Deep Learning-Aided Subspace-Based DOA Recovery for Sparse Arrays

Sparse arrays enable resolving more direction of arrivals (DoAs) than antenna elements using non-uniform arrays. This is typically achieved by reconstructing the covariance of a virtual large uniform linear array (ULA), which is then processed by subspace DoA estimators. However, these method assume that the signals are non-coherent and the array is calibrated; the latter often challenging to achieve in sparse arrays, where one cannot access the virtual array elements. In this work, we propose Sparse-SubspaceNet, which leverages deep learning to enable subspace-based DoA recovery from sparse miscallibrated arrays with coherent sources. Sparse- SubspaceNet utilizes a dedicated deep network to learn from data how to compute a surrogate virtual array covariance that is divisible into distinguishable subspaces. By doing so, we learn to cope with coherent sources and miscalibrated sparse arrays, while preserving the interpretability and the suitability of model-based subspace DoA estimators.

SubspaceNet: Deep Learning-Aided Subspace Methods for DoA Estimation

Direction of arrival (DoA) estimation is a fundamental task in array processing. A popular family of DoA estimation algorithms are subspace methods, which operate by dividing the measurements into distinct signal and noise subspaces. Subspace methods, such as Multiple Signal Classification (MUSIC) and Root-MUSIC, rely on several restrictive assumptions, including narrowband non-coherent sources and fully calibrated arrays, and their performance is considerably degraded when these do not hold. In this work we propose SubspaceNet; a data-driven DoA estimator which learns how to divide the observations into distinguishable subspaces. This is achieved by utilizing a dedicated deep neural network to learn the empirical autocorrelation of the input, by training it as part of the Root-MUSIC method, leveraging the inherent differentiability of this specific DoA estimator, while removing the need to provide a ground-truth decomposable autocorrelation matrix. Once trained, the resulting SubspaceNet serves as a universal surrogate covariance estimator that can be applied in combination with any subspace-based DoA estimation method, allowing its successful application in challenging setups. SubspaceNet is shown to enable various DoA estimation algorithms to cope with coherent sources, wideband signals, low SNR, array mismatches, and limited snapshots, while preserving the interpretability and the suitability of classic subspace methods.