Abstract Most existing methods for mixed far-field (FF) and near-field (NF) sources localization are based on uniform linear arrays (ULAs) or some special sparse linear arrays (SLAs) such as symmetric nested arrays. How to employ other linear arrays for mixed sources localization is still unknown. In this paper, we propose a generalized symmetric linear array framework which unifies all the symmetric ULAs or SLAs including the symmetric nested arrays, cantor array, fractal array and many other symmetric SLAs for mixed sources localization. To increase the degrees-of-freedom (DoFs) of these arrays, we utilize the high-order cumulant matrix of the array output from the coarray perspective. The atomic norm technique is employed for estimating the angles of the FF and NF sources from the gridless manner. The range information of the NF sources is obtained by applying the l1-norm minimization technique to the covariance signal model. Our method can be applied to any ULAs or symmetric SLAs for mixed FF and NF sources localization with high estimation accuracy. By exploiting the coarray property, our method can locate more sources than sensors with proper arrays. Extensive simulations are carried out to show the effectiveness of our proposed generalized symmetric linear array framework and method.

中文翻译：

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使用混合稀疏方法定位远场和近场信号：广义对称阵列视角

摘要 现有的混合远场（FF）和近场（NF）源定位方法大多基于均匀线阵（ULA）或一些特殊的稀疏线阵（SLA），如对称嵌套阵列。如何使用其他线性阵列进行混合源定位仍然未知。在本文中，我们提出了一个广义对称线性阵列框架，该框架统一了所有对称 ULA 或 SLA，包括对称嵌套阵列、康托阵列、分形阵列和许多其他用于混合源定位的对称 SLA。为了增加这些阵列的自由度 (DoF)，我们从 coarray 的角度利用阵列输出的高阶累积矩阵。原子范数技术用于从无网格方式估计 FF 和 NF 源的角度。NF 源的距离信息是通过将 l1-norm 最小化技术应用于协方差信号模型来获得的。我们的方法可以应用于任何 ULA 或对称 SLA，以实现具有高估计精度的混合 FF 和 NF 源定位。通过利用 coarray 属性，我们的方法可以定位比具有适当阵列的传感器更多的源。进行了广泛的模拟以显示我们提出的广义对称线性阵列框架和方法的有效性。