Asynchronous Time-of-Arrival-Based 5G Localization: Methods and Optimal Geometry Analysis

This article is dedicated to addressing the localization challenge in 5G environments, specifically utilizing time-of-arrival (TOA) measurements. The focus is on scenarios where the user equipment (UE) and base transceiver stations (BTSs) or first-generation NodeBs (gNBs) face challenges related to synchronization or inaccurate BTS or gNB positions. First, we present the range-weighted majorization minimization (RW-MM) algorithm, harnessing majorization minimization (MM) techniques for UE localization. We rigorously establish the algorithm’s monotonicity and demonstrate its convergence to a stationary point, providing a theoretical foundation for the RW-MM method. In addition, we present a novel UE localization method called robust range-weighted semidefinite relaxation (RRW-SDR). This method is specifically designed for situations involving bounded gNB position errors. The RRW-SDR algorithm optimizes the worst-case weighted least square function while uniquely addressing the individual error constraints associated with each gNB. Furthermore, we derive the Cramér-Rao lower bound (CRLB) for TOA-based UE localization. We additionally establish a more stringent lower bound on the determinant of the target estimation error covariance. This is particularly significant when dealing with scenarios that include independent measurement noise with varying variances. Moreover, we identify an optimal user-gNB geometrical configuration capable of achieving this lower bound. To validate the effectiveness and practical applicability of our contributions, we conduct a series of meticulous numerical simulations. These experiments affirm the robustness and utility of the developed methods.