We consider the potential for positioning with a system where antenna arrays are deployed as a large intelligent surface (LIS). We derive Fisher-informations and Cram\'{e}r-Rao lower bounds (CRLB) in closed-form for terminals along the central perpendicular line (CPL) of the LIS for all three Cartesian dimensions. For terminals at positions other than the CPL, closed-form expressions for the Fisher-informations and CRLBs seem out of reach, and we alternatively provide approximations (in closed-form) which are shown to be very accurate. We also show that under mild conditions, the CRLBs in general decrease quadratically in the surface-area for both the x and y dimensions. For the z-dimension (distance from the LIS), the CRLB decreases linearly in the surface-area when terminals are along the CPL. However, when terminals move away from the CPL, the CRLB is dramatically increased and then also decreases quadratically in the surface-area. We also extensively discuss the impact of different deployments (centralized and distributed) of the LIS.
@article{arxiv.1702.03131,
title = {Cram\'er-Rao Lower Bounds for Positioning with Large Intelligent Surfaces},
author = {Sha Hu and Fredrik Rusek and Ove Edfors},
journal= {arXiv preprint arXiv:1702.03131},
year = {2017}
}