Cram\'er-Rao Bounds for Near-Field Localization

TL;DR

This paper derives the Cramér-Rao Bound for near-field source localization using large antenna arrays, revealing fundamental limits and showing centimeter-level accuracy is achievable in mmWave bands.

Contribution

It introduces a novel CRB analysis for near-field localization with spherical wavefronts, combining wave propagation and estimation theories.

Findings

Surface size impacts localization accuracy.

Centimeter-level precision feasible in mmWave frequencies.

CRB analysis guides system design for optimal accuracy.

Abstract

Multiple antenna arrays play a key role in wireless networks for communications but also localization and sensing. The use of large antenna arrays pushes towards a propagation regime in which the wavefront is no longer plane but spherical. This allows to infer the position and orientation of an arbitrary source from the received signal without the need of using multiple anchor nodes. To understand the fundamental limits of large antenna arrays for localization, this paper fusions wave propagation theory with estimation theory, and computes the Cram{\'e}r-Rao Bound (CRB) for the estimation of the three Cartesian coordinates of the source on the basis of the electromagnetic vector field, observed over a rectangular surface area. To simplify the analysis, we assume that the source is a dipole, whose center is located on the line perpendicular to the surface center, with an orientation a priori known. Numerical and asymptotic results are given to quantify the CRBs, and to gain insights into the effect of various system parameters on the ultimate estimation accuracy. It turns out that surfaces of practical size may guarantee a centimeter-level accuracy in the mmWave bands.