Cram\'er-Rao Lower Bounds for Positioning with Large Intelligent Surfaces

TL;DR

This paper derives theoretical bounds on the accuracy of positioning using large intelligent surfaces, revealing how surface area and deployment affect localization precision in different dimensions.

Contribution

It provides closed-form CRLB expressions for terminals on the central perpendicular line and accurate approximations elsewhere, analyzing the impact of surface area and deployment strategies.

Findings

CRLB decreases quadratically with surface area for x and y dimensions.

CRLB decreases linearly with surface area along the z dimension on the CPL.

Deployment strategies significantly influence positioning accuracy.

Abstract

We consider the potential for positioning with a system where antenna arrays are deployed as a large intelligent surface (LIS). We derive Fisher-informations and Cram\'{e}r-Rao lower bounds (CRLB) in closed-form for terminals along the central perpendicular line (CPL) of the LIS for all three Cartesian dimensions. For terminals at positions other than the CPL, closed-form expressions for the Fisher-informations and CRLBs seem out of reach, and we alternatively provide approximations (in closed-form) which are shown to be very accurate. We also show that under mild conditions, the CRLBs in general decrease quadratically in the surface-area for both the $x$ and $y$ dimensions. For the $z$-dimension (distance from the LIS), the CRLB decreases linearly in the surface-area when terminals are along the CPL. However, when terminals move away from the CPL, the CRLB is dramatically increased and then also decreases quadratically in the surface-area. We also extensively discuss the impact of different deployments (centralized and distributed) of the LIS.