Two-Dimensional DOA Estimation via Deep Ensemble Learning

To achieve fast and accurate two-dimensional (2D) direction of arrival (DOA) estimation, a novel deep ensemble learning method is presented in this paper. First, a convolutional neural network (CNN) is employed to learn a mapping between the spatial covariance matrix of the received signals from the antenna elements and the directions of arrival. To avoid any explicit feature extraction step, the real and imaginary parts of the spatial covariance matrix are fed to the CNN. The output layer of the CNN uses three neurons, two of them are the sine and cosine values of the azimuth angle that are used to uniquely determine the azimuth angle, and the third neuron is a normalized value for representing the elevation angle. Second, to improve the prediction performance, since that a single CNN with limited training data has difficulties learning the highly complex and nonlinear mapping from the received signal to the angle of arrival, an ensemble learning method is proposed. Five different CNN networks are trained independently with different training conditions. The prediction results of each individual CNN are calculated as an average to obtain the final estimated results of the azimuth and elevation angles. Simulation results show that the processing time of the proposed deep ensemble learning method is dramatically reduced. In terms of the accuracy, it outperforms the neural network-based 2D DOA estimation and achieves performance comparable to the MUSIC algorithm.