Alternating Generalized Projection Method for Satellite Reflectarray Synthesis with Sequential Stages of Different Illuminations

Satellite reflectarray synthesis using the intersection approach by means of algorithms of the alternating generalized projection (AGP) method to avoid trap points with sequential stages of different illuminations is presented. In this scenario, we examine two distinct sets: the set of radiation patterns producible by the reflectarray and the set of radiation patterns which meet the mission’s criteria. These sets are generally non-convex. Therefore, it is expected that conventional algorithms of the method of alternating projections (MAP) converge to trap points (i.e., local minima of the distance between the involved sets). Thus, the AGP method, which takes into account the trap points, has been considered. When large reflectarrays are considered for satellite applications, several trap points can appear, producing oscillatory behavior between several trap points. A mathematical formalism which supports the idea that a reduction in the edge illumination of an antenna involves fewer trap points is described. Thus, the oscillatory behavior can be avoided by using sequential stages in the synthesis process with different edge illumination levels in each stage. In this work, we demonstrate this synthesis technique with sequential stages, using the proposed algorithm to avoid trap points.