Title: Cramér-Rao Lower Bounds for Positioning with Large Intelligent Surfaces,
Abstract: 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 Cramér-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.