This article presents a mapping-based optimization method for pattern synthesis via array element rotation. The optimization is carried out through optimizing the orientation of each array element to minimize the sidelobe and cross-polar level while maximizing the co-polar level of the main beam in a desired direction. The basic idea of the proposed method is to convert a variable definition domain problem into a fixed definition domain problem through coordinate transformation. Based on this, the optimization is well integrated with the method of moments (MoM), and it is convenient to calculate the radiation pattern properties and their sensitivities with respect to the design variables. Thus, the design optimization problem can be efficiently solved by use of any gradient-based algorithm. Additionally, benefiting from the combination of the mapping transformation and the full-wave MoM simulation, the mutual coupling between array elements is rigorously taken into account and the complex meshing of the surrounding radiation region is avoided. Furthermore, the change in the array performance is derived only associating with the transformation variables, thus remeshing for iteratively changed arrangements is avoided and the computing cost is saved. Typical numerical examples are provided to validate the effectiveness of the proposed method.

中文翻译：

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基于映射的阵列元素旋转模式合成优化方法

本文提出了一种基于映射的优化方法，用于通过阵列元素旋转进行模式合成。优化是通过优化每个阵元的方向来最小化旁瓣和交叉极化水平，同时最大化所需方向上的主波束的共极化水平。该方法的基本思想是通过坐标变换将可变定义域问题转化为固定定义域问题。在此基础上，优化与矩量法 (MoM) 很好地结合在一起，可以方便地计算辐射方向图属性及其对设计变量的敏感性。因此，可以使用任何基于梯度的算法有效地解决设计优化问题。此外，得益于映射变换与全波MoM模拟的结合，严格考虑了阵元之间的相互耦合，避免了周围辐射区域的复杂网格划分。此外，阵列性能的变化仅与变换变量相关联，从而避免了对迭代变化的排列的重新网格化，并节省了计算成本。提供了典型的数值例子来验证所提出方法的有效性。因此避免了对迭代更改的安排的重新网格化，并节省了计算成本。提供了典型的数值例子来验证所提出方法的有效性。因此避免了对迭代更改的安排的重新网格化，并节省了计算成本。提供了典型的数值例子来验证所提出方法的有效性。