Misspecified Cram\'er-Rao Bound of RIS-aided Localization under Geometry Mismatch

TL;DR

This paper derives a closed-form misspecified Cramér-Rao bound for RIS-aided localization systems considering geometry mismatch, revealing performance saturation at high SNR due to calibration errors.

Contribution

It introduces a novel closed-form solution for the pseudo-true parameters in MCRB analysis under RIS geometry mismatch, advancing understanding of practical localization limits.

Findings

RIS geometry mismatch causes performance saturation at high SNR

The derived pseudo-true parameters are validated by simulations

The MCRB provides a theoretical performance bound under mismatch conditions

Abstract

In 5G/6G wireless systems, reconfigurable intelligent surfaces (RIS) can play a role as a passive anchor to enable and enhance localization in various scenarios. However, most existing RIS-aided localization works assume that the geometry of the RIS is perfectly known, which is not realistic in practice due to calibration errors. In this work, we derive the misspecified Cram\'er-Rao bound (MCRB) for a single-input-single-output RIS-aided localization system with RIS geometry mismatch. Specifically, unlike most existing works that use numerical methods, we propose a closed-form solution to the pseudo-true parameter determination problem for MCRB analysis. Simulation results demonstrate the validity of the derived pseudo-true parameters and MCRB, and show that the RIS geometry mismatch causes performance saturation in the high signal-to-noise ratio regions.