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

TL;DR

SABER tackles the challenge of accurate AoA estimation with interpretable models by inverting beam patterns from a single scalar path-loss measurement using constrained symbolic regression. The framework learns closed-form, physics-consistent expressions for beam-pattern parameters and AoA, validated in both a controlled anechoic chamber and a RIS-aided indoor testbed. Stage I achieves sub-0.5° MAE with interpretable cosine-based beam models, while Stage II demonstrates near-zero AoA error in a RIS environment, with performance approaching the CRLB. These results establish SABER as an interpretable, accurate alternative to black-box ML methods for AoA estimation in next-generation wireless systems.

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.

Figures (11)

• Figure 1: System model of free-space scenario.
• Figure 2: Beam pattern with different $n$ and $m$ in polar coordinates.
• Figure 3: System model of RIS-aided system.
• Figure 4: Flow chart of SABER: from the data collection to verification.
• Figure 5: Experiment setup for the stage I (anechoic chamber verification). The probe antenna (Tx) is mounted on a motorized rotator at the left and the horn antenna (Rx) is fixed at the right, forming a 2 m free-space path (FSPL). Ports 1 and 2 of a Rohde & Schwarz ZVA40 VNA connect to the Tx and Rx, respectively, to measure the forward transmission coefficient $S_{21,\mathrm{FS}}$ across 26 to 31 GHz. A representative sweep is shown in the lower-left box.