Bezier surface optimization of amplitude weights for a curtain array

A multilayer dipole curtain array topology is presented and amplitude weights are synthesized to meet a specified sidelobe envelope. While direct optimization of the amplitude weights with a genetic algorithm meets the sidelobe requirement, the resulting optimized weights are observed to be highly oscillatory, which can lead to practical implementation problems. Better results are found when the genetic algorithm is used to synthesize the control points of Bezier surfaces, which are then sampled to produce aperture weights. The smoothing properties of the Bezier formulation encourage smooth continuous weighting functions and the genetic algorithm operates efficiently because of the close geometric proximity of the synthesized control points to the resulting curve. The method can be extended to arbitrary arrays, including conformal and volumetric arrays