Design of aperiodic spherical antenna arrays for wideband performance

This paper illustrates a highly nonlinear problem related to the design of aperiodic antenna arrays using spherical geometry for maximum performance. This synthesis of aperiodic spherical antenna arrays considers two design cases: (1) aperiodic arrays with a nonuniform spacing between rings assuming equal element spacings on the same ring (ASANRUE case) and (2) aperiodic arrays with a nonuniform spacing between rings and between antenna elements of the same ring (ASANRNE case). This process is carried out by using the differential evolution (DE) optimization technique with the goal of finding the optimum angular position of each element on the elevation and azimuthal planes to achieve the maximum performance in terms of the side lobe level, directivity, and number of antenna elements used in the array for three design objectives: natural response of the radiation pattern, beam scanning, and the restriction of a minimum distance among elements. The innovative contribution of this paper is the application of the differential evolution algorithm to a nontrivial and highly complex design problem: the aperiodic element distribution over a spherical antenna arrangement. The advantage of this approach with respect to the state of the art on the topic of spherical array design is that a lower side lobe level and maximum directivity for a spherical antenna array can be obtained for aperiodic element distributions with a reduced number of antenna elements and hence a smaller radius, which means less complexity and lower fabrication costs. Simulation results based on CST Microwave Studio are provided to take mutual coupling into account.