# SABER: Symbolic Regression-based Angle of Arrival and Beam Pattern Estimator

arXiv: https://arxiv.org/abs/2510.26340 · HTML: https://mlsanity.com/paper/2510.26340/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 55 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 18 of 18)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Deep Networks for Direction-of-Arrival Estimation in Low SNR](https://mlsanity.com/paper/2011.08848/) (2020)
- [Wireless Access in Ultra-Reliable Low-Latency Communication (URLLC)](https://mlsanity.com/paper/1810.06938/) (2018)
- [Deep Learning Based Predictive Beamforming Design](https://mlsanity.com/paper/2302.01035/) (2023)
- [Exploring the 6G Potentials: Immersive, Hyper Reliable, and Low-Latency Communication](https://mlsanity.com/paper/2407.11051/) (2024)
- [Reconfigurable Intelligent Surfaces: A Signal Processing Perspective With Wireless Applications](https://mlsanity.com/paper/2102.00742/) (2021)
- [The Energy Cost of Artificial Intelligence Lifecycle in Communication Networks](https://mlsanity.com/paper/2408.00540/) (2024)
- [Stability and Super-resolution of MUSIC and ESPRIT for Multi-snapshot Spectral Estimation](https://mlsanity.com/paper/2105.14304/) (2021)
- [5G-Advanced AI/ML Beam Management: Performance Evaluation with Integrated ML Models](https://mlsanity.com/paper/2404.15326/) (2024)
- [Deep Symbolic Optimization: Reinforcement Learning for Symbolic Mathematics](https://mlsanity.com/paper/2505.10762/) (2025)
- [Terahertz-Band Ultra-Massive Spatial Modulation MIMO](https://mlsanity.com/paper/1905.04732/) (2019)
- [DeepAoANet: Learning Angle of Arrival from Software Defined Radios with Deep Neural Networks](https://mlsanity.com/paper/2112.00695/) (2021)
- [Machine Learning Assisted Phase-less Millimeter-Wave Beam Alignment in Multipath Channels](https://mlsanity.com/paper/2109.14689/) (2021)
- [Angle of Arrival and Centimeter Distance Estimation on a Smart UWB Sensor Node](https://mlsanity.com/paper/2312.13672/) (2023)
- [Neural Network-Based Intelligent Reflecting Surface Assisted Direction of Arrival Estimation](https://mlsanity.com/paper/2406.18306/) (2024)
- [Automated Modeling Method for Pathloss Model Discovery](https://mlsanity.com/paper/2505.23383/) (2025)

## Abstract (arXiv)

Accurate Angle-of-arrival (AoA) estimation is essential for next-generation wireless communication systems to enable reliable beamforming, high-precision localization, and integrated sensing. Unfortunately, classical high-resolution techniques require multi-element arrays and extensive snapshot collection, while generic Machine Learning (ML) approaches often yield black-box models that lack physical interpretability. To address these limitations, we propose a Symbolic Regression (SR)-based ML framework. Namely, Symbolic Regression-based Angle of Arrival and Beam Pattern Estimator (SABER), a constrained symbolic-regression framework that automatically discovers closed-form beam pattern and AoA models from path loss measurements with interpretability. SABER achieves high accuracy while bridging the gap between opaque ML methods and interpretable physics-driven estimators. First, we validate our approach in a controlled free-space anechoic chamber, showing that both direct inversion of the known cosn beam and a low-order polynomial surrogate achieve sub-0.5 degree Mean Absolute Error (MAE). A purely unconstrained SR method can further reduce the error of the predicted angles, but produces complex formulas that lack physical insight. Then, we implement the same SR-learned inversions in a real-world, Reconfigurable Intelligent Surface (RIS)-aided indoor testbed. SABER and unconstrained SR models accurately recover the true AoA with near-zero error. Finally, we benchmark SABER against the Cram'er-Rao Lower Bounds (CRLBs). Our results demonstrate that SABER is an interpretable and accurate alternative to state-of-the-art and black-box ML-based methods for AoA estimation.