# Model-Based Learning for DOA Estimation with One-Bit Single-Snapshot Sparse Arrays

arXiv: https://arxiv.org/abs/2502.17473 · HTML: https://mlsanity.com/paper/2502.17473/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 62 references that are in the map.
- First posted on arXiv 15 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Deep Networks for Direction-of-Arrival Estimation in Low SNR](https://mlsanity.com/paper/2011.08848/) (2020)
- [Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation](https://mlsanity.com/paper/2401.01738/) (2024)
- [DA-MUSIC: Data-Driven DoA Estimation via Deep Augmented MUSIC Algorithm](https://mlsanity.com/paper/2109.10581/) (2021)
- [One-Bit Radar Processing with Time-Varying Sampling Thresholds](https://mlsanity.com/paper/1911.10170/) (2019)
- [Linear and Deep Neural Network-based Receivers for Massive MIMO Systems with One-Bit ADCs](https://mlsanity.com/paper/2008.03757/) (2020)
- [One-Bit MUSIC](https://mlsanity.com/paper/1901.05109/) (2019)
- [On the Performance of One-Bit DoA Estimation via Sparse Linear Arrays](https://mlsanity.com/paper/2012.14051/) (2020)
- [On Optimal MMSE Channel Estimation for One-Bit Quantized MIMO Systems](https://mlsanity.com/paper/2404.05536/) (2024)
- [One-Bit Sigma-Delta MIMO Precoding](https://mlsanity.com/paper/1903.03319/) (2019)
- [One-bit LFMCW Radar: Spectrum Analysis and Target Detection](https://mlsanity.com/paper/1905.09440/) (2019)
- [Sinusoidal Parameter Estimation from Signed Measurements via Majorization-Minimization Based RELAX](https://mlsanity.com/paper/2103.11500/) (2021)
- [Interpretable and Efficient Beamforming-Based Deep Learning for Single Snapshot DOA Estimation](https://mlsanity.com/paper/2309.07411/) (2023)
- [Automotive Radar Sensing with Sparse Linear Arrays Using One-Bit Hankel Matrix Completion](https://mlsanity.com/paper/2312.05423/) (2023)
- [Weighted SPICE Algorithms for Range-Doppler Imaging Using One-Bit Automotive Radar](https://mlsanity.com/paper/2103.17032/) (2021)
- [Channel Estimation for Movable-Antenna MIMO Systems Via Tensor Decomposition](https://mlsanity.com/paper/2407.18773/) (2024)
- [Collaborative Automotive Radar Sensing via Mixed-Precision Distributed Array Completion](https://mlsanity.com/paper/2403.08168/) (2024)
- [Deep Learning-Enabled One-Bit DoA Estimation](https://mlsanity.com/paper/2405.09712/) (2024)
- [Enhancing Off-Grid One-Bit DOA Estimation with Learning-Based Sparse Bayesian Approach for Non-Uniform Sparse Array](https://mlsanity.com/paper/2412.10976/) (2024)
- [Advancing Single-Snapshot DOA Estimation with Siamese Neural Networks for Sparse Linear Arrays](https://mlsanity.com/paper/2501.07008/) (2025)

## Built on by (most cited first, 1 of 1)

- [Compressive Toeplitz Covariance Estimation From Few-Bit Quantized Measurements With Applications to DOA Estimation](https://mlsanity.com/paper/2512.22527/) (2025)

## Abstract (arXiv)

We address the challenging problem of estimating the directions-of-arrival (DOAs) of multiple off-grid signals using a single snapshot of one-bit quantized measurements. Conventional DOA estimation methods face difficulties in tackling this problem effectively. This paper introduces a domain-knowledge-guided learning framework to achieve high-resolution DOA estimation in such a scenario, thus drastically reducing hardware complexity without compromising performance. We first reformulate DOA estimation as a maximum a posteriori (MAP) problem, unifying on-grid and off-grid scenarios under a Laplacian-type sparsity prior to effectively enforce sparsity for both uniform and sparse linear arrays. For off-grid signals, a first-order approximation grid model is embedded into the one-bit signal model. We then reinterpret one-bit sensing as a binary classification task, employing a multivariate Bernoulli likelihood with a logistic link function to enhance stability and estimation accuracy. To resolve the non-convexity inherent in the MAP formulation, we develop augmented algorithmic frameworks based on majorization-minimization principles. Further, we design model-based inference neural networks by deep unrolling these frameworks, significantly reducing computational complexity while preserving the estimation precision. Extensive simulations demonstrate the robustness of the proposed framework across a wide range of input signal-to-noise ratio values and off-grid deviations. By integrating the unified model-based priors with data-driven learning, this work bridges the gap between theoretical guarantees and practical feasibility in one-bit single-snapshot DOA estimation, offering a scalable, hardware-efficient solution for next-generation radar and communication systems.