Abstract

Reflectarray antennas are reflector structures which combine characteristics of both reflector and array antennas. They exhibit electrically large apertures in order to generate significant gain as conventional metallic reflector antennas. At the same time they are populated by several radiating elements which can be controlled individually like conventional phased array antennas. They are usually flat and can be folded and deployed permitting important saving in terms of volume. For these reasons they have been considered since several years for satellite applications. Initially constituted by truncated metallic waveguides and mainly considered for radar applications, they are now mainly constituted by a dielectric substrate, backed by a metallic plane (groundplane) on which microstrip elements with variable shape/size/orientation are printed. These elements are illuminated by the primary feed. The reflected wave from each element has a phase that can be controlled by the geometry of the element itself. By a suitable design of the elements that make up the reflectarray, it is therefore possible to compose the phase front of the reflected waves in the desired direction (steering direction), and to ensure that the obtained overall radiation pattern exhibits a secondary lobe profile which meets the design specifications. Reflectarrays may be used to synthesize pencil or shaped beams. The synthesis methods commonly used to achieve this goal are based on three different steps: (a) calculation of the nearfield “phase distribution” that the wave reflected by the reflectarray must exhibit to get the desired far-field behaviour; (b) discretization of such distribution into cells of size comparable to that of the elements of interest (i.e., the patches); (c) calculation of the geometry of each elementary cell that will provide the desired reflection coefficient. The first step (a) is a Phase Only approach and permits already to achieve fast preliminary indications on the performance achievable. Accurate results require the implementation of the steps (b) and (c) as well and it is thus of fundamental importance to have techniques capable of efficiently and accurately calculating the reflection coefficient associated with a given geometry of the element [in order to efficiently solve the step (c)]. This coefficient is mathematically represented by a 2x2 complex matrix, which takes into account the relationships between co-polar and cross-polar components of the incident (due to the feed) and reflected field. This matrix naturally depends on the geometry of the element, the direction of incidence of the wave (azimuth and elevation) and the operating frequency of the system. The computation of the reflection coefficient is usually performed using electromagnetic full-wave (FW) simulators; the computation is however time consuming and the generation of the unit cells scattering response database becomes often unfeasible. In this work, an innovative strategy based on an advanced statistical learning method is introduced to efficiently and accurately predict the electromagnetic response of complex-shaped reflectarray elements. The computation of the scattering coefficients of periodic arrangements, characterized by an arbitrary number of degrees-of-freedom, is firstly recast as a vectorial regression problem, then solved with a learning-by-example strategy exploiting the Ordinary Kriging paradigm. A set of representative numerical experiments dealing with different element geometries is presented to assess the accuracy, the computational efficiency, and the flexibility of the proposed technique also in comparison with state-of-the-art machine learning methods.