In this article, we propose two computationally efficient approaches to jointly estimate direction of arrival (DOA) and carrier for coherent signals using a given single snapshot with uniform linear array. First, the proposed methods construct the Khatri–Rao product-like data vector by introducing $P$ -level delays from the array output. Second, a row elementary transformation is applied to the structured data vector, the rotational invariance structure of the carrier vector is exploited and thereby the carrier is derived. To be able to proceed, the special structure of the data vector is also exploited to estimate the coherent waveform. As a result, the DOA estimation problem can be recast into two Frobenius-norm-based optimization problems: one is referred to as linear search-based covariance-like matrix fitting method, which is suitable for estimating spaced angles that are well separated. The other one is called subspace separation-based covariance-like matrix fitting method, which is suitable for estimating closely spaced angles. The proposed methods develop one-dimensional (1-D) search and $K$ 1-D search procedures, respectively, and hence they are computationally efficient compared to the classical methods. The simulation results illustrate that the performance of the proposed methods is better than the spatial smoothing-based multiple signal classification method under different scenarios.

中文翻译：

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使用单快照及其时延复制对相干信号进行计算有效的 DOA 和载波估计

在本文中，我们提出了两种计算效率高的方法，使用具有均匀线性阵列的给定单个快照来联合估计相干信号的到达方向 (DOA) 和载波。首先，所提出的方法通过从阵列输出引入 $P$ 级延迟来构建类似 Khatri-Rao 产品的数据向量。其次，对结构化数据向量应用行基本变换，利用载波向量的旋转不变性结构，从而导出载波。为了能够继续，还利用数据向量的特殊结构来估计相干波形。因此，可以将 DOA 估计问题改写为两个基于 Frobenius 范数的优化问题：一个称为基于线性搜索的类协方差矩阵拟合方法，这适用于估计分离良好的间隔角。另一种称为基于子空间分离的类协方差矩阵拟合方法，适用于估计距离较近的角度。所提出的方法分别开发了一维 (1-D) 搜索和 $K$ 1-D 搜索程序，因此与经典方法相比，它们在计算上是有效的。仿真结果表明，所提方法在不同场景下的性能优于基于空间平滑的多信号分类方法。所提出的方法分别开发了一维 (1-D) 搜索和 $K$ 1-D 搜索程序，因此与经典方法相比，它们在计算上是有效的。仿真结果表明，所提方法在不同场景下的性能优于基于空间平滑的多信号分类方法。所提出的方法分别开发了一维 (1-D) 搜索和 $K$ 1-D 搜索程序，因此与经典方法相比，它们在计算上是有效的。仿真结果表明，所提方法在不同场景下的性能优于基于空间平滑的多信号分类方法。