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A method for the optimization of the crosspolar component of dual-polarized reflectarrays using full-wave analysis at the element level is described and demonstrated. The reflectarray full-wave analysis is based on local periodicity and integrated within the optimization process in order to accurately characterize the crosspolar far field. The proposed method is based on the generalized Intersection Approach framework using the Levenberg-Marquardt Algorithm as backward projector, and the employed full-wave analysis is based on the Method of Moments assuming local periodicity (MoM-LP). Several strategies to accelerate the computations are exploited, such as the parallelization of all the algorithm building blocks. To minimize the impact of MoM-LP in the optimization process, a strategy to reduce the number of MoM-LP calls is described, further accelerating the algorithm. Moreover, the convergence is improved by working with the squared field amplitude, alleviating the trap problem of local optimizers. This method allows to optimize the crosspolar component in the whole visible region or only in the coverage zone to facilitate the convergence, reduce computing time and memory usage. Two test cases are provided to validate the technique, one with an isoflux pattern for global Earth coverage and another with European coverage for DBS application.

Abstract-A two-layer reflectarray is proposed as a central station antenna for a local multipoint distribution system (LMDS) in the 24.5-26.5 GHz band. The antenna produces three independent beams in an alternate linear polarization that are shaped both in azimuth (sectored) and in elevation (squared cosecant). The design process is divided into several stages. First, the positions of the three feeds are established as well as the antenna geometry to produce the three beams in the required directions. Second, the phase distribution on the reflectarray surface, which produces the required beam shaping, is synthesized. Third, the sizes of the printed stacked patches are adjusted so that the phase-shift introduced by them matches the synthesized phase distribution. Finally, the radiation patterns are computed for the central and lateral beams, showing a shaping close to the requirements. A breadboard has been manufactured and measured in an anechoic chamber, showing a good behavior, which validates the designing methodology.Index Terms-Local multipoint distribution system (LMDS), multibeam antenna, multifeed reflectarray, reflectarray, shaped beam antenna.

A machine learning technique is applied to the design and optimization of reflectarray antennas to considerably accelerate computing time without compromising accuracy. In particular, Support Vector Machines (SVMs), automatic learning structures that are able to deal with regression problems, are employed to obtain surrogate models of the reflectarray element to substitute the full-wave analysis tool for the characterization of the unit cell in the design and optimization algorithms. The analysis, design and optimization of a very large reflectarray antenna for Direct Broadcast Satellite applications are accelerated up to three orders of magnitude. This is here demonstrated with three examples: one showing the design of a reflectarray; and two for the crosspolar optimization, one with one coverage for each linear polarization (Europe and the Middle East) and another with a Middle East coverage working in dual-linear polarization. The accuracy of the proposed approach is validated by means of a comparison of the final designs with full-wave simulations based on local periodicity obtaining good agreement. The crosspolar dicrimination and crosspolar isolation are greatly improved using the SVMs while considerably reducing computing time.