LG-CNN: CNN Framework With Determinate Number of Convolutional Layers for DOA Estimation by Sensor Array

The convolutional neural network (CNN) has been widely utilized in imaging processing and gradually applied in array signal processing. However, its performance is dependent on the hyperparameters such as the number of convolutional layers and the channels of each layer, where the number of convolutional layers as the depth of feature extraction is critical for the CNN to have good generalization, be over-fitting or be under-fitting. In this article we have proposed a new CNN architecture, where we have derived a lower bound for the number of convolutional layers and propose a searching method for precisely determining the number of convolutional layers. The principle behind this is that direction-of-arrival (DOA) information are included in all the input elements of the network. Thus, in order to extract the global feature of the input data, we have derived that the output at each channel of the last convolutional layer is required to contain only one element, which then involves all the input elements of the neural network. Thus, the last layer and all the previous layers work together to achieve the global feature extraction from the input data. Meanwhile, each layer extracts local features. In order to facilitate the local feature extraction, we have proposed a new rearrangement for the input elements according to the element similarity. In summary, we have proposed a CNN framework to extract both the local features and global features from the array data, named LG-CNN. The theoretical analysis demonstrates that the proposed LG-CNN is much more lightweight than the existing CNN, which significantly reduces the number of trainable parameters to only 1/9 of that in the existing CNN. Simulation results demonstrate that the proposed LG-CNN offers high resolution and accuracy and outperforms the other deep neural network (DNN)-based methods and the classical DOA estimation methods, especially in conditions of low signal-to-noise ratios (SNRs) and a small number of snapshots. It is noted that its performance is even better than Cramér-Rao Bound (CRB) under low SNRs.