Theoretical and Practical Solutions for High-Order Superdirectivity of Circular Sensor Arrays
Theoretical and Practical Solutions for High-Order Superdirectivity of Circular Sensor Arrays
复制标题
圆形传感器阵列高阶超方向性的理论与实践解决方案
DOI：
10.1109/tie.2012.2185020
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发表时间：
2013-01-01
影响因子：
7.7
通讯作者：
Wang, Yingmin
中科院分区：
文献类型：
--
作者：
Ma, Yuanliang;Yang, Yixin;Wang, Yingmin
本文给出了圆阵超方向性问题的一个解析的、用初等函数表示的最优解。通过利用圆形传感器阵列的数据协方差矩阵的循环属性，这样的解决方案推导出准确地计算最佳波束形成矢量，最佳波束方向图，相应的方向性因子，和特征波束。基于这些解决方案，证明了这种阵列具有几个重要的性质，这有利于实际实现的特征波束分解和合成方法。进行的实验结果在超方向光束，其中包含零至第五和第六阶本征光束。作为一个典型的结果，包含零阶至五阶本征波束的超方向性波束具有28度的波束宽度和12 dB的方向性指数，具有0.267波长的小圆形阵列半径。
An analytical and closed-form optimal solution expressed in elementary functions for superdirectivity of a circular sensor array is proposed in this paper. By utilizing the circulant property of the data covariance matrix for circular sensor arrays, such solutions are derived to accurately calculate the optimal beamforming vector, optimal beam pattern, corresponding directivity factor, and eigenbeams. Based on these solutions, it is proved that such array possesses several important properties which facilitate an eigenbeam decomposition and synthesis approach for practical implementations. Experiments conducted result in superdirective beams which contain zeroth- to fifth-and sixth-order eigenbeams. As a typical result, the superdirective beam which contains zeroth- to fifth-order eigenbeams has a 28 degrees beamwidth and a 12-dB directivity index with a small circular array radius of 0.267 wavelength.