Aperiodic Array Layout Optimization by the Constraint Relaxation Approach

An optimization procedure for the layout assessment of electrically large but finite planar arrays is presented. The synthesis takes into account the desired directivity pattern that is prescribed employing bound constraints. Moreover, the size of the radiators is taken into account, which results in a hard nonoverlapping, between the elements, constraint. The latter should not be violated if we want the attained solution not only to obey the far-field mask, but also to be physically realizable. As stated, the optimization problem is twofold. An antenna design is associated with a packing problem. In order to take the constraints on the layout into account and solve the whole problem, we propose the constraint relaxation approach, which is equipped with a packing algorithm. Our study is applied to various initial geometries, and the resulting arrays appear to comply with the desired pattern and the nonoverlapping constraint. Several examples for different cases including symmetric arrays and a study on maximally sparse arrays are presented, which show the applicability and merit of the method.