Cramér-Rao Lower Bound Analysis of Multiple-RIS-Aided mmWave Positioning Systems

This paper investigates the lower bounds on the location estimation error for multiple reconfigurable intelligent surfaces (RISs)-aided millimeter-wave (mmWave) positioning systems. The error lower bound is quantified by Cramer-Rao lower bounds (CRLB), of which two are decisive, namely, the position error bound (PEB), and the rotation error bound (REB). This paper begins by deriving the analytical expressions of the PEB and REB as functions of the RIS phase shifts. Then, the lowest achievable PEB and REB are obtained by optimizing the phase shifts of all RISs using the particle swarm optimization (PSO) algorithm. Numerical results have shown that a three-RIS-aided system generates 38.6% lower PEB and REB with the most basic beam-alignment phase shifts strategy compared to the single-RIS system. With the RIS phase shifts optimized by the PSO algorithm, the PEB and REB can be further reduced by another 41.2%.