Millimeter-Wave Position Sensing Using Reconfigurable Intelligent Surfaces: Positioning Error Bound and Phase Shift Configuration

Millimeter-wave (mmWave) positioning has emerged as a promising technology for next-generation intelligent systems. The advent of reconfigurable intelligent surfaces (RISs) has revolutionized high-precision mmWave localization by enabling dynamic manipulation of wireless propagation environments. This paper investigates a three-dimensional (3D) multi-input single-output (MISO) mmWave positioning system assisted by multiple RISs. We introduce a measurement framework incorporating sequential RIS activation and directional beamforming to fully exploit virtual line-of-sight (VLoS) paths. The theoretical performance limits are rigorously analyzed through derivation of the Fisher information and subsequent positioning error bound (PEB). To minimize the PEB, two distinct optimization approaches are proposed for continuous and discrete phase shift configurations of RISs. For continuous phase shifts, a Riemannian manifold-based optimization algorithm is proposed. For discrete phase shifts, a heuristic algorithm incorporating the grey wolf optimizer is proposed. Extensive numerical simulations demonstrate the effectiveness of the proposed algorithms in reducing the PEB and validate the improvement in positioning accuracy achieved by multiple RISs.