Beyond Massive MIMO: The Potential of Positioning With Large Intelligent Surfaces
We consider the potential for positioning with a system where antenna arrays are deployed as a large intelligent surface (LIS), which is a newly proposed concept beyond massive multi-input multi-output (MIMO). In a first step, we derive Fisher-information matrix (FIM) and Cramér–Rao lower bound (CRLB) in closed form for positioning a terminal located perpendicular to the center of the LIS, whose location we refer to as being on the central perpendicular line (CPL) of the LIS. For a terminal that is not on the CPL, closed-form expressions of the CRLB seem out of reach, and we alternatively find approximations that are shown to be accurate. Under mild conditions, we show that the CRLB for all three Cartesian dimensions (<inline-formula><tex-math notation="LaTeX">$x$</tex-math> </inline-formula>, <inline-formula><tex-math notation="LaTeX">$y$</tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$z$</tex-math></inline-formula>) decreases quadratically in the surface area of the LIS. In a second step, we analyze the CRLB for positioning when there is an unknown phase <inline-formula> <tex-math notation="LaTeX">$\varphi$</tex-math></inline-formula> presented in the analog circuits of the LIS. We then show that the CRLBs are dramatically degraded for all three dimensions and decrease in the third order of the surface area. Moreover, with an infinitely large LIS, the CRLB for the <inline-formula><tex-math notation="LaTeX">$z$ </tex-math></inline-formula>-dimension with an unknown <inline-formula><tex-math notation="LaTeX">$\varphi$</tex-math> </inline-formula> is 6 dB higher than the case without phase uncertainty, and the CRLB for estimating <inline-formula> <tex-math notation="LaTeX">$\varphi$</tex-math></inline-formula> converges to a constant that is independent of the wavelength <inline-formula><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula>. At last, we extensively discuss the impact of centralized and distributed deployments of LIS, and show that a distributed deployment of LIS can enlarge the coverage and improve the overall positioning performance.