RIS-aided Near-Field Localization under Phase-Dependent Amplitude Variations

Abstract

We investigate the problem of reconfigurable intelligent surface (RIS)-aided near-field localization of a user equipment (UE) served by a base station (BS) under phasedependent amplitude variations at each RIS element. Through a misspecified Cramér-Rao bound (MCRB) analysis and a resulting lower bound (LB) on localization, we show that when the UE is unaware of amplitude variations (i.e., assumes unit-amplitude responses), severe performance penalties can arise, especially at high signal-to-noise ratios (SNRs). Leveraging Jacobi-Anger expansion to decouple range-azimuth-elevation dimensions, we develop a low-complexity approximated mismatched maximum likelihood (AMML) estimator, which is asymptotically tight to the LB. To mitigate performance loss due to model mismatch, we propose to jointly estimate the UE location and the RIS amplitude model parameters. The corresponding Cramér-Rao bound (CRB) is derived, as well as an iterative refinement algorithm, which employs the AMML method as a subroutine and alternatingly updates individual parameters of the RIS amplitude model. Simulation results indicate fast convergence and performance close to the CRB. The proposed method can successfully recover the performance loss of the AMML under a wide range of RIS parameters and effectively calibrate the RIS amplitude model online with the help of a user that has an a-priori unknown location.

MCRB-based Performance Analysis of 6G Localization under Hardware Impairments

“…Hence, η 0 can be found by solving (36) with the observation y = μ(η), which can be accomplished using the same algorithm in Sec. III, initialized with the true value η.…”

“…The matrices A η 0 and B η 0 can be obtained based on the pseudo-true parameter vector η 0 as [36] [A η 0 ] i,j = ˆ∂2 lnf MM (y|η)…”

“…Specifically, we consider an OFDM-based system by rigorously modeling the impact of various HWIs on the received observations, and assume that the corresponding channel estimation and localization algorithms have no knowledge about these HWIs, resulting in degradation of lo-calization and communication performance. The misspecified Cramér-Rao bound (MCRB) [34]- [36] is employed to quantify the estimation performance loss due to model mismatch. In addition, the effect of HWI on communication is evaluated numerically in terms of symbol error rate (SER) based on the developed model for a hardware-impaired channel under the same HWI levels, which allows a fair comparison of the impact of HWI on communication and localization.…”