pith. sign in

arxiv: 2511.05954 · v2 · submitted 2025-11-08 · 📡 eess.SP

Near-field Anchor-free Localization using Reconfigurable Intelligent Surfaces

Srikar Sharma Sadhu , Praful D. Mankar , Santosh Nannuru This is my paper

Pith reviewed 2026-05-18 00:04 UTC · model grok-4.3

classification 📡 eess.SP
keywords near-field localizationreconfigurable intelligent surfacesanchor-free localizationFisher information matrixRIS configuration optimizationposition estimation6G networks
0
0 comments X

The pith

Passive reconfigurable intelligent surfaces serve as synced reference nodes for accurate anchor-free near-field localization when their configurations maximize the averaged Fisher information trace.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how passive RIS units can replace active anchor nodes in near-field positioning by treating them as known, perfectly synchronized references. Optimal phase settings are chosen to maximize the block-wise averaged trace of the Fisher information matrix over the area of interest, which directly reduces the minimum possible localization variance. A two-stage estimator first matches the received signal against a coarse grid under these optimal configurations using cosine similarity, then refines the position on a finer local grid. The approach targets lower network overhead and energy use than traditional cooperative-anchor methods. Sympathetic readers would see value in supporting efficient positioning for dense 6G deployments without extra infrastructure.

Core claim

Optimal RIS configurations are derived that maximize the block-wise averaged trace of the Fisher information matrix so localization error variance is minimized across the area of interest. A two-stage anchor-free framework obtains a coarse position estimate from cosine similarity between the received signal and a pre-defined grid under those configurations, then refines the estimate on a finer grid centered at the coarse result. Numerical evaluation shows that this yields small root mean square error for practical values of SNR, RIS dimension, and number of user antennas.

What carries the argument

RIS phase configurations chosen to maximize the block-wise averaged trace of the Fisher information matrix, which serves as the design criterion for minimizing position error variance.

If this is right

  • Localization error variance is minimized uniformly across the area of interest.
  • Small root mean square error is obtained for practical SNR, RIS sizes, and user antenna counts.
  • The method eliminates the need for active cooperative anchor nodes and their associated overhead.
  • The two-stage coarse-to-fine grid search produces reliable position estimates from received signals alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same optimization criterion could be reused to design RIS patterns for joint communication and sensing tasks.
  • Hardware impairments such as phase quantization errors would need separate modeling to check robustness of the derived configurations.
  • Extending the framework to multiple users would require checking whether the block-averaged trace still yields good per-user accuracy.

Load-bearing premise

Passive RISs can be leveraged as perfectly synced reference nodes whose positions are known and whose configurations can be set to maximize the block-wise averaged trace of the Fisher information matrix.

What would settle it

Measurements in which root mean square localization error stays large at practical SNR values even after switching from random to the derived optimal RIS configurations would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2511.05954 by Praful D. Mankar, Santosh Nannuru, Srikar Sharma Sadhu.

Figure 1
Figure 1. Figure 1: RIS-assisted anchor-free localization system. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: NMSE of UE location (r, θ) for K = 8. The solid, dashed and dot￾dashed lines correspond to N = 64, N = 121 and N = 256 respectively. IV. NUMERICAL RESULTS AND DISCUSSION This section presents the numerical analysis of the NMSE performance of Algorithm 1. For the numerical results, we considered the parameters as number of RIS elements N with Ny = Nz = √ N ∈ {8, 10, 11, 12}, operational wavelength λ = 0.1 m… view at source ↗
Figure 3
Figure 3. Figure 3: NMSEs of r and θ for PT /σ2 = 10dB. grid points in the near-field with a resolution of ϵ = 0.55m along x and y axes. We perform the Monte Carlo simulation with 10,000 iterations to evaluate the NMSE performance of the proposed algorithm. In each iteration, we sample the UE location (r, θ) uniformly at random in the near-field region [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Impact of grid resolution ϵ on NMSE performance and number of iterations for PT /σ2 = 10dB. The solid, dashed and dot-dashed lines correspond to N = 100, N = 121 and N = 144 respectively. [2] Y. Zhao and et al., “6G near-field technologies white paper 2.0,” 2025. [Online]. Available: https://eprints.gla.ac.uk/354426/ [3] A. Bourdoux and et. al., “6G white paper on localization and sensing,” 2020. [Online].… view at source ↗
read the original abstract

Near-field localization is expected to play a crucial role in enabling a plethora of applications under the paradigm of 6G networks. The conventional localization methods rely on complex infrastructure for providing cooperative anchor nodes that often contribute to higher network overload and energy consumption. To address this, the passive reconfigurable intelligent surfaces (RISs) can be leveraged as perfectly synced reference nodes for developing anchor-free near-field localization. First, we obtain the optimal RIS configurations that maximizes the block-wise averaged trace of Fisher information matrix so that localization error variance can be minimized across the area-of-interest (AoI). Next, we present a two-stage anchor-free localization framework wherein first a coarse estimate is obtained using cosine similarity between the coarse grid and the signal received under pre-defined optimal RIS configurations. In second stage, we refine solution similarly using a finer grid constructed around the coarse estimate. The numerical results show that the proposed RIS-aided anchor-free localization provides small root mean square error for practical values of signal-to-noise ratio (SNR), RIS dimension, and number of antennas at user.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an anchor-free near-field localization scheme that treats passive RISs as synchronized reference nodes with known positions. Optimal RIS phase profiles are selected by maximizing the block-wise averaged trace of the Fisher information matrix over the area of interest. A two-stage estimator then obtains a coarse position via cosine-similarity matching against a pre-defined grid under these profiles, followed by refinement on a finer grid centered at the coarse estimate. Numerical results are reported to show small RMSE for practical SNR, RIS dimensions, and user-antenna counts.

Significance. If the central claims hold, the work offers a low-infrastructure alternative to conventional anchor-based localization by repurposing passive RISs expected in 6G deployments. The FIM-trace optimization supplies a principled configuration rule, and the two-stage grid search is computationally attractive. The emphasis on near-field spherical-wave models and the avoidance of dedicated anchors are timely contributions to integrated sensing and communication.

major comments (2)
  1. [§3] §3 (RIS configuration optimization): Maximizing the block-wise averaged trace of the FIM is load-bearing for the claim that localization error variance is minimized uniformly across the AoI. Because near-field channels vary rapidly with user position, the average can be dominated by favorable blocks while leaving others with low information content. The manuscript must demonstrate that this averaging does not produce high-error pockets; a spatial map of local RMSE or a worst-case error metric over the AoI is required to support the headline claim of small RMSE for practical parameters.
  2. [§5] §5 (Numerical results): The reported RMSE values are presented without Monte-Carlo trial counts, error bars, or explicit comparison against random RIS configurations or conventional near-field estimators. Without these controls it is impossible to judge whether the observed RMSE is attributable to the proposed optimization or to favorable simulation conditions.
minor comments (2)
  1. [§2] The partitioning of the AoI into blocks and the precise definition of the block-wise averaging operator should be stated with an equation reference in the optimization section for reproducibility.
  2. Figure captions should explicitly list the RIS size, number of user antennas, and SNR range used in each plot.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments highlight important aspects for strengthening the uniformity claim and the statistical rigor of the results. We address each major comment below and commit to revisions that directly respond to the concerns without altering the core contributions.

read point-by-point responses

  1. Referee: [§3] §3 (RIS configuration optimization): Maximizing the block-wise averaged trace of the FIM is load-bearing for the claim that localization error variance is minimized uniformly across the AoI. Because near-field channels vary rapidly with user position, the average can be dominated by favorable blocks while leaving others with low information content. The manuscript must demonstrate that this averaging does not produce high-error pockets; a spatial map of local RMSE or a worst-case error metric over the AoI is required to support the headline claim of small RMSE for practical parameters.

    Authors: We agree that rapid spatial variation in near-field channels means block-wise averaging alone does not automatically guarantee uniform performance, and the manuscript as written does not include a spatial RMSE map or worst-case metric. In the revised version we will add a spatial heatmap of local RMSE across the AoI under the optimized configurations together with the maximum RMSE value observed in the area. These additions will directly verify the absence of high-error pockets and support the claim of small RMSE for practical parameters. revision: yes

  2. Referee: [§5] §5 (Numerical results): The reported RMSE values are presented without Monte-Carlo trial counts, error bars, or explicit comparison against random RIS configurations or conventional near-field estimators. Without these controls it is impossible to judge whether the observed RMSE is attributable to the proposed optimization or to favorable simulation conditions.

    Authors: The current numerical section indeed omits explicit Monte-Carlo counts, error bars, and baseline comparisons. We will revise the results section to state the number of Monte-Carlo trials performed, include error bars on all RMSE curves, and add direct comparisons against both random RIS phase profiles and a conventional near-field estimator (e.g., a grid-search method without RIS optimization). These controls will allow readers to attribute performance gains to the proposed FIM-trace optimization. revision: yes

Circularity Check

0 steps flagged

No circularity; optimization and validation are independent steps

full rationale

The paper derives optimal RIS configurations by maximizing the block-wise averaged trace of the Fisher information matrix over the AoI as a design criterion to reduce localization error variance bounds. It then applies a separate two-stage cosine-similarity estimator on those configurations and reports numerical RMSE results for practical SNR, RIS size, and antenna counts. This is a standard proxy-optimization followed by empirical performance evaluation with no reduction of the final RMSE claim to the optimization inputs by construction, no self-citation load-bearing for the core result, and no fitted parameters renamed as predictions. The derivation chain remains self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; full derivations, parameter choices, and assumptions are not visible.

axioms (2)
  • domain assumption RIS elements can be configured to maximize block-wise averaged trace of Fisher information matrix for localization
    Stated as the first step in the abstract
  • domain assumption RIS positions are known and perfectly synchronized
    Described as 'perfectly synced reference nodes'

pith-pipeline@v0.9.0 · 5486 in / 1218 out tokens · 40827 ms · 2026-05-18T00:04:23.233356+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages

  1. [1]

    Leveraging RIS-enabled smart signal prop- agation for solving infeasible localization problems: Scenarios, key research directions, and open challenges,

    K. Keykhosravi and et.al., “Leveraging RIS-enabled smart signal prop- agation for solving infeasible localization problems: Scenarios, key research directions, and open challenges,”IEEE Vehicular Technology Magazine, vol. 18, no. 2, pp. 20–28, 2023. 0.15 0.35 0.5 0.75 1.25 2·10 −6 6·10 −6 ϵ(m) NMSE K= 12 K= 16 (a) NMSE performance of UE locationu. 0.15 0....

    work page 2023

  2. [2]

    6G near-field technologies white paper 2.0,

    Y . Zhao and et al., “6G near-field technologies white paper 2.0,” 2025. [Online]. Available: https://eprints.gla.ac.uk/354426/

    work page 2025

  3. [3]

    6G white paper on localization and sensing,

    A. Bourdoux and et. al., “6G white paper on localization and sensing,”

    work page

  4. [4]

    Available: https://arxiv.org/abs/2006.01779

    [Online]. Available: https://arxiv.org/abs/2006.01779

    work page arXiv 2006

  5. [5]

    Near-field 5D pose estimation using reconfigurable intelligent surfaces,

    S. S. Sadhu, P. D. Mankar, and S. Nannuru, “Near-field 5D pose estimation using reconfigurable intelligent surfaces,” inIEEE Global Communications Conference (GLOBECOM), 2025. [Online]. Available: https://arxiv.org/abs/2505.01829

    work page arXiv 2025

  6. [6]

    Reconfigurable intelligent surfaces: Potentials, appli- cations, and challenges for 6G wireless networks,

    S. Basharat, S. A. Hassan, H. Pervaiz, A. Mahmood, Z. Ding, and M. Gidlund, “Reconfigurable intelligent surfaces: Potentials, appli- cations, and challenges for 6G wireless networks,”IEEE Wireless Communications, vol. 28, no. 6, pp. 184–191, 2021

    work page 2021

  7. [7]

    Survey of cellular mobile radio localization methods: From 1G to 5G,

    J. A. del Peral-Rosado, R. Raulefs, J. A. L ´opez-Salcedo, and G. Seco- Granados, “Survey of cellular mobile radio localization methods: From 1G to 5G,”IEEE Communications Surveys & Tutorials, vol. 20, no. 2, pp. 1124–1148, 2018

    work page 2018

  8. [8]

    A survey of localization in wireless sensor network,

    L. Cheng, C. Wu, Y . Zhang, H. Wu, M. Li, and C. Maple, “A survey of localization in wireless sensor network,”International Journal of Distributed Sensor Networks, vol. 8, no. 12, p. 962523, 2012

    work page 2012

  9. [9]

    A survey of indoor localization systems and technologies,

    F. Zafari, A. Gkelias, and K. K. Leung, “A survey of indoor localization systems and technologies,”IEEE Communications Surveys & Tutorials, vol. 21, no. 3, pp. 2568–2599, 2019

    work page 2019

  10. [10]

    An enhanced path planning model for anchor- free localization in wireless sensor networks,

    T. K. Mishra and et.al., “An enhanced path planning model for anchor- free localization in wireless sensor networks,” inInternational Confer- ence on Information Technology (ICIT), 2018, pp. 204–209

    work page 2018

  11. [11]

    A novel range-free anchor- free localization in WSN using sun flower optimization algorithm,

    V . C. S. R. Rayavarapu and A. Mahapatro, “A novel range-free anchor- free localization in WSN using sun flower optimization algorithm,” in 2021 Advanced Communication Technologies and Signal Processing (ACTS), 2021, pp. 1–6

    work page 2021

  12. [12]

    UWB radar SLAM: An anchor- less approach in vision denied indoor environments,

    H. A. G. C. Premachandra and et.al., “UWB radar SLAM: An anchor- less approach in vision denied indoor environments,”IEEE Robotics and Automation Letters, vol. 8, no. 9, pp. 5299–5306, 2023

    work page 2023

  13. [13]

    Anchor-free relative 3D pose estimation using ultra-wideband and inertial data fusion,

    X. Cai, L. Wang, S. Sun, H. Han, and K. Han, “Anchor-free relative 3D pose estimation using ultra-wideband and inertial data fusion,” in 2024 IEEE SENSORS, 2024, pp. 1–4

    work page 2024

  14. [14]

    RISs and sidelink communications in smart cities: The key to seamless localization and sensing,

    H. Chen, H. Kim, M. Ammous, G. Seco-Granados, G. C. Alexandropou- los, S. Valaee, and H. Wymeersch, “RISs and sidelink communications in smart cities: The key to seamless localization and sensing,”IEEE Communications Magazine, vol. 61, no. 8, pp. 140–146, 2023

    work page 2023

  15. [15]

    RIS-enabled self-localization: Leveraging controllable reflections with zero access points,

    K. Keykhosravi, G. Seco-Granados, G. C. Alexandropoulos, and H. Wymeersch, “RIS-enabled self-localization: Leveraging controllable reflections with zero access points,” inICC 2022 - IEEE International Conference on Communications, 2022, pp. 2852–2857

    work page 2022

  16. [16]

    RIS-enabled and access-point- free simultaneous radio localization and mapping,

    H. Kim, H. Chen, M. F. Keskin, Y . Ge, K. Keykhosravi, G. C. Alexan- dropoulos, S. Kim, and H. Wymeersch, “RIS-enabled and access-point- free simultaneous radio localization and mapping,”IEEE Transactions on Wireless Communications, vol. 23, no. 4, pp. 3344–3360, 2024

    work page 2024

  17. [17]

    3D cooperative positioning via RIS and sidelink communications with zero access points,

    M. Ammous, H. Chen, H. Wymeersch, and S. Valaee, “3D cooperative positioning via RIS and sidelink communications with zero access points,”IEEE Transactions on Mobile Computing, vol. 24, no. 7, pp. 6119–6136, 2025

    work page 2025

  18. [18]

    RIS-enabled self-localization with FMCW radar,

    N. Hyowon Kim, M. F. Keskin, Z. S. He, J. Gil, G.-S. Granados, and H. Wymeersch, “RIS-enabled self-localization with FMCW radar,”

    work page

  19. [19]

    Available: https://arxiv.org/abs/2503.21021

    [Online]. Available: https://arxiv.org/abs/2503.21021

    work page arXiv

  20. [20]

    Near- field communications: A tutorial review,

    Y . Liu, Z. Wang, J. Xu, C. Ouyang, X. Mu, and R. Schober, “Near- field communications: A tutorial review,”IEEE Open Journal of the Communications Society, vol. 4, pp. 1999–2049, 2023

    work page 1999