In this paper, we consider circular array design in the presence of a far-field or a near-field signal source. The location of the source is introduced to our optimization problem by its probability density function (PDF) as a priori information. We consider Bayesian Cramer–Rao bound as the cost function to be minimized to specify the best locations of the sensors on a circular boundary. In the far-field case, a closed form solution is derived for an arbitrary PDF of the bearing. In the near-field scenario, we divide the design problem into three categories: known source bearing, known source range, and the general case. We present some examples to exhibit the process of array design by the proposed method. Finally, we show the array optimized by the proposed method outperforms arrays with other configurations in source localization.

中文翻译：

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基于贝叶斯克拉默-饶界的圆阵设计

在本文中，我们考虑存在远场或近场信号源的圆形阵列设计。源的位置通过其概率密度函数 (PDF) 作为先验信息引入到我们的优化问题中。我们将贝叶斯 Cramer-Rao 边界视为要最小化的成本函数，以指定圆形边界上传感器的最佳位置。在远场情况下，可以为轴承的任意 PDF 导出封闭形式的解。在近场场景中，我们将设计问题分为三类：已知源方位、已知源范围和一般情况。我们提供了一些例子来展示通过所提出的方法进行阵列设计的过程。最后，我们展示了通过所提出的方法优化的阵列在源定位方面优于具有其他配置的阵列。