Compressed-Sensing-Based 3D Localization with Distributed Passive Reconfigurable Intelligent Surfaces

In this paper, the programmable signal propagation paradigm, enabled by Reconfigurable Intelligent Surfaces (RISs), is exploited for high accuracy $3$-Dimensional (3D) user localization with a single multi-antenna base station. Capitalizing on the tunable reflection capability of passive RISs, we present a two-stage user localization method leveraging the multi-reflection wireless environment. In the first stage, we deploy an off-grid Compressive Sensing (CS) approach, which is based on the atomic norm minimization, for estimating the angles of arrival associated with each RIS, which is followed, in the second stage, by a maximum likelihood location estimation initialized with a least-squares line intersection technique. The presented numerical results showcase the high accuracy of the proposed 3D localization method, verifying our theoretical Cram\'er Rao lower bound analysis.