Nested U-Shape Network for Robust Direction-of-Arrival Estimation

This work proposes a new deep learning method by extracting multiple-scale features from both local and global aspects for Direction-of-Arrival (DOA) estimation tasks. A nested U-shaped convolutional neural network (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$U^{2} Net$</tex-math></inline-formula>, where the superscript 2 refers to the nesting level) is exploited to predict the directions of two sources scattered in a 120-degree space. The highlights of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$U^{2} Net$</tex-math></inline-formula> are to design an inner U-net for local features and another outer U-net to fuse local features for global feature patterns. The DOA problem is designed as a multi-label classification task with on-grid patterns, and train data set is generated at low SNR regimes by specifying sample covariance matrix as input features and source direction as labels. Simulation results demonstrate that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$U^{2} Net$</tex-math></inline-formula> achieves excellent and robust performances in multiple-target DOA estimation tasks, especially under challenging conditions with high noise levels, small snapshots and coherent sources. Moreover, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$U^{2} Net$</tex-math></inline-formula> has a potential to resolve source angles within grid resolution. Finally, comparative studies verified that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$U^{2} Net$</tex-math></inline-formula> outperforms traditional DOA methods as well as convolutional neural network with low SNR, limited snapshots and coherent sources presented.