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.

翻译：波达方向估计是阵列处理中的一项基本任务。子空间方法是波达方向估计中一类常用算法，其通过将测量值划分为不同的信号子空间和噪声子空间来实现。诸如多重信号分类和Root-MUSIC等子空间方法依赖于若干限制性假设，包括窄带非相干源和完全校准阵列，当这些条件不满足时其性能会显著下降。本研究提出SubspaceNet：一种数据驱动的波达方向估计器，通过学习如何将观测数据划分为可区分子空间。该方法通过专用深度神经网络学习输入信号的经验自相关函数，将其作为Root-MUSIC算法的组成部分进行训练，利用该特定波达方向估计器固有的可微性，同时无需提供真实可分解的自相关矩阵。训练完成后，所得SubspaceNet可作为通用替代协方差估计器，可与任何基于子空间的波达方向估计方法结合使用，从而在复杂场景中实现成功应用。实验表明SubspaceNet能使多种波达方向估计算法适应相干源、宽带信号、低信噪比、阵列失配及有限快拍等挑战性条件，同时保持经典子空间方法的可解释性与适用性。