The widespread adoption of 5G wireless communication devices has significantly increased the demand for precise 5G-based positioning services. This study presents a beam-switching time-of-arrival (TOA) ranging technique that leverages commercial 5G new radio (NR) signals and channel state information (CSI) extracted from the physical broadcast channel (PBCH). Initially, theoretical conditions for consistent multi-beam TOA estimation are derived, along with a multi-beam demodulation method designed to meet these conditions. To overcome the challenge of unknown base station (BS) radiation patterns, a signal quality-based beam-switching strategy is developed. Furthermore, a TOA tracking framework is introduced, integrating orthogonal matching pursuit (OMP) for multipath resolution, second-order frequency-locked loop (FLL)-assisted third-order delay-locked loop (DLL) for robust TOA tracking, and total variation regularization for anomaly removal. A software-defined radio (SDR) 5G receiver tailored for commercial beamforming BSs is implemented to validate the proposed system. With clock effects removed, the proposed system yields root-mean-square ranging errors of 3.73m and 4.99m in two distinct complex scenarios, corresponding to an average improvement of 69% in ranging accuracy over single-beam methods.

The proliferation of 5G wireless devices creates a pressing need for high-precision positioning services. This paper presents an integrated acquisition–and–tracking framework that leverages physical broadcast channel (PBCH) transmissions from commercial 5G New Radio (NR) base stations (BSs). To select the strongest downlink beam without prior knowledge of the BS radiation pattern, we use an adaptive beam-switching strategy based on reference signal received power (RSRP), reference signal received quality (RSRQ), and signal-to-noise ratio (SNR). For coarse acquisition, direction-of-arrival (DOA) and time-of-arrival (TOA) estimates are produced by a two-stage procedure that combines three-dimensional sparse Bayesian learning (SBL) with gradient-ascent off-grid refinement. A closed-loop tracker then continuously refines these estimates through azimuth-locked loop (ALL), elevation-locked loop (ELL), and delay-locked loop (DLL) modules. We further derive information-theoretic limits that bound acquisition and tracking and elucidate the key factors shaping these limits. The complete framework is implemented on a software-defined radio (SDR) 5G receiver and validated in outdoor field trials. Results indicate robust performance, with an average TOA root-mean-square error (RMSE) of 3.58 m, an azimuth RMSE of 5.77°, and an elevation RMSE of 2.74°, while requiring only 2.64 switching events per minute.

The proliferation of 5G Internet of Things (IoT) devices in daily life has significantly increased the demand for 5G-based positioning services. This article presents a methodology for accurate time-of-arrival (TOA) estimation of commercial 5G new radio (NR) signals, specifically addressing the severe interference commonly encountered in challenging environments. To mitigate high noise levels, we first apply a raised cosine filter for initial denoising of channel state information (CSI), followed by frequency-domain averaging and normalization to further suppress residual noise. For precise TOA estimation, we develop an algorithm that leverages a delay lock loop (DLL) for robust signal tracking, enhanced by initialization and relocking mechanisms supported by space-alternating generalized expectation-maximization (SAGE). Additionally, we adapt several classic global positioning system (GPS) delay discriminators for compatibility with 5G NR signals, aiming to identify DLLs that perform effectively under adverse conditions. Comprehensive validation through simulations and field tests demonstrates the proposed system’s robustness and practical applicability. Furthermore, we identify delay discriminators that are particularly well-suited for deployment in challenging environments.

Tracking is promising in various applications, such as elderly care and security monitoring. Prior works require multiple access points (AP) deployed in the tracking region or to utilize elaborately selected multipaths in an indoor environment to achieve tracking. However, this prevents their wide adoption because scenarios like homes typically only have a single AP, and using multipaths is vulnerable to unexpected interferences due to the complex indoor environment. This paper proposes a tracking system using only a single AP. The insight behind the proposed system is to mine the multi-dimensional channel parameters from the direct path to realize tracking. Therefore, we develop a model that establishes the correlation between the target motion and channel parameters, including the direct path's angle of arrival (AoA) and angle of departure (AoD). Then, we can formulate the tracking problem as the state transition with the observations. Since the nonlinear observation equation, we use particle filters to solve the problem accurately. Finally, we validate the proposed system via simulation using ray-tracing software. The simulation results show that the median tracking error is 0.21 m based on a 20 dB signal-to-noise ratio (SNR), comparable to previous state-of-the-art systems.

Abstract symbolic reasoning, as required in domains such as mathematics and logic, is a key component of human intelligence. Solvers for these domains have important applications, especially to computer-assisted education. But learning to solve symbolic problems is challenging for machine learning algorithms. Existing models either learn from human solutions or use hand-engineered features, making them expensive to apply in new domains. In this paper, we instead consider symbolic domains as simple environments where states and actions are given as unstructured text, and binary rewards indicate whether a problem is solved. This flexible setup makes it easy to specify new domains, but search and planning become challenging. We introduce five environments inspired by the Mathematics Common Core Curriculum, and observe that existing Reinforcement Learning baselines perform poorly. We then present a novel learning algorithm, Contrastive Policy Learning (ConPoLe) that explicitly optimizes the InfoNCE loss, which lower bounds the mutual information between the current state and next states that continue on a path to the solution. ConPoLe successfully solves all four domains. Moreover, problem representations learned by ConPoLe enable accurate prediction of the categories of problems in a real mathematics curriculum. Our results suggest new directions for reinforcement learning in symbolic domains, as well as applications to mathematics education.