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

2025-10-30

AI Summary

Traditional high-accuracy Angle-of-Arrival (AoA) estimation relies on multi-element antenna arrays and numerous signal snapshots, while generic machine learning approaches lack physical interpretability. To address this, we propose SABER—a novel framework that pioneers the integration of constrained symbolic regression into AoA estimation. SABER automatically discovers closed-form beam patterns and analytically tractable AoA models directly from path-loss measurements, achieving both high accuracy and explicit physical interpretability. The method jointly incorporates path-loss modeling, inverse beam-pattern inference, and constrained optimization, with the Cramér–Rao Lower Bound (CRLB) serving as its theoretical performance benchmark. Experimental results demonstrate an average absolute AoA estimation error below 0.5° in free-space scenarios and accurate recovery of ground-truth AoAs in RIS-assisted indoor environments—approaching the CRLB. SABER thus unifies estimation precision with physical interpretability, establishing a new paradigm for trustworthy wireless sensing.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Neuro-Symbolic Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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 $cos^n$ 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 Cramér-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.

Problem

• Estimates Angle of Arrival using interpretable symbolic regression
• Overcomes black-box ML limitations in wireless beamforming systems
• Achieves high accuracy without requiring extensive snapshot collection

Innovation

• Symbolic regression framework for interpretable AoA estimation
• Constrained SR discovers closed-form beam pattern models
• Achieves high accuracy with physics-driven interpretability