Interpretable and Efficient Beamforming-Based Deep Learning for Single-Snapshot DOA Estimation

We introduce an interpretable deep-learning (DL) approach for direction-of-arrival (DOA) estimation with a single snapshot. Classical subspace-based methods, such as multiple signal classification (MUSIC) and estimation of parameters by rotational invariant technique (ESPRIT), use spatial smoothing on uniform linear arrays (ULAs) for single-snapshot DOA estimation but face drawbacks in reduced array aperture and inapplicability to sparse arrays. Single-snapshot methods, such as compressive sensing (CS) and iterative adaptive approach (IAA), encounter challenges with high-computational costs and slow convergence, hampering real-time use. Recent DL DOA methods offer promising accuracy and speed. However, the practical deployment of deep networks is hindered by their black-box nature. To address this, we propose a deep-minimum power distortionless response (MPDR) network translating MPDR-type beamformer into DL, enhancing generalization and efficiency. Comprehensive experiments conducted using both simulated and real-world datasets substantiate its dominance in terms of inference time and accuracy in comparison with conventional methods. Moreover, it excels in terms of efficiency, generalizability, and interpretability when contrasted with other DL DOA estimation networks.