Asynchronous RIS-assisted Localization: A Comprehensive Analysis of Fundamental Limits

The reconfigurable intelligent surface (RIS) has drawn considerable attention for its ability to enhance the performance of not only the wireless communication but also the indoor localization with low-cost. This paper investigates the performance limits of the RIS-based near-field localization in the asynchronous scenario, and analyzes the impact of each part of the cascaded channel on the localization performance. The Fisher information matrix (FIM) and the position error bound (PEB) are derived. Besides, we also derive the equivalent Fisher information (EFI) for the position-related intermediate parameters. Enabled by the derived EFI, we show that the information for both the distance and the direction of the user can be obtained when the near-field spherical wavefront is considered for the RIS-User equipment (UE) part of the channel, while only the direction of the UE can be inferred in the far-field scenario. For the base station (BS)-RIS part of the channel, we reveal that this part of the channel determines the type of the gain provided by the BS antenna array. We also show that the well-known focusing control scheme for RIS, which maximizes the received SNR, is not always a good choice and may degrade the localization performance in the asynchronous scenario. The simulation results validate the analytic work. The impact of the focusing control scheme on the PEB performances under synchronous and asynchronous conditions is also investigated.