Parametric Diffraction-Based Object Sensing: Modeling, Estimation, and Fundamental Limits

2026-07-14

AI Summary

This work addresses high-precision sensing of geometric parameters—specifically shape, distance, and incident direction—of obstacles in the environment by exploiting wireless signal diffraction. The study proposes a frequency-agnostic, parameterized diffraction channel modeling framework that unifies multiple wave propagation approximations, including far-field, paraxial Fresnel, and exact near-field regimes. A scaling law based on the Fresnel number is established to enable consistent mapping of diffraction patterns across varying frequencies, object sizes, and distances. Parameter inversion is performed via maximum likelihood estimation, and the Cramér–Rao Bound (CRB) is employed to rigorously quantify the fundamental performance limits of diffraction-based sensing. Experimental results demonstrate that, under moderate to high signal-to-noise ratios, the estimation accuracy approaches the CRB, thereby validating both the effectiveness and theoretical optimality of the proposed method for high-fidelity obstacle characterization.

Abstract

This paper proposes a rigorous framework for sensing of environmental objects using diffraction mechanisms prevalent at wireless communication frequencies. Specifically, we develop a physics-consistent parameterized diffraction channel model, derive maximum likelihood (ML) approaches for estimating the blockage shape, range, and source directions of arrival (DoAs), and quantify fundamental performance limits via the Cramér--Rao bound (CRB). In our physics-based modeling, we integrate various approximations for the wave propagation (far-field, paraxial Fresnel, and exact near-field regimes), enabling a wide range of applicability. The underlying model is frequency-agnostic, and we derive Fresnel-number scaling laws that map the diffraction pattern, and hence the estimation problem, across carrier frequency, object size, and range. We quantify the maximum likelihood estimation performance and its relationship to the CRB, and we study the impact of the modeling approximations developed in this work. Numerical results demonstrate that ML estimators closely approach the CRB at moderate to high signal-to-noise ratio (SNR), and highlight the utility of diffraction-based modeling for high-fidelity blockage characterization.

Problem

• diffraction-based sensing
• object characterization
• parameter estimation
• wireless propagation
• blockage sensing

Innovation

• diffraction-based sensing
• parameterized channel model
• maximum likelihood estimation
• Cramér–Rao bound
• Fresnel-number scaling