A feedforward neural network for direction-of-arrival estimation.

This paper examines the relationship between conventional beamforming and linear supervised learning, then develops a nonlinear deep feed-forward neural network (FNN) for direction-of-arrival (DOA) estimation. First, conventional beamforming is reformulated as a real-valued, linear inverse problem in the weight space, which is compared to a support vector machine and a linear FNN model. In the linear formulation, DOA is quickly and accurately estimated for a realistic array calibration example. Then, a nonlinear FNN is developed for two-source DOA and for K-source DOA, where K is unknown. Two training methodologies are used: exhaustive training for controlled accuracy and random training for flexibility. The number of FNN model hidden layers, hidden nodes, and activation functions are selected using a hyperparameter search. In plane wave simulations, the 2-source FNN resolved incoherent sources with 1° resolution using a single snapshot, similar to Sparse Bayesian Learning (SBL). With multiple snapshots, K-source FNN achieved resolution and accuracy similar to Multiple Signal Classification and SBL for an unknown number of sources. The practicality of the deep FNN model is demonstrated on Swellex96 experimental data for multiple source DOA on a horizontal acoustic array.