This paper proposes a method based on Khatri-Rao (KR) product, sparse prior, and convolutional neural networks (CNN) to solve the direction-of-arrival (DOA) estimation problem. Firstly, we use the KR product to expand the degree of freedom (DOF) of the 2-D antenna array. Then we calculate the sparse power spectrum of signals and obtain an RGB image tensor of the spectrum. Finally, we design a CNN group with three different sub-networks to estimate 2-D DOA information. Two of the sub-networks are used for obtaining the spectrum of azimuth angle and elevation angle, respectively. One specific network is designed as the pairing network used for paring azimuth angle with the correct elevation angle. The proposed CNN group is data-driven and does not rely on any prior knowledge of incidence signals. We investigate the feature of estimation error, the root mean squared error (RMSE) responses under different experiment environments, the resolution of the proposed estimation CNN group, and the pairing performance of the proposed pairing network. Comparing with prior estimation methods, the proposed CNN group shows satisfactory estimation accuracy and stability.

本文提出了一种基于Khatri-Rao（KR）乘积，稀疏先验和卷积神经网络（CNN）的方法来解决到达方向（DOA）估计问题。首先，我们使用KR产品扩展二维天线阵列的自由度（DOF）。然后，我们计算信号的稀疏功率谱，并获得该谱的RGB图像张量。最后，我们设计了一个具有三个不同子网的CNN组，以估计二维DOA信息。两个子网分别用于获得方位角和仰角的频谱。一个特定的网络被设计为用于配对具有正确仰角的方位角的配对网络。提议的CNN小组是数据驱动的，并且不依赖于入射信号的任何先验知识。我们研究估计误差的特征，不同实验环境下的均方根误差（RMSE）响应，建议的CNN估计组的分辨率以及建议的配对网络的配对性能。与现有的估计方法相比，提出的CNN组显示出令人满意的估计准确性和稳定性。