Cramér-Rao Lower Bounds for Positioning with Large Intelligent Surfaces using Quantized Amplitude and Phase

We envision the use of large intelligent surface (LIS) technology, which is a promising concept that goes beyond massive multiple-input multiple-output (MIMO), for positioning applications due to its ability to focus energy in the 3D space. The Cramér-Rao lower bounds (CBLBs) for positioning using a LIS which can resolve amplitude and phase with full resolution have already been determined in the previous literature. However, in real applications, and specially if we consider cheap hardware components to enable the deployment of LIS at reasonable costs, the phase and amplitude have to be quantized before any information can be extracted from them. Furthermore, the phase information is more difficult to resolve due to phase noise, non-coherence, etc. In this paper we compute the CRLBs for positioning using LIS with quantized phase and amplitude. We also derive analytical bounds for the CRLB for positioning with LIS when all phase information is disregarded and amplitude is measured with full resolution. We present numerical results in the form of tables including the CRLB loss due to the different quantization resolutions, which can serve as a design guideline for hardware developers.