(SP)$^2$-Net: A Neural Spatial Spectrum Method for DOA Estimation

We consider the problem of estimating the directions of arrival (DOAs) of multiple sources from a single snapshot of an antenna array, a task with many practical applications. In such settings, the classical Bartlett beamformer is commonly used, as maximum likelihood estimation becomes impractical when the number of sources is unknown or large, and spectral methods based on the sample covariance are not applicable due to the lack of multiple snapshots. However, the accuracy and resolution of the Bartlett beamformer are fundamentally limited by the array aperture. In this paper, we propose a deep learning technique, comprising a novel architecture and training strategy, for generating a high-resolution spatial spectrum from a single snapshot. Specifically, we train a deep neural network that takes the measurements and a hypothesis angle as input and learns to output a score consistent with the capabilities of a much wider array. At inference time, a heatmap can be produced by scanning an arbitrary set of angles. We demonstrate the advantages of our trained model, named (SP)$^2$-Net, over the Bartlett beamformer and sparsity-based DOA estimation methods.