Fundamental Limits of RIS-Aided Near-Field Localization: EFI Analysis and Phase Optimization

Reconfigurable intelligent surface (RIS) has been widely explored to improve channel performance and positioning accuracy. This paper investigates the performance limits of near-field positioning assisted by a RIS. Specifically, we derive the equivalent Fisher information (EFI) of the intermediate parameters. And the position error bound (PEB) is derived for positioning performance analysis. In addition, we design the RIS phase shifts by minimizing the scalar metric of the Cramér-Rao lower bound (CRLB) matrix for the intermediate parameters. The proposed optimization problem under discrete phase shifts constraints is efficiently solved via the block coordinate descent (BCD). Our simulation results indicate that both the angle and distance information can be obtained when considering the nearfield scenario, while the distance information can not be obtained in the far-field model. And the proposed optimization scheme of RIS phase shifts can significantly enhance the positioning performance.