Single-Snapshot Localization for Near-Field RIS Model Using Atomic Norm Minimization

Reconfigurable intelligent surfaces (RISs) are expected to play a significant role in the next generation of wireless cellular technology. This paper proposes an uplink localization scheme using a single-snapshot solution for user equipment (UE) that is located in the near-field of the RIS. We propose utilizing the atomic norm minimization method to achieve super-resolution localization accuracy. We formulate an optimization problem to estimate the UE location parameters (i.e., angles and distances) by minimizing the atomic norm. Then, we propose to exploit strong duality to solve the atomic norm problem using the dual problem and semidefinite programming (SDP). The RIS is controlled and designed using estimated parameters to enhance the beamforming capabilities. Finally, we compare the localization performance of the proposed atomic norm minimization with compressed sensing (CS) in terms of the localization error. The numerical results show a superior performance of the proposed atomic norm method over the CS where a sub-cm level of accuracy can be achieved under some of the system configuration conditions using the proposed atomic norm method.