# SubspaceNet: Deep Learning-Aided Subspace Methods for DoA Estimation

arXiv: https://arxiv.org/abs/2306.02271 · HTML: https://mlsanity.com/paper/2306.02271/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 68 references that are in the map.
- First posted on arXiv 4 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound](https://mlsanity.com/paper/1811.08252/) (2018)
- [Nonsmooth Implicit Differentiation for Machine Learning and Optimization](https://mlsanity.com/paper/2106.04350/) (2021)
- [Deep Networks for Direction-of-Arrival Estimation in Low SNR](https://mlsanity.com/paper/2011.08848/) (2020)
- [Adaptive Ultrasound Beamforming using Deep Learning](https://mlsanity.com/paper/1909.10342/) (2019)
- [Unsupervised Learned Kalman Filtering](https://mlsanity.com/paper/2110.09005/) (2021)
- [Broadband DOA estimation using Convolutional neural networks trained with noise signals](https://mlsanity.com/paper/1705.00919/) (2017)
- [Discriminative and Generative Learning for Linear Estimation of Random Signals [Lecture Notes]](https://mlsanity.com/paper/2206.04432/) (2022)
- [DeepMUSIC: Multiple Signal Classification via Deep Learning](https://mlsanity.com/paper/1912.04357/) (2019)
- [DA-MUSIC: Data-Driven DoA Estimation via Deep Augmented MUSIC Algorithm](https://mlsanity.com/paper/2109.10581/) (2021)
- [Ziv-Zakai Bound for DOAs Estimation](https://mlsanity.com/paper/2209.03700/) (2022)
- [Unsupervised Parameter Estimation using Model-based Decoder](https://mlsanity.com/paper/2211.01849/) (2022)

## Built on by (most cited first, 7 of 7)

- [Physically Parameterized Differentiable MUSIC for DoA Estimation with Uncalibrated Arrays](https://mlsanity.com/paper/2411.15144/) (2024)
- [Model-based learning for multi-antenna multi-frequency location-to-channel mapping](https://mlsanity.com/paper/2407.07719/) (2024)
- [Near Field Localization via AI-Aided Subspace Methods](https://mlsanity.com/paper/2504.00599/) (2025)
- [HYPERDOA: Robust and Efficient DoA Estimation using Hyperdimensional Computing](https://mlsanity.com/paper/2510.10718/) (2025)
- [Model-based Implicit Neural Representation for sub-wavelength Radio Localization](https://mlsanity.com/paper/2506.06387/) (2025)
- [NeuralMUSIC: A Hybrid Neural-Subspace Framework for Robot Sound Source Localization](https://mlsanity.com/paper/2606.18664/) (2026)
- [Learning Array Signal Topologies as Conditional Neural Manifolds](https://mlsanity.com/paper/2609.18616/) (2026)

## Abstract (arXiv)

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.