A complete and unified time- and frequency-domain study on 4-D antenna arrays including mutual coupling effect is presented in this article. The “instantaneous” active reflection coefficient (ARC) or power pattern as a function of time and the “averaged” ARC or power pattern as a function of frequency are introduced to evaluate the port matching and the mutual coupling in 4-D arrays, respectively. The two analysis approaches from different viewpoints are demonstrated to be unified and complementary through Fourier transform. Based on the Fourier transform, five unified equations corresponding to the power pattern, ARC, input power, reflected power, and radiated power are shown to explain the working principle of 4-D arrays from time domain and frequency domain. Other antenna parameters including directivity, efficiency, and gain are also thoroughly investigated. A novel optimization method is proposed to synthesize a 16-element 4-D linear array with tightly coupled elements, and the results are used to validate the five unified equations and illustrate its working principle. Moreover, an ${S}$ -band eight-element 4-D linear array is constructed and measured to demonstrate these studies.

中文翻译：

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包含互耦效应的四维天线阵列完整统一的时域和频域研究

本文对包括互耦合效应的 4-D 天线阵列进行了完整而统一的时域和频域研究。引入作为时间函数的“瞬时”有源反射系数 (ARC) 或功率模式和作为频率函数的“平均”ARC 或功率模式，分别用于评估 4-D 阵列中的端口匹配和互耦合. 通过傅里叶变换证明了来自不同观点的两种分析方法是统一和互补的。基于傅里叶变换，给出了对应于功率方向图、ARC、输入功率、反射功率和辐射功率的五个统一方程，从时域和频域解释了四维阵列的工作原理。其他天线参数包括方向性、效率、和增益也被彻底调查。提出了一种新的优化方法来合成具有紧耦合单元的 16 单元 4-D 线性阵列，并将结果用于验证五个统一方程并说明其工作原理。此外，构建并测量了 ${S}$ 波段八元素 4-D 线性阵列以证明这些研究。