A new approach for the synthesis of one-dimensional (1D) and 2D reconfigurable sparse arrays generating sum and difference power patterns is presented in this study. In the case of 1D arrays, the design procedure provides solutions in which only one set of amplitude coefficients is required and the reconfigurability is obtained by modifying only the excitation phases. In the case of 2D arrays, the simplification of the antenna system is investigated by sharing some excitations for the sum and difference channels. An iterative scheme is used where the array response in the main lobe direction is cast as a multi-convex problem at each step that the non-convex lower bound constraint is relaxed while concurrently minimising a reweighted objective function based on the magnitudes of the element excitations. To ensure the robustness of the array, worst-case performance optimisation technique and white noise gain constraint are introduced in the array. Numerical tests and electromagnetic simulations, referred to known optimal solutions, show that the proposed design is able to obtain good radiation performance with a smaller number of elements.

中文翻译：

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通过多凸编程优化可重构稀疏数组的综合

这项研究提出了一种新的方法来合成一维（1D）和2D可重构稀疏阵列，生成和和差幂模式。在一维阵列的情况下，设计程序提供的解决方案仅需要一组振幅系数，并且仅通过修改激励相位即可获得可重构性。在2D阵列的情况下，通过共享一些求和和差信道的激励来研究天线系统的简化。使用迭代方案，其中在放宽非凸下界约束的同时，基于元素激发的幅度同时最小化重新加权的目标函数的每一步，将主瓣方向上的阵列响应转换为多凸问题。为了确保阵列的健壮性，在阵列中引入了最坏情况下的性能优化技术和白噪声增益约束。数值测试和电磁仿真，涉及到已知的最佳解决方案，表明所提出的设计能够以较少的元素获得良好的辐射性能。