Reconfigurable Intelligent Surfaces for Localization: Position and Orientation Error Bounds

Abstract

Next-generation cellular networks will witness the creation of smart radio environments (SREs), where walls and objects can be coated with reconfigurable intelligent surfaces (RISs) to strengthen the communication and localization coverage by controlling the reflected multipath. In fact, RISs have been recently introduced not only to overcome communication blockages due to obstacles but also for high-precision localization of mobile users in GPS denied environments, e.g., indoors. Towards this vision, this paper presents the localization performance limits for communication scenarios where a single next generation NodeB base station (gNB), equipped with multiple-antennas, infers the position and the orientation of a user equipment (UE) in a RIS-assisted SRE. We consider a signal model that is valid also for near-field propagation conditions, as the usually adopted far-field assumption does not always hold, especially for large RISs. For the considered scenario, we derive the Cramr-Rao lower bound (CRLB) for assessing the ultimate localization and orientation performance of synchronous and asynchronous signaling schemes. In addition, we propose a closed-form RIS phase profile that well suits joint communication and localization. We perform extensive numerical results to assess the performance of our scheme for various localization scenarios and RIS phase design. Numerical results show that the proposed scheme can achieve remarkable performance, even in asynchronous signaling and that the proposed phase design approaches the numerical optimal phase design that minimizes the CRLB.

A Tutorial on Terahertz-Band Localization for 6G Communication Systems

“…2) Conventional MIMO Model: Assume that in a MIMO system, each antenna is connected to an independent RFC. Although this MIMO structure is impractical when the array size is large, as explained before, it is helpful in deriving the fundamental limits of MIMO localization systems and is thus widely used in localization works [43], [44], [55], [126]- [128].…”

“…U ×1 is the additive white Gaussian noise (AWGN) vector with a complex normal distribution CN (0, σ 2 n ). The transmitted signal can be chosen randomly or obtained using a directional beamforming matrix with positioning reference signals (PRS) as discussed in [43], [44], [55], [128]. We use (29) as the benchmark MIMO signal model for mmWave systems.…”

“…In direct localization, the parameters are estimated directly by optimizing an objective function. The measurement parameter vector is identical to the state parameter vector [128], i.e.,…”

“…The error bound for 3D scenarios is analyzed in [44], where the differences between uplink and downlink are discussed. Recent works have also explored the potential of positioning with RISs, which are also called intelligent reflective surfaces (IRSs) [17], large intelligent surfaces (LISs) [55], where promising results are noted [55], [110], [128], [150]. Near-field propagation conditions with RISs are further analyzed in [128].…”

“…Recent works have also explored the potential of positioning with RISs, which are also called intelligent reflective surfaces (IRSs) [17], large intelligent surfaces (LISs) [55], where promising results are noted [55], [110], [128], [150]. Near-field propagation conditions with RISs are further analyzed in [128]. However, practical RIS optimization methods and RIS-assisted localization algorithms have yet to be developed.…”