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 (ASA_NRUE case) and (2) aperiodic arrays with a nonuniform spacing between rings and between antenna elements of the same ring (ASA_NRNE 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.

本文阐述了与非球面天线阵列设计相关的高度非线性问题，该非周期性天线阵列使用球形几何结构以获得最佳性能。非周期性球面天线阵列的这种综合考虑了两种设计情况：（1）假设环在同一环上的元素间距相等，则环之间具有非均匀间隔的非周期性阵列（ASA _NRUE情况）和（2）环与环之间非均匀间隔的非周期性阵列同一环的天线元件（ASA _NRNE案件）。此过程是通过使用差分演化（DE）优化技术进行的，目的是找到每个元素在仰角和方位角平面上的最佳角度位置，以在旁瓣电平，方向性和数量上获得最佳性能。阵列中用于三个设计目标的天线元件的数量：辐射方向图的自然响应，波束扫描以及元件之间最小距离的限制。本文的创新贡献是将差分演化算法应用于非平凡且高度复杂的设计问题：非球面元素在球形天线装置上的分布。这种方法相对于球形阵列设计方面的最新技术的优势在于，对于非周期性的元素分布，可以减少天线元件的数量，从而获得较低的旁瓣电平和球形天线阵列的最大方向性。因此，半径较小，这意味着较少的复杂性和较低的制造成本。提供基于CST Microwave Studio的仿真结果以考虑相互耦合。