M.F. Catedra

Efficient ray-tracing techniques for three-dimensional analyses of propagation in mobile communications: application to picocell and microcell scenarios

The application of several ray-tracing techniques, in combination with GTD/UTD (geometrical theory of diffraction/uniform theory of diffraction), for an efficient analysis of propagation in urban scenarios is presented. The frequency of the analysis is in the UHF band, and a three-dimensional model of the geometry, using flat facets, is considered. After a review of the most commonly used ray-tracing techniques, a new method, called the angular z-buffer (AZB) technique, is presented. As is shown and validated with results, the AZB appears to be extremely efficient for GTD/UTD applications.

Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces

The paper presents a method for the computation of the monostatic radar cross section (RCS) of electrically large conducting objects modeled by nonuniform rational B-spline (NURBS) surfaces using the physical optic (PO) technique. The NURBS surfaces are expanded in terms of rational Bezier patches by applying the Cox-De Boor transform algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. The PO integral is evaluated over the parametric space of the Bezier surfaces using asymptotic integration. The scattering field contribution of each Bezier patch is expressed in terms of its geometric parameters. Excellent agreement with PO predictions is obtained. The method is quite efficient because it makes use of a small number of patches to model complex bodies, so it requires very little memory and computing time. >

Propagation model based on ray tracing for the design of personal communication systems in indoor environments

A ray tracing technique to predict the propagation channel parameters in indoor scenarios is presented. It is a deterministic technique, fully three-dimensional, based on geometrical optics (GO) and the uniform theory of diffraction (UTD). A model of plane facets is used for the geometrical description of the environment. The ray tracing is accelerated considerably by using the angular Z-buffer algorithm. Some comparisons between predicted results and measurements are presented to validate the method.

Application of the Characteristic Basis Function Method Utilizing a Class of Basis and Testing Functions Defined on NURBS Patches

A novel implementation of the characteristic basis function method (CBFM) is given, in which the high-level basis functions, called characteristic basis functions (CBFs), are represented in terms of curved rooftops generated from nonuniform rational B-splines (NURBS) in the parametric (u,v) domain. The associated macro-testing functions are defined by using curved razor-blade functions corresponding to each rooftop. The underlying objective of the CBFM is the reduction of the number of unknowns that arise from the discretization process when applying the conventional method of moments (MoM). The result is, therefore, an approach which can handle many complex cases via direct solvers, without suffering from convergence problems as many of the iterative techniques are known to do when dealing with ill-conditioned matrices. As a result of the combination of the CBFM with the special class of low-level basis and testing functions directly located over NURBS surfaces, complex and realistic geometries can be efficiently analyzed to yield accurate results while reducing the CPU time as well as required memory resources.

Stationary phase method application for the analysis of radiation of complex 3-D conducting structures

The stationary phase method is used to calculate the radiation pattern of antennas on complex structures. Physical optics (PO) approximation has been applied for the induced currents. The problem is stated directly over the parametric surfaces used to model the geometry and no translation of geometrical formats is required. The integral comes from the contribution of certain points on the surface (specular, boundary and vertices) where the phase term of the integrand presents a stationary behavior. In general, the asymptotic integration behaves similar to the numerical one but being more efficient in execution time than the latter.

Computation of the RCS of complex bodies modeled using NURBS surfaces

The paper presents the RANURS code (radar cross section-NURBS surfaces) for the analysis of the monostatic radar cross section (RCS) of electrically large complex targets. The geometric representation of the targets is given in terms of parametric surfaces, which allow an excellent fit between the model and the real surface. The parametric surfaces used are NURBS (non-uniform rational B-spline) surfaces. This technique of modeling is used in many industries to represent complex bodies. Most of the CAGD (computer aided geometric design) tools use the NURBS format for modeling, because it can represent complicated objects using limited information. Therefore, an important feature of the code is its compatibility with most of the available CAGD codes, in order to ensure that the entire design process, involving different engineering aspects (structural, mechanical, aerodynamical, electrical, etc.) can be developed with compatible models. The scattered fields are calculated by using the physical optics and the equivalent currents methods (PO+ECM). The following contributions to the RCS are taken into account: reflected field, diffracted field, double-reflected field, and diffracted-reflected field. In addition, a method for determining the hidden parts of the targets is used. The PO+ECM approach is directly applied on the parametric surfaces, and the final expressions of the fields are given as functions of the coefficients of the numerical description of the NURBS patches.

An Iterative Solution for Electrically Large Problems Combining the Characteristic Basis Function Method and the Multilevel Fast Multipole Algorithm

An iterative scheme for the rigorous computation of electrically large problems is presented. The approach is based on a combination of the characteristic basis function method (CBFM) and the multilevel fast multipole algorithm (MLFMA) that can deal with very large problems that require an iterative solution process, even considering that the application of the CBFM entails an important reduction of the number of unknowns when compared to Method of Moments approaches based on subdomain functions. This reduction is due to the fact that the number of macro-basis functions, called characteristic basis functions (CBFs), is lesser than the number of low-level subsectional functions used to sample the geometry. In addition, the use of the MLFMA avoids the need to calculate and store the coupling terms in the reduced matrix that are not on or close to the diagonal, thereby optimizing the CPU time and the memory storage requirements. non-uniform rational B-splines (NURBS) surfaces are employed for the representation of the geometry and the CBFs are described in terms of curved rooftops generated in the parametric space. The associated macro-testing functions are defined as aggregations of curved razor-blade functions.

Analysis of antennas on board arbitrary structures modeled by NURBS surfaces

An accurate and efficient numerical scheme has been developed for predicting high-frequency radiation patterns of antennas mounted on arbitrary structures modeled by parametric surfaces. The method is based on geometric optics (GO) and the uniform theory of diffraction (UTD). Nonuniform rational B-splines (NURBS) surfaces have been used to describe the geometry of the structure. As most of the computer-aided geometric design (CAGD) tools available in the industry are biased on NURBS, the scheme can perform the electromagnetic analysis without any new or additional remeshing of the geometrical model. A special ray-tracing technique that combines GO and UTD with NURBS has been developed. This technique uses some selective criteria in order to identify rapidly the NURBS where a ray impact may occur. Impact point coordinates are obtained by means of an optimization procedure based on the conjugate gradient method (CGM). The accuracy and efficiency of the approach are shown comparing it with other methods.

Method based on physical optics for the computation of the radar cross section including diffraction and double effects of metallic and absorbing bodies modeled with parametric surfaces

A method to compute the monostatic radar cross section (RCS) of complex bodies modeled by nonuniform rational B-spline (NURBS) surfaces is presented. The bodies can be covered by any kind of radar absorbing material (RAM) with electric and/or magnetic losses. Physical optics (PO) is used to obtain the scattered field of each surface. Fresnel coefficients are included in the stationary phase method (SPM) in order to take into account the effect of the RAM material. The contribution of diffraction by edges and double effects is also considered, improving the results of the PO approach. The diffraction is computed by the equivalent current method (ECM). A combination of geometrical optics (GO) with PO and ECM is used for the double reflection and double interaction between edges and surfaces respectively. Some simple cases are shown to validate the proposed method. The reliability of the method to analyzing the effect of covering a realistic target with RAM is also illustrated.

Efficient Multilevel Approach for the Generation of Characteristic Basis Functions for Large Scatters

An efficient approach for deriving the characteristic basis functions (CBFs) for analyzing radiation and scattering problems is proposed. The spectrum of the incident plane waves is partitioned into several angular regions that are progressively enlarged in a multilevel procedure to generate orthogonal functions. The CBFs are obtained at the final orthogonalization level, so that they cover the entire angular range. This approach to generating the CBFs is better suited for electrically large objects than the conventional approach, which utilizes the entire angular range (visible) of the plane wave spectrum in a single level.