# DOA Estimation from One-Bit Magnitude-Only Measurements via Sign-Consistency Optimization

arXiv: https://arxiv.org/abs/2607.12491 · HTML: https://mlsanity.com/paper/2607.12491/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 43 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 4 of 4)

- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [One-Bit Phase Retrieval: More Samples Means Less Complexity?](https://mlsanity.com/paper/2203.08982/) (2022)
- [One-Bit MUSIC](https://mlsanity.com/paper/1901.05109/) (2019)
- [A New Atomic Norm for DOA Estimation With Gain-Phase Errors](https://mlsanity.com/paper/1910.02207/) (2019)

## Abstract (arXiv)

The direction-of-arrival (DOA) estimation problem using one-bit quantized magnitude-only measurements is studied, where magnitude-only measurements offer robustness against phase errors, thereby avoiding the need for array calibration, while one-bit quantization significantly reduces hardware cost and system complexity. As their direct combination results in meaningless constant measurements, we formulate a sign-consistency optimization problem using a smooth logistic surrogate with ell_2,1-norm regularization to promote joint sparsity. To solve this problem, a proximal-gradient algorithm is developed with guaranteed convergence to a critical point. Numerical results demonstrate that the proposed method achieves accuracy comparable to coherent one-bit baselines under ideal conditions, while maintaining robust performance under severe phase errors that substantially impair coherent methods.