Modular XL-Array-Enabled 3-D Localization based on Hybrid Spherical-Planar Wave Model in Terahertz Systems

Abstract: This work considers the three-dimensional (3-D) positioning problem in a Terahertz (THz) system enabled by a modular extra-large (XL) array with sub-connected architecture. Our purpose is to estimate the Cartesian Coordinates of multiple user equipments (UEs) with the received signal of the RF chains while considering the spatial non-stationarity (SNS). We apply the hybrid spherical-planar wave model (HSPWM) as the channel model owing to the structual feature of the modular array, and propose a 3-D localization algorithm with relatively high accuracy and low complexity. Specifically, we first distinguish the visible sub-arrays (SAs) located in the VR and estimate the angles-of-arrival (AoAs) from each UE to typical visible SAs with the largest receive power via compressed sensing (CS) method. In addition, we apply the weighted least square (WLS) method to obtain a coarse 3-D position estimation of each UE according to the AoA estimations. Then, we estimate the AoAs of the other SAs with a reduced dictionary (RD)-CS-based method for lower computational complexity, and utilize all the efficient AoA estimations to derive a fine position estimation. Simulation results indicate that the proposed positioning framework based on modular XL-array can achieve satisfactory accuracy with evident reduction in complexity. Furthermore, the deployment of SAs and the allocation of antenna elements need to be specially designed for better positioning performance.