An Efficient Modified MUSIC Algorithm for RIS-Assisted Near-Field Localization

In this paper, we consider a single-anchor localization system assisted by a reconfigurable intelligent surface (RIS), where the objective is to localize multiple user equipments (UEs) placed in the radiative near-field region of the RIS by estimating their azimuth angle-of-arrival (AoA), elevation AoA, and distance to the surface. The three-dimensional (3D) locations can be accurately estimated via the conventional MUltiple SIgnal Classification (MUSIC) algorithm, albeit at the expense of tremendous complexity due to the 3D grid search. In this paper, capitalizing on the symmetric structure of the RIS, we propose a novel modified MUSIC algorithm that can efficiently decouple the AoA and distance estimation problems and drastically reduce the complexity compared to the standard 3D MUSIC algorithm. Additionally, we introduce a spatial smoothing method by partitioning the RIS into overlapping sub-RISs to address the rank-deficiency issue in the signal covariance matrix. We corroborate the effectiveness of the proposed algorithm via numerical simulations and show that it can achieve the same performance as 3D MUSIC but with much lower complexity.