Reconfigurable Intelligent Surfaces for Localization: Position and Orientation Error Bounds

Next-generation cellular networks could witness the creation of smart radio environments (SREs), where walls and objects will be coated with reconfigurable intelligent surfaces (RISs) to strengthen the communication and localization performance. 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 such a 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 reconfigurable intelligent surface (RIS)-assisted smart radio environment (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 Cramér-Rao lower bound (CRLB) for assessing the ultimate localization and orientation performance of synchronous and asynchronous signalling schemes. In addition, we propose a closed-form RIS phase profile that well suits joint communication and localization, and we perform extensive numerical results to assess the performance of our scheme for various localization scenarios and for various RIS phase design. Numerical results show that the proposed scheme can achieve remarkable performance even in asynchronous signalling, and that the proposed phase design, based on signal-to-noise ratio (SNR), approaches the numerical optimal phase design that minimizes the CRLB.