This paper reviews the basic concepts of rays, ray tracing algorithms, and radio propagation modeling using ray tracing methods We focus on the fundamental concepts and the development of practical ray tracing algorithms The most recent progress and a future perspective of ray tracing are also discussed We envision propagation modeling in the near future as an intelligent, accurate, and real-time system in which ray tracing plays an important role This review is especially useful for experts who are developing new ray tracing algorithms to enhance modeling accuracy and improve computational speed

Ray Tracing for Radio Propagation Modeling: Principles and Applications

The application scenarios and requirements are more diverse in the fifth-generation (5G) era than before. In order to successfully support the system design and deployment, accurate channel modeling is important. Ray-tracing (RT) based deterministic modeling approach is accurate with detailed angular information and is a suitable candidate for predicting time-varying channel and multiple-input multiple-output (MIMO) channel for various frequency bands. However, the computational complexity and the utility of RT are the main concerns of users. Aiming at 5G and beyond wireless communications, this paper presents a comprehensive tutorial on the design of RT and the applications. The role of RT and the state-of-the-art RT techniques are reviewed. The features of academic and commercial RT based simulators are summarized and compared. The requirements, challenges, and developing trends of RT to enable the visions are discussed. The practices of the design of high-performance RT simulation platform for 5G and beyond communications are introduced, with the publicly available high-performance cloud-based RT simulation platform as the main reference. The hardware structure, networking, workflow, data flow and fundamental functions of a flexible high-performance RT platform are discussed. The applications of high-performance RT are presented based on two 5G scenarios, i.e., a 3.5 GHz Beijing vehicle-to-infrastructure scenario and a 28 GHz Manhattan outdoor scenario. The questions on how to calibrate and validate RT based on measurements, how to apply RT for mobile communications in moving scenarios, and how to evaluate MIMO beamforming technologies are answered. This tutorial will be especially useful for researchers who work on RT algorithms development and channel modeling to meet the evaluation requirements of 5G and beyond technologies.

The Design and Applications of High-Performance Ray-Tracing Simulation Platform for 5G and Beyond Wireless Communications: A Tutorial

Mobile communication links are severely influenced by propagation effects. Wave propagation in the VHF/UHF frequency range over natural and man-made terrain is strongly dependent on topography and morphography. Propagation modeling is based on a ray-optical approach. Wave interactions, like diffraction and scattering, over the propagation path are described by the uniform theory of diffraction (UTD) and physical optics (PO). Propagation models for rural and urban areas are presented for 2-D and 3-D ray tracing. Near-range models apply to the corresponding areas in forest and urban sites. The field-strength delay spectrum describes ray contributions with deterministic amplitudes but statistical phases are used to derive time-and frequency-domain channel characteristics. Comparisons between measured and predicted data are presented. >

Concepts and results for 3D digital terrain-based wave propagation models: an overview

A new heuristic UTD diffraction coefficient for non-perfectly conducting wedges is proposed. The coefficient is an extension of the heuristic one given by Luebbers (1984) and as simple as that to compute. In the case of forward-scattering and neglecting the surface wave effects, the new coefficient gives a result close to Maliuzhinets's (1958) solution, also deep in the shadow region where the previous one fails. Moreover, it makes the special care used by Luebbers to deal with grazing incidence unnecessary.

A new heuristic UTD diffraction coefficient for nonperfectly conducting wedges

A summary of various high-frequency techniques is presented for analyzing the electromagnetic radiation from antennas in the presence of their host environment. These techniques provide physical insight into antenna radiation mechanisms and are found to be highly efficient and accurate for treating a variety of practical antenna configurations. Examples to which these techniques have been applied include open-ended waveguide antennas, horn and reflector antennas, and antennas on aircraft and spacecraft. The accuracy of these techniques is established via numerical results which are compared with those based on other independent methods or with measurements. These high frequency methods can be combined with other techniques, through a hybrid scheme, to solve an even greater class of problems than those which can be solved in an efficient and tractable manner by any one technique alone. >

High frequency techniques for antenna analysis

A uniform high-frequency solution is presented for the diffraction by a wedge with impedance faces illuminated by a plane wave perpendicularly incident on its edge. Arbitrary uniform isotropic impedance boundary conditions may be imposed on the faces of the wedge, and both the transverse electric (TE) and transverse magnetic (TM) cases are considered. This solution is formulated in terms of a diffraction coefficient which has the same structure as that of the uniform geometrical theory of diffraction (UTD) for a perfectly conducting wedge. Its extension to the present case is achieved by introducing suitable multiplying factors, which have been derived from an asymptotic evaluation of the exact solution given by Maliuzhinets. When the field point is located on the surface near the edge, a more accurate asymptotic evaluation is employed to obtain a high-frequency expression for the diffracted field, which is suitable for several specific applications. The formulation described in this paper may provide a useful, rigorous basis to search for a more numerically efficient but yet accurate approximation.

A uniform GTD formulation for the diffraction by a wedge with impedance faces

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. >

High-frequency scattering from a wedge with impedance faces illuminated by a line source. I. Diffraction

The application of a high-frequency solution for the field doubly diffracted in the far zone from a pair of parallel wedges illuminated by a plane wave is described. It is shown how a spectral extension of the uniform geometrical theory of diffraction (GTD) is used to obtain closed-form expressions for the field that are valid at any incidence and observation aspects. These expressions exhibit the proper discontinuities and singularities so that they can be suitably combined with the other singly diffracted fields to provide a uniformly valid ray description of the scattering in the far zone by an obstacle which is illuminated by a plane wave. They smoothly reduce both to those derived by directly applying the uniform GTD solution for single diffraction augmented by slope diffraction and to those recently obtained for grazing illumination of the edges, in their respective regions of validity. The solutions to the scalar problems are then used to construct a dyadic diffraction coefficient for the doubly diffracted field in the ray-fixed coordinate system. Examples of triangular cylinders are considered, and numerical results are presented. >

High-frequency electromagnetic scattering of plane waves from double wedges

A hybrid technique which combines the method of moments (MM) with ray methods is employed to analyze the radiation of wires in the presence of a plane interface In this technique, which is an extension of that proposed for combining the MM with the uniform geometrical theory of diffraction (GTD), a piecewise sinusoid (PWS) Galerkin method formulation is used In this paper the basic assumption is made that a PWS dipole can be replaced by three sources of transverse, spherical waves, so that their fields can be treated separately by standard ray methods Via this procedure the MM matrix can be easily augmented to account for the wire-interface interactions Calculations of the field both radiated in the antenna half-space and transmitted through a plane interface are found in very good agreement with those performed by using the rigorous Sommerfeld integral representation These results show that this technique provides an accuracy which is widely acceptable in most engineering applications, even when the wire is placed very close to the interface This approach, which employs ray methods to calculate reflected and transmitted field contributions, appears promising to treat the case of curved interfaces

R. Tiberio

Papers

A uniform GTD formulation for the diffraction by a wedge with impedance faces

High-frequency scattering from a wedge with impedance faces illuminated by a line source. I. Diffraction

High-frequency electromagnetic scattering of plane waves from double wedges

A hybrid technique for analyzing wire antennas in the presence of a plane interface

High-frequency diffraction by a double wedge