Direction-of-arrival (DOA) estimation problems arise in many applications such as wireless communication and localization. Recently, a number of deep learning (DL) based methods have been studied for one dimensional (1D) DOA estimation with relatively fewer studies for 2D-DOA estimation. In this study, we propose a low-complexity DL based method to estimate both elevation and azimuth DOAs of sources along with their pairing. To this end, first a classification neural network is proposed to estimate both elevation and azimuth DOAs of multiple sources. Next, a residual classification network is introduced to estimate the pairing between the estimated DOAs. In particular, we consider two perpendicular linear arrays which are located on -axis and -axis, respectively. The first proposed network uses the Sample Covariance Matrix (SCM) of the former array to estimate elevation angles and utilizes the latter array to estimate the corresponding azimuth DOAs. The second network, is responsible for estimating the pairing between the estimated elevation and azimuth DOA sets. Numerical simulations demonstrate the enhanced performance of our proposed 2D-DOA estimator scheme, surpassing existing 1D and 2D deep learning (DL) methods. Notably, our approach closely approaches the Ziv–Zakai bound (ZZB), particularly in low signal-to-noise ratio (SNR) and low-angle-difference scenarios, even in the presence of multiple highly correlated signals. Moreover, our complexity analysis validates the superiority of the proposed method.

中文翻译：

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使用 L 形阵列的基于深度学习的 2D-DOA 估计

到达方向 (DOA) 估计问题出现在许多应用中，例如无线通信和定位。最近，已经研究了许多基于深度学习（DL）的方法来进行一维（1D）DOA估计，而针对2D-DOA估计的研究相对较少。在本研究中，我们提出了一种基于深度学习的低复杂度方法来估计源的仰角和方位角 DOA 及其配对。为此，首先提出分类神经网络来估计多个源的仰角和方位角 DOA。接下来，引入残差分类网络来估计估计的 DOA 之间的配对。特别地，我们考虑分别位于 -axis 和 -axis 上的两个垂直线性阵列。第一个提出的网络使用前一个阵列的样本协方差矩阵（SCM）来估计仰角，并利用后一个阵列来估计相应的方位角 DOA。第二个网络负责估计估计的仰角和方位角 DOA 集之间的配对。数值模拟证明了我们提出的 2D-DOA 估计器方案的增强性能，超越了现有的 1D 和 2D 深度学习 (DL) 方法。值得注意的是，我们的方法非常接近 Ziv-Zakai 界（ZZB），特别是在低信噪比（SNR）和低角度差场景中，即使存在多个高度相关的信号。此外，我们的复杂性分析验证了所提出方法的优越性。