LEO-based Carrier-Phase Positioning for 6G: Design Insights and Comparison with GNSS

The integration of non-terrestrial networks (NTN) into 5G new radio (NR) enables a new class of positioning capabilities based on cellular signals transmitted by Low-Earth Orbit (LEO) satellites. In this paper, we investigate joint delay-and-carrier-phase positioning for LEO-based NR-NTN systems and provide a convergence-centric comparison with Global Navigation Satellite Systems (GNSS). We show that the rapid orbital motion of LEO satellites induces strong temporal and geometric diversity across observation epochs, thereby improving the conditioning of multi-epoch carrier-phase models and enabling significantly faster integer-ambiguity convergence. To enable robust carrier-phase tracking under intermittent positioning reference signal (PRS) transmissions, we propose a dual-waveform design that combines wideband PRS for delay estimation with a continuous narrowband carrier for phase tracking. Using a realistic simulation framework incorporating LEO orbit dynamics, we demonstrate that LEO-based joint delay-and-carrier-phase positioning achieves cm-level accuracy with convergence times on the order of a few seconds, whereas GNSS remains limited to meter-level accuracy over comparable short observation windows. These results establish LEO-based cellular positioning as a strong complement and potential alternative to GNSS for high-accuracy positioning, navigation, and timing (PNT) services in future wireless networks.

A New Statistical Approach to Calibration-Free Localization Using Unlabeled Crowdsourced Data

Fingerprinting-based indoor localization methods typically require labor-intensive site surveys to collect signal measurements at known reference locations and frequent recalibration, which limits their scalability. This paper addresses these challenges by presenting a novel approach for indoor localization that utilizes crowdsourced data {\em without location labels}. We leverage the statistical information of crowdsourced data and propose a cumulative distribution function (CDF) based distance estimation method that maps received signal strength (RSS) to distances from access points. This approach overcomes the limitations of conventional distance estimation based on the empirical path loss model by efficiently capturing the impacts of shadow fading and multipath. Compared to fingerprinting, our {\em unsupervised} statistical approach eliminates the need for signal measurements at known reference locations. The estimated distances are then integrated into a three-step framework to determine the target location. The localization performance of our proposed method is evaluated using RSS data generated from ray-tracing simulations. Our results demonstrate significant improvements in localization accuracy compared to methods based on the empirical path loss model. Furthermore, our statistical approach, which relies on unlabeled data, achieves localization accuracy comparable to that of the {\em supervised} approach, the $k$-Nearest Neighbor ($k$NN) algorithm, which requires fingerprints with location labels. For reproducibility and future research, we make the ray-tracing dataset publicly available at [2].

Impact of Frequency on Diffraction-Aided Wireless Positioning

This paper tackles the challenge of accurate positioning in Non-Line-of-Sight (NLoS) environments, with a focus on indoor public safety scenarios where NLoS bias severely impacts localization performance. We explore Diffraction MultiPath Components (MPC) as a critical mechanism for Outdoor-to-Indoor (O2I) signal propagation and its role in positioning. The proposed system comprises outdoor Uncrewed Aerial Vehicle (UAV) transmitters and indoor receivers that require localization. To facilitate diffraction-based positioning, we develop a method to isolate diffraction MPCs at indoor receivers and validate its effectiveness using a ray-tracing-generated dataset, which we have made publicly available. Our evaluation across the FR1, FR2, and FR3 frequency bands within the 5G/6G spectrum confirms the viability of diffraction-based positioning techniques for next-generation wireless networks.

Indoor Positioning for Public Safety: Role of UAVs, LEOs, and Propagation-Aware Techniques

Effective indoor positioning is critical for public safety, enabling first responders to locate at-risk individuals accurately during emergency scenarios. However, traditional Global Navigation Satellite Systems (GNSS) often perform poorly indoors due to poor coverage and non-line-of-sight (NLOS) conditions. Moreover, relying on fixed cellular infrastructure, such as terrestrial networks (TNs), may not be feasible, as indoor signal coverage from a sufficient number of base stations or WiFi access points cannot be guaranteed for accurate positioning. In this paper, we propose a rapidly deployable indoor positioning system (IPS) leveraging mobile anchors, including uncrewed aerial vehicles (UAVs) and Low-Earth-Orbit (LEO) satellites, and discuss the role of GNSS and LEOs in localizing the mobile anchors. Additionally, we discuss the role of sidelink-based positioning, which is introduced in 3rd Generation Partnership Project (3GPP) Release 18, in enabling public safety systems. By examining outdoor-to-indoor (O2I) signal propagation, particularly diffraction-based approaches, we highlight how propagation-aware positioning methods can outperform conventional strategies that disregard propagation mechanism information. The study highlights how emerging 5G Advanced and Non-Terrestrial Networks (NTN) features offer new avenues to improve positioning in challenging indoor environments, ultimately paving the way for cost-effective and resilient IPS solutions tailored to public safety applications.

Deterministic and Statistical Analysis of the DoF of Continuous Linear Arrays in the Near Field

This paper examines the number of communication modes, that is, the degrees of freedom (DoF), in a wireless setup comprising a small continuous linear intelligent antenna array in the near field of a large one. The framework allows for any orientations between the arrays and any positions in a two-dimensional space assuming that the transmitting array is placed at the origin. Therefore, apart from the length of the two continuous arrays, four key parameters determine the DoF and are hence considered in the analysis: the Cartesian coordinates of the center of the receiving array and two angles that model the rotation of each array around its center. The paper starts with the calculation of the deterministic DoF for a generic geometric setting, which extends beyond the widely studied paraxial case. Subsequently, a stochastic geometry framework is proposed to study the statistical DoF, as a first step towards the investigation of the system-level performance in near field networks. Numerical results applied to millimeter wave networks reveal the large number of DoF provided by near-field communications and unveiled key system-level insights.

Age of Positioning with Stochastic Motion Models

Age of Information (AoI) is a key metric used for evaluating data freshness in communication networks, particularly in systems requiring real-time updates. In positioning applications, maintaining low AoI is critical for ensuring timely and accurate position estimation. This paper introduces an age-informed metric, which we term as Age of Positioning (AoP), that captures the temporal evolution of positioning accuracy for agents following random trajectories and sharing sporadic location updates. Using the widely adopted Random Waypoint (RWP) mobility model, which captures stochastic user movement through waypoint-based trajectories, we derive closed-form expressions for this metric under various queuing disciplines and different modes of operation of the agent. The analytical results are verified with numerical simulations, and the existence of optimal operating conditions is demonstrated.

Determinantal Learning for Subset Selection in Wireless Networks

Subset selection is central to many wireless communication problems, including link scheduling, power allocation, and spectrum management. However, these problems are often NP-complete, because of which heuristic algorithms applied to solve these problems struggle with scalability in large-scale settings. To address this, we propose a determinantal point process-based learning (DPPL) framework for efficiently solving general subset selection problems in massive networks. The key idea is to model the optimal subset as a realization of a determinantal point process (DPP), which balances the trade-off between quality (signal strength) and similarity (mutual interference) by enforcing negative correlation in the selection of {\em similar} links (those that create significant mutual interference). However, conventional methods for constructing similarity matrices in DPP impose decomposability and symmetry constraints that often do not hold in practice. To overcome this, we introduce a new method based on the Gershgorin Circle Theorem for constructing valid similarity matrices. The effectiveness of the proposed approach is demonstrated by applying it to two canonical wireless network settings: an ad hoc network in 2D and a cellular network serving drones in 3D. Simulation results show that DPPL selects near-optimal subsets that maximize network sum-rate while significantly reducing computational complexity compared to traditional optimization methods, demonstrating its scalability for large-scale networks.

Two-Stage Weighted Projection for Reliable Low-Complexity Cooperative and Non-Cooperative Localization

In this paper, we propose a two-stage weighted projection method (TS-WPM) for time-difference-of-arrival (TDOA)-based localization, providing provable improvements in positioning accuracy, particularly under high geometric dilution of precision (GDOP) and low signal-to-noise ratio (SNR) conditions. TS-WPM employs a two-stage iterative refinement approach that dynamically updates both range and position estimates, effectively mitigating residual errors while maintaining computational efficiency. Additionally, we extend TS-WPM to support cooperative localization by leveraging two-way time-of-arrival (TW-TOA) measurements, which enhances positioning accuracy in scenarios with limited anchor availability. To analyze TS-WPM, we derive its error covariance matrix and mean squared error (MSE), establishing conditions for its optimality and robustness. To facilitate rigorous evaluation, we develop a 3rd Generation Partnership Project (3GPP)-compliant analytical framework, incorporating 5G New Radio (NR) physical layer aspects as well as large-scale and small-scale fading. As part of this, we derive a generalized Cram{\'e}r-Rao lower bound (CRLB) for multipath propagation and introduce a novel non-line-of-sight (NLOS) bias model that accounts for propagation conditions and SNR variations. Our evaluations demonstrate that TS-WPM achieves near-CRLB performance and consistently outperforms state-of-the-art weighted nonlinear least squares (WNLS) in high GDOP and low SNR scenarios. Moreover, cooperative localization with TS-WPM significantly enhances accuracy, especially when an insufficient number of anchors (such as 2) are visible. Finally, we analyze the computational complexity of TS-WPM, showing its balanced trade-off between accuracy and efficiency, making it a scalable solution for real-time localization in next-generation networks.

Geolocation with Large LEO Constellations: Insights from Fisher Information

Interest in the use of the low earth orbit (LEO) in space - from $160 \text{ km}$ to $2000 \text{ km}$ - has skyrocketed; this is evident by the fact that National Aeronautics and Space Administration (NASA) has partnered with various commercial platforms like Axiom Space, Blue Origin, SpaceX, Sierra Space, Starlab Space, ThinkOrbital, and Vast Space to deploy satellites. %and platforms like Northrop Grumman and Boeing to transport cargo and crew. The most apparent advantage of satellites in LEO over satellites in Geostationary (GEO) and medium earth orbit (MEO) is their closeness to the earth; hence, signals from LEOs encounter lower propagation losses and reduced propagation delay, opening up the possibility of using these LEO satellites for localization. This article reviews the existing signal processing algorithms for localization using LEO satellites, introduces the basics of estimation theory, connects estimation theory to model identifiability with Fisher Information Matrix (FIM), and with the FIM, provides conditions that allow for $9$D localization of a terrestrial receiver using signals from multiple LEOs (unsynchronized in time and frequency) across multiple time slots and multiple receive antennas. We also compare the structure of the information available in LEO satellites with the structure of the information available in the Global Positioning System (GPS).

Impact of Model Mismatch on DOA Estimation with MUSIC: Near-Field and Far-Field

There has been substantial work on developing variants of the multiple signal classification (MUSIC) algorithms that take advantage of the information present in the near-field propagation regime. However, it is not always easy to determine the correct propagation regime, which opens the possibility of incorrectly applying simpler algorithms (meant for far-field) in the near-field regime. Inspired by this, we use simulation results to investigate the performance drop when there is a mismatch between the signal model in the MUSIC algorithm and the propagation regime. For direction of arrival (DOA) estimation, we consider the cases when the receiver is in the near-field region but uses i) the near-field model, ii) the approximate near-field model (ANM) model, and iii) the far-field model to design the beamforming matrix in the MUSIC algorithm. We also consider the case when the receiver is in the far-field region, and we use the correct far-field model to design the beamforming matrix in the MUSIC algorithm. One contribution is that in the near-field, we have quantified the loss in performance when the ANM and the far-field model are used to create the beamforming matrix for the MUSIC algorithm, causing a reduction in estimation accuracy compared to the case when the correct near-field model is used to design the beamforming matrix. Another result is that in the near-field, when we incorrectly assume that the receiver is in the far-field and subsequently use the far-field beamforming matrix, we underestimate the DOA estimation error. Finally, we show that the MUSIC algorithm can provide very accurate range estimates for distances less than the Fraunhofer distance. This estimate gradually becomes inaccurate as the distances exceed the Fraunhofer distance.