modified finite-difference time-domain (FDTD) method, and the frequency dependence of the relevant parameters can readily be found using the Fourier transform of the transient current.
Abstract: The study of microstrip patch antennas is directly treated in the time domain, using a modified finite-difference time-domain (FDTD) method. Assuming an appropriate choice of excitation, the frequency dependence of the relevant parameters can readily be found using the Fourier transform of the transient current. The FDTD method allows a rigorous treatment of one or several dielectric interfaces. Different types of excitation can be taken into consideration (coaxial, microstrip lines, etc.). Plotting the spatial distribution of the current density gives information about the resonance modes. The usual frequency-dependent parameters (input impedance, radiation pattern) are given for several examples. >

Journal ArticleDOI
TL;DR: The method described first eliminates the distortion of the signal component of the the covariance matrix and then applies spatial smoothing to decorrelate the coherence between sources.
Abstract: Estimating angles of arrival of radiation sources using an antenna array with mutual coupling between elements is investigated. The presence of mutual coupling distorts phase vectors of radiation sources and the eigenstructure of the covariance matrix. Two approaches are proposed to counteract that distortion so that eigenstructure methods can perform well. The method described first eliminates the distortion of the signal component of the the covariance matrix and then applies spatial smoothing to decorrelate the coherence between sources. Computers simulation results show that this method successfully counteracts mutual coupling. >

Journal ArticleDOI
TL;DR: In this article, an analysis of the characteristics of a broad wall radiating slot, offset from the center line and tilted with respect to the longitudinal axis of a rectangular waveguide, is presented.
Abstract: An analysis is presented of the characteristics of a broad wall radiating slot, offset from the center line and tilted with respect to the longitudinal axis of a rectangular waveguide. Pertinent integral equations are developed, taking into account finite wall thickness, and are solved for the slot aperture E-field using the method of moments. Compound slot characteristics are then deduced, including resonant length and dominant mode scattering. Numerical results for the scattering from resonant slots are presented over a range of offsets, tilt angles, frequencies and waveguide dimensions. For resonant compound slots, offset and tilt are shown to control the aperture electric-field amplitude with a phase variability of 360 degrees . The results have significant applications in the design of compound slot arrays. >

Journal ArticleDOI
TL;DR: In this paper, a hybrid combination of asymptotic high-frequency and modal techniques is employed for highfrequency electromagnetic scattering by open-ended waveguide cavities with an interior termination.
Abstract: The problem of high-frequency electromagnetic scattering by open-ended waveguide cavities with an interior termination is analyzed via three different approaches. When cavities can be adequately modeled by joining together piecewise separable waveguide sections, a hybrid combination of asymptotic high-frequency and modal techniques is employed. In the case of more arbitrarily shaped waveguide cavities for which modes cannot even be defined in the conventional sense, the geometrical optics ray approach proves to be highly useful. However, at sufficiently high frequencies, both of these approaches tend to become inefficient; hence, a paraxial Gaussian beam technique, which retains much of the simplicity of the ray approximation but is potentially more efficient, is investigated. Typical numerical results based on the different approaches are discussed. >

Journal ArticleDOI
TL;DR: In this article, the electromagnetic wave scattering properties of a moving, perfectly conducting mirror are analyzed using a numerical technique based on the finite-difference time domain (FD-TD) method.
Abstract: The electromagnetic wave scattering properties of a moving, perfectly conducting mirror are analyzed using a numerical technique based on the finite-difference time domain (FD-TD) method. This numerical technique does not require a system transformation where the object is at rest, but gives a solution to the problem directly in the laboratory frame. Two canonical one-dimensional cases are considered, the uniformly moving and the uniformly vibrating mirror. Numerical results for the scattered field spectrum are compared to available analytical results, and an excellent agreement is demonstrated. The ability of the FD-TD model to obtain the physics of the double-Doppler effect (for the uniform translation case), and frequency-modulation-like reflected spectrum (for the uniform vibration case) is highlighted. The method is then extended to two-dimensions where a plane wave at oblique incidence on an infinite vibrating mirror is considered. A good agreement with published results is demonstrated for this case. >

Journal ArticleDOI
TL;DR: The technique described uses the adaptive conjugate method instead of the popularly used method of steepest descent to eliminate the jammer components, thus minimizing the error between the received signal and the actual one.
Abstract: The problem of iterative adjustments of the weights of a phased array with a look-direction constraint in the presence of jammers is presented. The technique described uses the adaptive conjugate method instead of the popularly used method of steepest descent to eliminate the jammer components, thus minimizing the error between the received signal and the actual one. This iterative method minimized the L/sub 2/ norm (the mean square error) and is guaranteed to converge in a finite number of steps which is not available for the present techniques utilized to solve this problem. Improvement in rate of convergence is thus achieved at the expense of algorithmic complexity. >

Journal ArticleDOI
TL;DR: In this paper, a technique for self-calibrating a large antenna array system in the absence of a beamforming point source that uses the spatial correlation properties of radar clutter is presented.
Abstract: A technique for self-calibrating a large antenna array system in the absence of a beamforming point source is presented that uses the spatial correlation properties of radar clutter. The array could be real or synthetic. It is shown that if R(X), the spatial autocorrelation function of the field (as measured by adjacent element pairs), is ensured to be real and positive in the neighborhood of the origin, both periodic and aperiodic arrays can be synchronized, forming retrodirective beams pointing at the axis of symmetry of the radar transmitter, provided that the interelement spacing does not exceed some limit (the order of the size of the transmitting aperture). If the spatial autocorrelation function is complex but has a linear phase, it is shown that one can still synchronize both periodic and aperiodic arrays, while if the phase of R(X) is nonlinear, only periodic arrays can be synchronized. In both cases of complex R(X), a residual beam-pointing error occurs. Computer simulations and airborne sea clutter data are reported that verify the theory and practicality of the algorithm. >

Journal ArticleDOI
TL;DR: Field tests related to planned mobile satellite systems (MSS) were performed, and results that add to the existing database of propagation measurements at L-band (1.5 GHz) are described.
Abstract: Field tests related to planned mobile satellite systems (MSS) were performed, and results that add to the existing database of propagation measurements at L-band (1.5 GHz) are described. They are considered particularly useful in that propagation effects were studied systematically with repeated and controlled runs pertaining to different path elevation angles, road types, and path geometries defining shadowing and line-of-sight modes. In addition, simultaneous L-band and UHF measurements were performed for the purpose of establishing scaling factors applicable to previous UHF (870 MHz) results. The control of the experimental parameters was made possible by using a helicopter as the source platform and a mobile van which housed the receiver. >

Journal ArticleDOI
TL;DR: An analysis of an infinite array of aperture-coupled microstrip patch antennas is described; this type of element is well suited to integrated phased-array applications, offering several advantages over other array configurations.
Abstract: An analysis of an infinite array of aperture-coupled microstrip patch antennas is described; this type of element is well suited to integrated phased-array applications, offering several advantages over other array configurations. The solution uses the spectral-domain moment-method approach, and combines features of a previous solution of infinite arrays of probe-fed patches and a reciprocity analysis of single-aperture-coupled microstrip element. The theoretical analysis is described and data are presented for the active input impedance of several arrays. Experimental data from a waveguide simulator confirm the theory. >

Journal ArticleDOI
TL;DR: In this article, the results obtained by two different methods are compared for the problem of electromagnetic scattering from dielectric objects, the surface integral formulation, utilizing equivalent electric and magnetic surface currents, and the volume formulation utilizing the equivalent electric polarization current.
Abstract: Far-field results obtained by two different methods are compared for the problem of electromagnetic scattering from dielectric objects. The two methods are the surface integral formulation, utilizing equivalent electric and magnetic surface currents, and the volume formulation, utilizing the equivalent electric polarization current. Triangular patches are used in the surface formulation and cubical cells are used in the volume formulation. The far-scattered fields obtained by the two methods are in good agreement, thereby validating both the approaches for the analysis of scattering problems. Numerical problems associated with the fields in the source region are also addressed. >

Journal ArticleDOI
TL;DR: In this article, a comparison between the waveguide modal approach and the shooting-and-bouncing ray (SBR) approach is made for a cavity opening on the order of ten wavelengths or larger, and it is observed that the SBR results deviate from the more accurate modal results.
Abstract: The radar cross-section (RCS) analysis of open-ended cavities with rectangular and circular cross sections is carried out using the waveguide modal approach and the shooting-and-bouncing ray (SBR) approach. For a cavity opening on the order of ten wavelengths or larger, the comparison between the two approaches is excellent. It is also observed that at lower frequencies the SBR results deviate from the more accurate modal results. On the other hand, the SBR approach allows for greater flexibility in geometrical modeling, and can be applied to problems where waveguide modes cannot be easily found. SBR results for an offset rectangular cavity and a circular cavity with rounded endplate are presented. >

Journal ArticleDOI
J.J. Maciel1, L.B. Felsen
TL;DR: In this article, a simple test case of a one-dimensional linearly phased cosine-aperture distribution has been undertaken, where Gaussian beams are used as basis elements in field representations.
Abstract: Gaussian beams are used as basis elements in field representations. To gain insight into how the choice of beam parameters affects the final representation, a systematic study for the simple test case of a one-dimensional linearly phased cosine-aperture distribution has been undertaken. By successively adding individual displaced and/or tilted beams with large, narrow, or matched waists, one can assess how the elements in various portions of the lattice contribute to the build-up of the actual field in the aperture, near zone, and far zone. Adding enough beams always guarantees homing in on the exact solution, as is verified here by independent comparison. Different beam choices imply different modeling of the radiation process. The understanding gained thereby is helpful for selecting beam parameters in subsequent applications where it is necessary to balance requirements of good convergence, ease of computation, and ability to track the beams through perturbing environments like a radome. Indications are that the narrow beams provide the most robust and versatile formulation to deal with these generalized conditions. >

Journal ArticleDOI
TL;DR: In this paper, an iterative method based on the conjugate gradient (CG) algorithm is developed for the efficient treatment of equations involving multiple excitations, and significant time savings can be obtained as compared to treating each excitation individually with the CG algorithm.
Abstract: An iterative method based on the conjugate gradient (CG) algorithm is developed for the efficient treatment of equations involving multiple excitations. Examples show that significant time savings can be obtained as compared to treating each excitation individually with the conjugate gradient algorithm. However, these savings are not obtained without the drawback of increased memory requirements to store the additional excitations, residuals, and solutions. The efficiency of this algorithm tends to increase as additional excitations are added. >

Journal ArticleDOI
TL;DR: In this article, an improved theoretical model of the coaxial colinear (COCO) antenna is presented that takes into account different element lengths and power transfers between the antenna and the transmission lines.
Abstract: An improved theoretical model of the coaxial colinear (COCO) antenna is presented that takes into account different element lengths and power transfers between the antenna and the transmission lines. The antenna equation now contains an exact kernel instead of an approximate kernel and a piecewise constant basis function is used instead of a piecewise linear function, yielding faster results. More points are used for better accuracy and yet faster computations. The linear systems of equations of the theoretical model are solved using a preconditioned conjugate gradient method. Uniform and tapered current distributions are obtained experimentally and theoretically on end-fed coaxial colinear antennas. There is reasonable agreement between theory and measurements. The gains of a few COCO antennas relative to equivalent lengths of half-wave dipoles are given. >

Journal ArticleDOI
TL;DR: In this article, the coupled dipole approximation method was extended to compute the scattering characteristics of three-dimensional, homogeneous, lossless, anisotropic objects, which does not require the solution of any integrodifferential equations.
Abstract: The coupled dipole approximation method has been extended to compute the scattering characteristics of three-dimensional, homogeneous, lossless, anisotropic objects. This method is simple, and does not require the solution of any integrodifferential equations. The method will work for any constitutive dyadic, provided it is lossless; furthermore, scatterers of any shape can be accommodated. Thus, this procedure will work well for any three-dimensional, lossless, anisotropic scatterer. Numerical results are given for uniaxial spheres made of titanium dioxide. >

Journal ArticleDOI
TL;DR: In this article, the authors proposed to use a single shaped reflector with a single feed element for a prescribed contour beam and feed, an optimization method for designing the reflector shape is given.
Abstract: Eliminating the corporate feed network in shaped contour beam antennas will reduce the expense, weight, and RF loss of the antenna system. One way of producing a shaped contour beam without using a feed network is to use a single shaped reflector with a single feed element. For a prescribed contour beam and feed, an optimization method for designing the reflector shape is given. As a design example, a shaped reflector is designed to produce a continental-United-States (CONUS) coverage beam. The RF performance of the shaped reflector is then verified by physical optics. >

Journal ArticleDOI
TL;DR: In this paper, the authors considered the problem of evaluating the scattered field at a finite distance from the edge of an impedance wedge which is illuminated by a line source, and derived an exact expression for the diffracted field and the surface wave contributions.
Abstract: The canonical problem of evaluating the scattered field at a finite distance from the edge of an impedance wedge which is illuminated by a line source is considered. The presentation of the results is divided into two parts. In this first part, reciprocity and superposition of plane wave spectra are applied to the left far-field response of the wedge to a plane wave, to obtain exact expression for the diffracted field and the surface wave contributions. In addition, a high-frequency solution is given for the diffracted field contribution. Its expression, derived via a rigorous asymptotic procedure, has the same structure as that of the uniform geometrical theory of diffraction (UTD) solution for the field diffracted by a perfectly conducting wedge. This solution for the diffracted field explicitly exhibits reciprocity with respect to the direction of incidence and scattering. >