Near-Field Localization for Holographic RIS Assisted mmWave Systems

In this letter, we envision the integration of holographic reconfigurable intelligent surface (HRIS) into a millimeter-wave (mmWave) localization system. The large aperture of HRIS in the mmWave band allows the system to operate in the near-field propagation regime, where the wavefront tends to be spherical and contains distance information. To investigate the fundamental limits of localization accuracy of the proposed system, we obtain the Fisher information matrix (FIM) and Cramér-Rao lower bound (CRLB) taking into account the radiation patterns of antennas. The analytical results reveal that the FIM quadratically increases with the size of HRIS. Then, to explore the potential of HRIS passive beamforming for improving localization quality, we formulate the HRIS phases optimization problem to minimize a worst-case CRLB with respect to an uncertainty set of user equipment (UE) positions. To address this formulated problem, an iterative entropy regularization (IER) based method is proposed. Numerical results evaluate the effect of key parameters on the squared position error bound and verify the effectiveness of the proposed IER-based method.