Optimal synthesis of contonuous aperture sources and their discretization into isophoric sparse arrays

An innovative deterministic approach to the optimal power synthesis of mask-constrained shaped beams through concentric-ring isophoric sparse arrays is presented and tested. The design procedure exploits at best the state-of-the-art techniques respectively available in the cases of circular-ring isophoric arrays radiating pencil beams and of linear isophoric arrays generating shaped beams. Moreover, it avoids the exploitation of global-optimization algorithms (with the inherent advantages in terms of computational burden) and compares favourably to the (few) available procedures. The proposed deterministic design procedure starts from the definition of the power mask constraints for the radiation pattern for the overall azimuth cuts. After that, the work flow foresees the definition of the optimal continuous circular aperture (which acts as a reference and benchmark in the following step) able to meet the requirements for the far field. Finally, the array synthesis is performed by means an optimal discretization of the reference source where, by minimizing the difference between the array’s and continuous source’s cumulative functions, an optimal isophoric sparse array arranged in circular rings is obtained. The optimal results achieved in the first part of the research activity suggested to apply the proposed approach also to the optimal, mask-constrained power synthesis of circular continuous aperture sources able to dynamically reconfigure their radiation behavior by just modifying their phase distribution. The design procedure relies on an effective a-priori exploration of the search space which guarantees the achievement of the globally-optimal solution. The synthesis is cast as a convex programming problem and can handle an arbitrary number of pencil and shaped beams. The achieved solutions are then exploited as reference and benchmark in order to design phase-only reconfigurable isophoric circular-ring sparse arrays. Numerical results concerning new-generation telecommunication systems are provided in support of the given theory.