A Simplified Algorithm for Joint Real-Time Synchronization, NLoS Identification, and Multi-Agent Localization

Real-time, high-precision localization in large-scale wireless networks faces two primary challenges: clock offsets caused by network asynchrony and non-line-of-sight (NLoS) conditions. To tackle these challenges, we propose a low-complexity real-time algorithm for joint synchronization and NLoS identification-based localization. For precise synchronization, we resolve clock offsets based on accumulated time-of-arrival measurements from all the past time instances, modeling it as a large-scale linear least squares (LLS) problem. To alleviate the high computational burden of solving this LLS, we introduce the blockwise recursive Moore-Penrose inverse (BRMP) technique, a generalized recursive least squares approach, and derive a simplified formulation of BRMP tailored specifically for the real-time synchronization problem. Furthermore, we formulate joint NLoS identification and localization as a robust least squares regression (RLSR) problem and address it by using an efficient iterative approach. Simulations show that the proposed algorithm achieves sub-nanosecond synchronization accuracy and centimeter-level localization precision, while maintaining low computational overhead.

Localization and Discrete Beamforming with a Large Reconfigurable Intelligent Surface

In millimeter-wave (mmWave) cellular systems, reconfigurable intelligent surfaces (RISs) are foreseeably deployed with a large number of reflecting elements to achieve high beamforming gains. The large-sized RIS will make radio links fall in the near-field localization regime with spatial non-stationarity issues. Moreover, the discrete phase restriction on the RIS reflection coefficient incurs exponential complexity for discrete beamforming. It remains an open problem to find the optimal RIS reflection coefficient design in polynomial time. To address these issues, we propose a scalable partitioned-far-field protocol that considers both the near-filed non-stationarity and discrete beamforming. The protocol approximates near-field signal propagation using a partitioned-far-field representation to inherit the sparsity from the sophisticated far-field and facilitate the near-field localization scheme. To improve the theoretical localization performance, we propose a fast passive beamforming (FPB) algorithm that optimally solves the discrete RIS beamforming problem, reducing the search complexity from exponential order to linear order. Furthermore, by exploiting the partitioned structure of RIS, we introduce a two-stage coarse-to-fine localization algorithm that leverages both the time delay and angle information. Numerical results demonstrate that centimeter-level localization precision is achieved under medium and high signal-to-noise ratios (SNR), revealing that RISs can provide support for low-cost and high-precision localization in future cellular systems.