Uniform Geometrical Theory Of Diffraction Research Articles

Equivalence of knife‐edge diffraction model and uniform geometrical theory of diffraction applying Fresnel approximation for an absorbing screen

AbstractThe knife‐edge diffraction model (KED) and the uniform geometrical theory of diffraction (UTD) have been widely used to predict the shadowing effect at millimetre‐wave (mmWave) bands. This letter proposes a mathematical derivation to rigorously prove that, for an absorbing screen, UTD applying the narrow‐angle Fresnel approximation is equivalent to KED. The simulation scenarios are designed to validate the proposal by comparing KED with UTD in the narrow‐angle (less than 20°) and wide‐angle (over 20°) regions at mmWave bands (20100 GHz). Simulated results agree with the proposal that KED is identical to UTD with a low error of less than 0.1 dB in the narrow‐angle region, while they have a difference with an error of over 1 dB in the wide‐angle region. In addition, the average computational time is measured and results in both UTD and KED taking approximately 8.0 ms for one test. From the proposal, it can be theoretically explained the differences and similarities between KED and UTD for an absorbing screen.

Research on the computational method of creeping waves diffraction of arbitrary complex target based on the planar mesh model.

For a long time, due to the difficulty of obtaining accurate propagation trajectories, the research on creeping waves is limited to canonical geometries or simple targets, which leads to the situation that it is relatively mature in theoretical research on creeping waves, while the practical application scope of creeping waves for complex targets is narrow. In this paper, a thorough electromagnetic computation method for creeping waves on complex planar mesh model is systematically proposed. This approach broadens the field of creeping waves applications due to the generality of planar mesh models in electromagnetic engineering. The contents consist of the tracing of creeping waves, the calculation of the diffraction field, and the coupling effect with other scattering mechanisms. Aiming at the trajectory of creeping waves, we propose a set of tracing algorithms that enable rapid, real-time tracing based on analytical geometry and related computer graphics algorithms. Utilizing information such as vertices, triangles, and topological relations in the mesh model, one can recover the mathematical properties of the surfaces of the model and then, the corresponding parameters can be obtained. Therefore, the uniform geometrical theory of diffraction (UTD) can be used to accurately calculate the diffraction field. Moreover, for complex targets, the multiple coupling effect caused by creeping waves is the main source of radar echoes in many cases, which is not unimportant. Hence based on the electromagnetic accurate modeling, the coupling mechanism of creeping waves and various scattering mechanisms are studied. The research content is expected to have high application values in target recognition and characteristics.

A PO-Based Uniform Asymptotic Procedure for the Scattering From a Magnetically Conductive Half-Screen

This article addresses reflection, transmission, and diffraction mechanisms due to a magnetically conductive half-screen lit by an incident plane wave. The proposed method is founded on the physical optics approximation of the equivalent surface currents under the validity of proper boundary conditions and works according to the uniform geometrical theory of diffraction. Resulting formulas are presented in simple form and are easy to manage. The validation tests employ data resulting from the radio frequency unit of a full-wave numerical tool.

A Solution for the Plane Wave Diffraction by the Discontinuity Between Two Co-Planar Metamaterial Sheets

A high-frequency approach is described to investigate the scattering by a junction between double negative metamaterial (DNG MTM) sheets. These last are lit by an incident plane wave and have same thickness, but different electric and magnetic parameters, thus assuring discontinuities of reflected and transmitted fields across the junction. The proposed methodology permits to evaluate the diffraction contribution as the sum of two independent terms arising from the scattering process including electric and magnetic equivalent sources under the physical optics (PO) approximation. The formulation of this wave contribution permits its use in the enclosure of the uniform geometrical theory of diffraction (UTD). Useful approximations and integral representations are adopted together with asymptotic evaluations to obtain the diffraction matrix elements. Accordingly, these last account for convenient reference systems, the approximated equivalent currents, and the typical function of the UTD. A full-wave numerical tool is exploited to assess the correctness of the proposed formulation.

Geometry based parameter extraction and creeping wave evaluation for triangulated convex surfaces

Asymptotic solutions based on the uniform geometrical theory of diffraction (UTD) are available for creeping waves traveling along geodesic paths between source and field points on convex surfaces. The application of these UTD solutions to discretized convex surfaces requires extraction of geometry based parameters such as path length, surface curvature, Fock parameter, surface torsion and divergence factor. As unique contributions of this study, accurate and efficient closed-form expressions and algorithms are proposed to extract these parameters from a triangulated conducting convex surface, and UTD surface fields are predicted using the extracted parameters. A quadratic surface mapping is used in barycentric coordinates to define a curved surface on each triangular facet, first. Then, closed-form expressions are obtained for path length, surface curvature and Fock parameter. Algorithms are developed for surface torsion and divergence factor as well. The extracted and actual values for these parameters are compared for primary and secondary paths between source and field points on a circular cylinder and a sphere. The results obtained by applying a UTD solution to triangulated conducting convex surfaces are also validated with the analytical UTD results for surface fields on a circular cylinder, a sphere and a prolate spheroid.

Radiation From a Monopole Antenna Array on an Electrically Large Conducting Convex Surface

Asymptotic solutions based on the uniform geometrical theory of diffraction (UTD) are well developed and efficient for analyzing radiation, mutual coupling, and scattering associated with electrically large conducting convex surfaces. Relevant UTD solutions are available mostly for infinitesimal sources on or far away from the surface. Hence, UTD solutions have been extensively used to analyze radiation from conformal antennas and antenna arrays on an electrically large convex surface. In this letter, it is proposed to predict far and near field radiations from a monopole antenna array on an electrically large conducting convex surface as a nonconformal array. A UTD solution that allows sources to be on or slightly off the surface is employed after identifying ray paths. UTD results are validated with those of the multilevel fast multipole method.

Performance assessment of GNSS diffraction models in urban areas

<h3>Abstract</h3> The GNSS performance is significantly degraded in urban canyons because of the signal interferences caused by buildings. Besides the multipath and nonline-of-sight (NLOS) receptions, the diffraction effect frequently occurs in urban canyons, which will severely attenuate the signal strength when the satellite line-of-sight (LOS) transmitting path is close to the building edge. It is essential to evaluate the performance of current diffraction models for GNSS before applying mitigation. The detailed steps of applying the knife-edge model and the uniform geometrical theory of diffraction (UTD) model on GNSS are given, including the 𝐶∕𝑁₀ and pseudorange simulation of the diffracted signal. The performances of both models are assessed using real data from two typical urban scenarios. The result shows the UTD can adequately model the GNSS diffraction effect even in a complicated urban area. Compared with the knife-edge model, the UTD achieves better modeling accuracy, whereas it requires higher computational loads.

Спрямовані властивості випромінювання двох імпедансних монополів, розташованих на ідеально провідному прямокутному екрані

Subject and Purpose. Two impedance resonant monopoles of electric length 0.2 £ l / l £ 0.3 are mounted on a rectangular screen perpendicularly to the screen surface and studied for the directional radiation properties (directive gain and radiation patterns) depending on the monopole separation and the side length and aspect ratio of the screen. Methods and Methodology. A three-dimensional diffraction vector problem of two impedance monopoles mounted on a perfectly conducting rectangular screen is solved in terms of the uniform geometric theory of diffraction. Allowances are made for the diffracted field asymptotics of the secondary diffraction at the screen edges and for the electric current distribution asymptotics of a thin impedance dipole in the free space. Results. For a lattice of two impedance monopoles mounted on a rectangular screen, 3-D programs have been developed for calculating its radiation patterns, directive gain Dmax at a radiation maximum, and radiation resistance in view of the secondary diffraction at the screen edges. The radiation pattern shaping for the diffraction and total fields and the directive gain Dmax have been analyzed depending on the monopole separation x / l  0.1...1, the screen side length x / l  1.2…4, and the screen aspect ratio W / L  0.5…3. It has been shown that the so obtained optimum separation x opt  0.65, optimum length Lopt and optimum ratio (W / L) opt make Dopt three times greater than the lowest Dmax value. Conclusions. The three-dimensional vector problem of field diffraction of two impedance monopoles mounted on an ideally conducting rectangular screen has been solved. It is of interest that given an optimum monopole separation xopt and an optimum side length Lopt of the square screen, a lattice of two monopoles offers a greater radiation resistance and a two times larger Dopt than a single monopole on the same screen does. The developed computational programs and the obtained numerical results enable efficient actual wireless communication systems to be modelled for both ideally conducting and impedance resonant monopoles.

Wave Scattering by a Planar Junction Between Anomalously Reflecting Metasurface and Impedance Sheets

Metasurface technology has become one of the promising structures for controlling and manipulating of the phase and amplitude characteristics of the electromagnetic waves in recent years. For this reason, the determination of the exact diffracted fields is also crucial especially in the edge or discontinuity points of these types of materials. In the paper, the discontinuity problem by the junction between the layers of an anomalously reflecting metasurface and an impedance half-screen is taken into consideration. These two planar layers have a common edge discontinuity where the diffracted waves occur. The scattered waves from the structure are obtained by the novel technique of the method of transition boundary, which especially offers the relation between the diffracted and scattered geometrical optical waves at the transition boundaries. The diffracted wave expressions are derived by the technique of the method of transition boundary and the uniform wave expressions are obtained by the method of uniform geometrical theory of diffraction. The behaviors of the total wave and its components are analyzed numerically.

High-frequency diffraction contribution by planar metallic–DNG metamaterial junctions

AbstractThe plane wave diffraction by a planar junction consisting of a thick metallic sheet and a lossy double-negative metamaterial slab is studied by using the Uniform Asymptotic Physical Optics approach. This approach assumes the radiation integral as a starting point and uses the physical optics surface currents as sources to be integrated. The integral is manipulated by taking advantage of useful approximations and evaluations, and re-formulated in order to apply an asymptotic procedure able to generate a closed-form approximate solution in the framework of the Uniform Geometrical Theory of Diffraction. Accordingly, advantages and drawbacks result from the application of the proposed solution. The jumps of the geometrical optics field are compensated. Implementation and handling of the computer code are facilitated by the evaluation of well-known functions and parameters. No differential/integral equations or special functions must be computed.

Apply Ray Tracing to Back Track Partial Discharge in Transformer Based on Combined Array Sensor

To locate partial discharge (PD) in power transformer, a combined array sensor is manufactured which consists of a cross-shaped ultrasonic array with 25 elements and an ultra-high frequency (UHF) array with 2*2 elements. Algorithms for PD location are studied based on the sensor arrangement, and a total of 193 ultrasonic and 13 UHF virtual elements are achieved via virtual expansion. At first, two-sided correlation transformation based on the UHF virtual expanded array is employed to pre-estimate the PD’s direction, and then rotated signal sub-space based on the ultrasonic array is used to direct accurately. To enhance the accuracy and success rate of an array, ray tracing technique which consists of geometrical optics and uniform geometric theory of diffraction is studied to backtrace the wave emitted by PD, considering the UHF signal as an example. The PD location experiments in a transformer model indicate that the location algorithms based on the proposed combined array sensor adapt the PD’s broadband signal well, and ray tracing of the electromagnetic wave emitted by PD makes the location much accurate and successful than that of a single array. The PD location based the proposed combined array takes the advantages of the high sensitivity of UHF array and the high accuracy of the ultrasonic array.

Heuristic UTD Solution for Antennas Near a Complex Platform

This paper is aimed at developing an approximate and relatively simple but closed-form uniform geometrical theory of diffraction (UTD) solution for describing the radiated and scattered fields by an antenna near a complex platform consisting of a three-dimensional (3-D) thin material-coated metallic surface, including edges and corners. Unlike the previous works that consider primarily plane wave scattering, the developed solution can also treat radiation/scattering problems of antennas near finite material-coated metallic surfaces which are composed of edges and corners. The developed solution, which is formulated by using a heuristic approach, recovers the proper local plane wave Fresnel reflection coefficient. In addition, the developed UTD-diffracted fields will satisfy the radiation condition, boundary conditions on the conductor. The accuracy of the developed solution is verified by comparing with simulation results from a computer software. It is found that the results from our developed solution agree well with those of references. However, some small discrepancies occur but it is good enough for engineering applications. The proposed solution can be very useful for antenna engineers to design multiple antennas with an electrically large complex material-coated platform.

On Two Alternative Uniformly Asymptotic Procedures for Analyzing the High-Frequency Diffraction of a Complex Source Beam by a Straight Wedge

When spectral wave integrals, representing the radiation and diffraction of electromagnetic waves, are characterized by a first-order saddle point and poles in the integrand, they can usually be evaluated, in essentially closed form, at high frequencies by the leading terms of any of the two well-known alternative uniformly asymptotic procedures, namely, the Pauli–Clemmow method (PCM) and the Van der Waerden method (VWM), respectively. The PCM has the advantage that its leading terms directly yield a solution in the simple ray format of the uniform geometrical theory of diffraction (UTD). On the other hand, it is commonly noted that it is not the leading term of the PCM but that of the VWM which remains valid for the case of complex waves. Nevertheless, it is shown here that the PCM can surprisingly work even for some special complex wave cases, only if certain conditions are met. Indeed, it is demonstrated here that the PCM meets these conditions for the special case of the diffraction of a complex source beam (CSB) by a wedge. Also, the PCM directly yields a UTD like solution for this case. The latter result is significant as it provides a strong justification for obtaining a simple UTD type solution for the more general problem of the diffraction of a CSB incident from an arbitrary direction on a wedge with arbitrary curvature, directly via analytic continuation of the corresponding UTD result available for a curved wedge illuminated by a point source in real space. It is also shown that the VWM solution can be trivially cast in the UTD format, by expressing it as a sum of the PCM solution plus a UTD slopelike correction term; a similar result was obtained previously using a higher order term from a generalization of the PCM procedure given elsewhere.

A Comprehensive Review of Efficient Ray-Tracing Techniques for Wireless Communication

A comprehensive review of ray tracing (RT) techniques for wireless communication systems is presented in this paper. The conventional techniques are described with respect to the existing problems and solutions. The development of the computational speed in computer produced a significant change in electromagnetic theory by increasing the performance and by speeding up the numerical calculation method. Nowadays, it is effectively used in cellular wireless propagation investigation. Here, some ray- tracing techniques have been presented to remove the limitation of the uniform geometrical theory of diffraction (UTD) and geometrical optics(GO). Outlines to decrease the computational time and to increase accuracy are the main focus. A very clear synopsis of ray tracing is presented in this paper, with a very exceptional consideration to future high-frequency applications. New challenges in high frequency are described and some new smart ideas for solving those challenges are presented. First, ray-tracing elemental methods are described and the later recently upgraded methods are reviewed. Second, numerous ray-tracing progressive methods are reviewed and then grouped into several categories like heuristic, effective deterministic and special brute force. Finally, the hybrid ray tracing methods which used physical optics are reviewed along with the effective unevenness model to increase the outcome accuracy.

An Introduction to the GTD Edge Diffraction via Equivalent Currents [Education Corner]

The geometrical theory of diffraction (GTD) is a popular method for the analysis of diffraction from edges of electrically large conducting surfaces. It is also easy to use, as it involves only algebraic expressions and geometrical considerations. However, GTD is awkward to teach because a rigorous derivation of the diffraction coefficients requires mathematical skills that are beyond the reach of most students and many practitioners. This article presents an alternative derivation of the GTD edge diffraction equations. This approach begins with a relatively simple stationary-phase analysis of a radiation integral formed from equivalent currents postulated to flow along the edge. This analysis yields expressions in GTD form but with unspecified diffraction coefficients. Diffraction coefficients in the original GTD (Keller) form or the uniform GTD (UTD) (Kouyoumjian and Pathak) form can then be introduced as an alternative to the equivalent currents in the final expressions. This approach is suitable for a concise introduction to GTD edge diffraction for students with no previous experience in asymptotic high-frequency methods.

The Diffraction Research of Cylindrical Block Effect Based on Indoor 45 GHz Millimeter Wave Measurements

In this paper, four kinds of block diffraction models were proposed on the basis of the uniform geometrical theory of diffraction, and these models were validated by experiments with 45 GHz millimeter wave in the laboratory. The results are in agreement with the theoretical analysis. Some errors exist in the measurement results because of the unsatisfactory experimental environment. Single conducting cylindrical block measurement error was less than 0.5 dB, and single man block measurement error in the school laboratory was less than 1 dB, while in the factory laboratory environment, the peak to peak error reached 1.6 dB. Human body block attenuation was about 5.9–9.2 dB lower than that of the single conducting cylinder. A human body and a conducting cylinder were used together as a block in model (c) and model (d), but the positions of the cylinder in the two models were different. The measurement results showed that the attenuation of model (d) is about 3 dB higher than that of model (c).

Modeling the Effect of Human Body on ToA Ranging Using Ray Theory

In line-of-sight (LoS) conditions, the accuracy of time-of-arrival (ToA) based localization has proven to be superior to the received-signal-strength (RSS) and the angle-of-arrival (AoA) localization techniques. The accuracy of TOA ranging is limited to unexpected ranging errors caused by the human body obstructing the direct path (DP) between a transmitter and a receiver. Validated analysis of this effect is a challenging problem, and this paper proposes an analytical Uniform Geometrical Theory of Diffraction (UTD) approach, based on a hybrid applicability of conductor cylinder, wedge, and screen models, to analyze behavior of first path in proximity of human body that is in angular motion. The model introduced can cover for a variety of antenna positioning in respect to human body by addressing creeping waves for on-body, far-field and near-field waves for off-body propagations. Result of analytically calculated ToA and path-loss for shortest diffracted path is validated with UWB measurements conducted by a vector network analyzer sweeping 3–5 GHz of bandwidth. The analytical approach proposes an enhancement to existing RT algorithm to include the effect of human body.

High-Frequency Asymptotic Description of Resonant Antenna Formed by Two Metallic Parallel Disks

High-frequency asymptotic electromagnetic field solution is described for a resonant antenna formed by two perfectly conducting circular disks. The double-disk resonator is excited by a vertical electric dipole located at the center of the cylindrical space between the two horizontal disks. The solution is valid for comparatively large disks (at least few wavelengths in diameter). At the same time, the separation of the disks can be arbitrary. The proposed analysis is similar to the uniform geometrical theory of diffraction and provides asymptotic formulas describing the radiated field in both the far- and near-field zones. However, the method is novel since it is based on the canonical problem of diffraction on an open end of a parallel-plate waveguide and therefore takes into account the presence of higher order guided modes travelling between the disks. The method allows calculation of the total radiated power, which has maxima at frequencies equal to real parts of resonator's complex eigenfrequencies. Obtained theoretical directivity patterns in a broad frequency range show good agreement with full-wave numerical simulation.

Orthogonal Basis Functions in Discrete-Time Electromagnetics and Their Implementation to Compute the Matrix-Type UTD Transition Function for PEC Wedge Diffractions

A set of orthogonal global time-domain (TD) basis functions of numerical robust is presented and examined for the applications of discrete time electromagnetics (DT-EM). The matrix equations or integrals arising from the expansion of TD field signals by this basis set can be effectively computed since they can be diagonalized by eigenvalue and vector decomposition method. This characteristic is particularly useful in the computation of TD solutions transformed from the corresponding frequency domain formulations such as in the computation of transition functions for the implementation of DT uniform geometrical theory of diffraction (DT-UTD). It may not only avoid the TD field signal divergence along propagation, but also simplify the computational complexity by avoiding the numerical integration of matrix integral. In this paper, the characteristics are examined via the implementation of plane wave propagation and DT-UTD for the diffraction from curved wedges. Numerical examples are presented to demonstrate their validity in DT-EM applications.

Novel approximate UTD ray solution for the radiation and scattering by antennas near a planar material junction on PEC ground plane

A novel approximate uniform geometrical theory of diffraction (UTD) for analyzing an electromagnetic wave diffracted by a planar material junction on PEC ground plane has been developed in this research. The proposed UTD solution is based on an ansatz obtained from the Weiner–Hopf (W–H) solution by approximating the W–H split functions. This makes the proposed UTD solution to be a relatively simple and closed form expression. Additionally, the proposed UTD solution can deal with both a planar material junction on PEC ground plane and a two-part problem with any types of wave illumination such as a plane wave, a cylindrical wave, and a spherical wave. The accuracy of the proposed UTD solution is compared with the W–H solution and finite different time domain (FDTD) which provides very good agreement. The proposed UTD solution has very small numerical errors. However, the accuracy of the proposed UTD solution is good enough for engineering applications.