A new ray-tracing method has been developed for the analysis of antennas on-board complex structures and the propagation at indoor/outdoor environments considering n-bounces. The structures (satellites, ships, aircrafts, etc.) are modeled by planar and/or curved surfaces defined by perfectly electrical conductors or dielectric materials (with or without losses). The structures are defined as parametric surfaces, in particular by NURBS (Non-Uniform Rational B-Spline) surfaces. The approach is based on the Uniform Theory of Diffraction (UTD) for the field computation and Physical Optics (PO). In previous approaches some selective criteria in order to identify the NURBS where the rays impact [1] were used. The coordinates of the reflection points were obtained with the Image Theory when the surfaces were planar. When the surfaces were curved surfaces the reflection points were found by means of an optimization procedure based on the conjugate gradient method (CGM). Most of the CPU-time is spent calculating the rays that reach such points, including the visibility study of the ray (shadowing tests). That means that the solution of electromagnetic radiation problems of antennas on board arbitrary structures, when double or higher order is considered, can be very cumbersome and computationally expensive. The new algorithm has been improved to treat ray field contributions with any kind of bounces or multiple bounces in flat and/or curved surfaces: reflection, diffraction, transmission, creeping waves or any combination of them. The electrical field is calculated as the sum of all contributing rays that reach the observation point using UTD or PO. The new ray-tracing has been improved in order to compute efficiently the reflection and/or diffraction points on curved surfaces. Also another new algorithm to speed up the ray-tracing in creeping waves has been implemented. The new ray tracing algorithms developed are based on a recursive application of the Angular Z-buffer (AZB) [2] together with the A* heuristic search method, [3]. The AZB matrix contains the information about the surfaces which are visible from a source or a facet. These matrices are used to determine the possible victim surfaces which can produce an n-order reflection. The space seen from a point or a facet is divided into several angular regions (anxels). The AZB matrix can be saved in a file, so that it only has to be calculated once for each structure. In a preprocessing stage, the curved surfaces are turned into small flat facets according to the curvature of the surface. So, the reflection points are calculated on the facets applying the Image Theory and the Z-Buffer algorithm. The new ray-tracing algorithm is able to compute bounces of n-order. Once the n points of reflection are calculated they are used as point’s seed in the CGM since the real points on the curved surface is calculated using the CGM. The minimization takes place in each point separately. Therefore, this method is able to reduce the expensive minimization of the CGM. Once, the reflection points are calculated, its field contribution due to the reflection in the curved surface is computed. When this new method is applied we have not approximations computing the reflections on curved surfaces but the CPU time in the searching of the n-reflection and/or diffraction point presents a notably reduction. To improve the computation of creeping waves in arbitrary surfaces, a heuristic search algorithm based on the A* heuristic search [3] with single searching way or bidirectional searching way has been developed to improve the efficiency of the computation of the method. To validate this method the near and far-field of antennas on board mock up of CNES satellites have been considered. The new algorithm permits the analysis of triple reflection or higher order reflections. It has been implemented in a new version of computer tool FASANT and is about 20 times faster than the version that uses the previous algorithm [1]

References:
[1] I. González, D. De La Torre, O. Gutiérrez, F. Saez de Adana, M.F. Cátedra, "Analysis of Antennas On-Board Using FASANT", 26 ESA Antenna Worshop, ESTEC, November 2003.
[2] M. F. Cátedra, J. M. Gómez, F. Saéz de Adana, O. Gutiérrez, "Application of Ray Tracing Acceleration Techniques for The Analysis of Antennas on Complex Platforms Modelled by NURBS", IEEE Antennas and Propagation International Symposium, vol. 4A, pag. 167-170, 2005.
[3] Stuart Russel, Peter Norving, "Artificial Intelligence. A Modern Approach", Second Edition, Prentice Hall, 2003.

One of the typical problems of antenna farm analysis is the characterisation of the source antennas. Two typical approaches are followed and are both available within EAML: use of the antenna pattern (sampled on as Spherical Wave Expansion) and use of equivalent currents on a suitable equivalence surface. In both cases the main issue is to obtain an accurate and suitable model from simulated or measured data, which are intrinsically associated to different boundary conditions that those seen by the antenna installed on the platform. A typical example is that of a small antenna measured in "free" space that is installed on a rather large ground plane. Several approaches have been developed during the EAML study to overcome these problems.

In this paper, the pattern distortions of the 2 low gain TTC S-Band antennas mounted on the ESA's Cryosat-2 satellite are analyzed. These antennas, one helix antenna and one patch antenna, are used to ensure a minimum link budget between the satellite and ground station during all mission phases, irrespective of the position and attitude of the spacecraft with respect to the ground station.

In the operational mission mode, access is via one antenna predominantly. Shortly after launch, the attitude of the spacecraft can be such, that access can in principle be required from all angular directions over the sphere.

Therefore it is of importance to predict the antenna pattern distortions due to its surrounding satellite structure environment, which might lead to null pattern and a potential outage in the communication link. The pattern distortions are dependent of several factors, mainly the location of the antenna with respect to the satellite platform, the shape of the satellite platform itself, the presence of obstacles and the influence of other antennas on the satellite. The main objective of the study is to verify that the TTC communication link for CryoSat-2 is safely established.

Current real-life designs involving antennas and EMC in antenna farm issues call for unprecedented levels of complexity, and require accurate, virtual-prototyping predictions, which are best obtained using cutting-edge modelling technology applied in a computational environment that offers a seamless workplace to the antenna engineer from CAD to design verification. Furthermore as predicted results are increasingly used to replace costly tests on hardware models the issue of fidelity becomes more and more important. The new baseline full-wave modelling being developed for ADF-EMS is based on the existing MoM capabilities with the inclusion of: 1) Fast Multiple Method (FMM), both in its single- and multi-level (MLFMA) implementations; 2) Multi-resolution (MR) hierarchic basis functions. The FMM/MLFMA is arguably the most proven and efficient approach for large problems; being an iterative method, the issue of convergence is of paramount importance especially in the presence of geometrical (structural) complexities. In this regard, the MR is a technique that allows a tight control of the conditioning of the MoM matrix in complex environments.

Separately and in combinations, these techniques allow stable, fast and accurate solutions for complex problems with minimal intervention on the part of the user. At the same time ADF-EMS offers PO/ITD and UTD capabilities allowing the selection of the best modelling strategy for different aspects of a same problem. One specific problem of antenna farm modelling is the virtually unbounded error toward low field levels. Often predictions show deep nulls in the field that are seldom observed in reality and are due to the assumption of perfect specular reflections on the satellite body.

Asymptotic (GTD) analysis of antenna farms and of the scattering form the satellite structure and appendages is commonly used to predict installed antenna patterns. Yet the overwhelming majority of existing tools requires dedicated models or incurs in very large computational costs when a meshed geometry, like those used for integral methods, is used. Besides other possible problems the fact alone of being forced to use several different electromagnetic models of the same object posed problems of traceability and duplication of effort making a complete analysis quite expensive. The Asymptotic Beam Tracer developed under previous Agency activities has been updated to improve its performance with large meshed geometries achieving a unique modelling capability.

For the analysis of large antennas structure the use of rigorous techniques based on the Method of Moments (MM) is usually a serious computational burden due to the large number of unknowns to deal with. Even the use of the efficient Fast Multilevel Multipole Method may represent an unfeasible effort for most of the computing systems available at the present time. In order to handle these problems appropriately, it is common to resort to high-frequency techniques, such as Physical Optics (PO), or ray-tracing based methods. In this work we propose an alternative approach to increase the accuracy of the asymptotic techniques where we compartmentalize the geometry into windows and we consider that only the currents contained inside the same window are fully coupled. For the analysis of each of these windows, which can be electrically large, we use the Characteristic Basis Function Method (CBFM) [1-2]. The resulting coupling matrix associated to each window is much smaller than that obtained by the pure Method of Moments and direct solvers can be applied to obtain the induced currents.

The first step of the proposed method consists of setting up several windows which completely cover the entire antenna surface. The electrical size of each side of these windows may go up to several wavelengths. All the coupling terms inside a window are computed rigorously, and the corresponding induced currents are calculated considering it as an isolated part of the geometry. However, it is important to point out that we should consider an extension of the inner borders in order to avoid the singular behavior of the induced currents. This extension corresponds to a fraction of a wavelength (0.1wavelength up to 0.5 wavelength), and after calculating the induced currents we discard the part of them that extends outside of the original window domain (i.e, non-extended window). Fig. 1(a) shows this concept for an arbitrarily-shaped geometry. After setting up the partitioning scheme of the geometry in terms of windows, we need to deal with the problem of calculating the induced currents over each of them. To do so, we use the CBFM due to its capacity to handle moderate-sized problems via direct solvers, which represents an advantage for obtaining the induced currents corresponding to multiple excitations. The CBFM requires a partitioning of the structure to be analyzed as a set of blocks, and it is possible to arrange this partitioning inside the window. To avoid the effects introduced by the artificial edges included, we use extended blocks in a similar way as we did before, as shown in Fig. 1(b).

The approach have been validated considering reflector antenna systems and other large antennas.

Fig 1. (a): Partitioning scheme for the windows over the original geometry; (b): Partitioning scheme for the blocks inside a given window

References:

[1] V. V. S. Prakash, and R. Mittra, "Characteristic Basis Function Method: A New Technique for Efficient Solution of Method of Moments Matrix Equation", Microwave and Optical Technology Letters, Vol. 36, Issue 2, pp 95-100, Jan. 2003..
[2]C. Delgado, F. Catedra, R. Mittra: Application of the Characteristic Basis Function Method Utilizing a Class of Basis and Testing Functions Defined on NURBS Patches, to appear in IEEE Trans. Antennas Propagat.

The radiation and coupling of antennas is affected by the surface of the vehicles (i.e. aircraft, satellites, cars) hosting them. High frequency methods, like UTD, are frequently used to characterize their behaviour and creeping waves need to be modeled on curved surfaces. A very effective technique based on forward tracing of flux-tubes and able to handle generic 3D objects described by a triangular mesh has been demonstrated in the past. However no attempt were made to handle the effect of curvature, owing to the difficulty of including creeping-waves, which are well known to generate significant scattering under suitable conditions. The most important prerequisite to application of the UTD formulation for the analysis of creeping waves is the knowledge of geodesic on the surface, given by a second-order differential equation, the geodesic equation (GE), based on differential geometry satisfying the generalized Fermat's principle.

Two classes of surface approximations are generally used in electromagnetic modelling: polygonal meshes and parametric surfaces (e.g. NURBS). Approximate discrete solutions to the GE can be achieved for both classes with different algorithms. Standard methods can be used for parametric surfaces, e.g. Runge-Kutta in case of initial-value problem (IVP) and finite difference methods in case of boundary value problem (BVP), but they have some drawbacks. For IVP it is not easy to determine the geodesics passing through a given point while, for BVP it is possible to have many solutions or even no solution. Moreover, complex calculations are required especially for evaluating the derivatives of surfaces. Easier calculations are required instead for polygonal meshes, but only heuristic methods have been proposed up to now in the contest of electromagnetic applications and their accuracy and efficiency are not proved. This paper proposes a new method that overcomes these difficulties. It is based on a two steps procedure, the first step determines all possible discrete geodesic paths on the mesh using a straightforward application of the generalized Fermat's principle and a suitable database, the second step determines a specific geodesic path passing through a source point and an observation point exploiting database information. Accuracy and efficiency of the method are proved and realistic applications are shown.

A new strategy is proposed for an efficient and accurate analysis of the performance of a radiating system in a complex multiscale environment, like a space platform. The overall complex problem is decomposed into interacting subdomain problems and the interactions are described through a network formalism using complex source point (CSP) beams as propagators. More specifically, each scatterer is characterized by a scattering matrix, where the ports are associated to CSP beams emerging from an equivalent surface enclosing the scatterer. After expanding the source field into CSP beams, all the interactions among the source and the obstacles and among different obstacles are taken into account by properly combining the scattering matrices associated with the obstacles with the vector of the excitation coefficients associated with the sources. Due to the spatial selectivity of the CSP beams, the interactions only involve a limited number of CSP beams.

The coefficients of the CSP beam expansion are obtained by projecting the radiated field onto the CSP basis through a numerical procedure (K. Tap et al., ICEAA 2007). This procedure only requires the knowledge of the electric field samples at a set of points on a properly defined closed surface.

The main advantage of the proposed approach is that the different parts of the complex scenario can be characterized independently once and for all, and, nonetheless, all the multiple interactions can be accounted for by connecting the relevant scattering matrices in accordance with the given topology. As a consequence, the approach is particularly suited for a parallel implementation. Furthermore, it permits the use of different methods for the analysis of different parts of the complex scenario thus well adapting to multiscale problems. Finally, the efficiency of the connection scheme is ensured by the directional properties of the complex source point beams.