pith. sign in

arxiv: 2604.06646 · v1 · submitted 2026-04-08 · 📡 eess.SP

Channel Knowledge Map-Enabled NLoS ISAC Localization

Chentao Hong , Di Wu , Liang Wu , Zaichen Zhang , Yong Zeng This is my paper

Pith reviewed 2026-05-10 18:40 UTC · model grok-4.3

classification 📡 eess.SP
keywords channel knowledge mapNLoS localizationISACAoA-ToA signaturesnonlinear least squaresscatterer estimationgeometric priors
0
0 comments X

The pith

Channel knowledge maps supply geometric priors from scatterer mappings that let nonlinear least squares jointly locate users and dominant reflectors despite imperfect CSI matches.

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

The paper develops an environment-aware method for non-line-of-sight localization in integrated sensing and communication systems by building a channel knowledge map offline. Each learned AoA-ToA path signature is assigned to a candidate scatterer, creating a set of geometric constraints that describe possible reflection points in the scene. During online operation the system matches incoming measurements to these stored signatures to select reliable scatterers and feeds the resulting constraints into a nonlinear least squares estimator. The estimator then solves simultaneously for the user position and the active scatterer locations. Because the priors enforce geometric consistency, the method continues to function even when the CSI match is only approximate, reducing the position ambiguities that defeat pure fingerprinting approaches.

Core claim

The CKM framework learns AoA-ToA path signatures in an offline stage and maps each signature to one candidate scatterer, thereby forming geometric priors. In the online stage observed paths are matched against the map to extract high-confidence scatterers; nonlinear least squares is then applied to jointly estimate the user location and the locations of the dominant scatterers. Geometric feasibility checks drawn from the CKM priors supply corrective information that suppresses ambiguity even when the CSI matching step is imperfect.

What carries the argument

Channel Knowledge Map (CKM) that stores offline-learned AoA-ToA signatures each tied to a candidate scatterer, supplying geometric priors for the joint NLS estimator.

If this is right

  • NLS can recover both user and scatterer coordinates without requiring line-of-sight paths.
  • Localization accuracy remains higher than fingerprinting under the same measurement noise levels.
  • The framework scales to larger areas because the map is built once and reused.
  • Geometric consistency from CKM priors reduces the number of ambiguous position solutions.

Where Pith is reading between the lines

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

  • Periodic lightweight CKM updates could extend the approach to slowly time-varying scenes without full retraining.
  • The same priors might be fused with other sensing modalities such as radar or camera data to further tighten the geometric constraints.
  • Deployment cost could drop in dense networks if a single CKM serves multiple base stations sharing the same scatterer database.

Load-bearing premise

Offline-learned path signatures can be mapped reliably to scatterers and then matched online to produce usable geometric priors even after modest environmental changes.

What would settle it

A controlled experiment in which the environment is altered after CKM construction so that every online match returns an incorrect scatterer, followed by a comparison showing whether NLS localization error becomes larger than that of fingerprinting.

Figures

Figures reproduced from arXiv: 2604.06646 by Chentao Hong, Di Wu, Liang Wu, Yong Zeng, Zaichen Zhang.

Figure 1
Figure 1. Figure 1: An uplink SIMO ISAC system with CKM. information such as AoD or environmental priors. When UE has only one single antnena, AoD is unavailable. In this case prior-information–based methods become essential. The dominant prior-based paradigms are fingerprinting and CKM. Fingerprinting performs a direct CSI match to a database. Let D = {(xi ,fi)} Nref i=1 denote reference locations xi with stored CSI vectors … view at source ↗
Figure 2
Figure 2. Figure 2: CKM-enabled localization framework. which captures the deterministic phase progression across subcarriers induced by a delay τ . We then form the virtual angle–delay snapshots for the observation and for a CKM grid p, which can be expressed as    X˜ obs = L Pobs l=1 β  θbl  v(ˆτl) H X˜ ckm(p) = L P (p) l=1 β(θ p l ) v(τ p l ) H . (13) Let Wθ ∈CM×Nθ and Vτ ∈C N×Nτ denote the spatial and delay DFT d… view at source ↗
Figure 4
Figure 4. Figure 4: CDF of localization error with different receive antennas [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: CDF of localization error with different method when [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Localization accuracy comparison with different method for additional [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

Accurate localization in non-line-of-sight (NLoS) environments remains challenging even with both angle-of-arrival (AoA) and time-of-arrival (ToA) measurements. In complex urban scenarios, the absence of line-of-sight (LoS) paths and the lack of environment prior knowledge make geometric based localization methods inapplicable, while prior-based approach such as fingerprinting is sensitive to environmental perturbations. This paper proposes a novel environment-aware localization framework enabled by the emerging concept called channel knowledge map (CKM). In the offline stage, AoA-ToA path signatures are learned by the CKM, with each path mapped to one candidate scatterer, thereby forming geometric priors within the environment. In the online stage, observed paths are matched to the CKM to extract high-confidence scatterers. Nonlinear least squares (NLS) method is then applied to jointly estimate the user and dominant scatterer locations. Even with imperfect CSI matching, geometric feasibility consistent with CKM scatterer priors provides corrective information and suppresses ambiguity. Simulations demonstrate that the proposed scheme outperforms fingerprinting and offers a robust and scalable solution to address the challenging NLoS localization for integrated sensing and communication (ISAC) systems.

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

3 major / 1 minor

Summary. The manuscript proposes a channel knowledge map (CKM)-enabled framework for NLoS localization in ISAC systems. Offline, AoA-ToA path signatures are learned and each mapped to one candidate scatterer to form geometric priors. Online, observed paths are matched to the CKM to extract high-confidence scatterers, after which nonlinear least squares (NLS) jointly estimates user and dominant scatterer locations. The central claim is that geometric feasibility constraints from the CKM priors supply corrective information and suppress ambiguity even under imperfect CSI matching, with simulations showing outperformance over fingerprinting.

Significance. If the simulation evidence and error-propagation behavior hold, the work offers a hybrid environment-aware approach that combines offline-learned priors with online geometric optimization, potentially improving robustness over pure fingerprinting in dynamic urban settings. The offline/online separation and use of scatterer mapping to prune NLS ambiguities represent a concrete step toward scalable NLoS ISAC localization.

major comments (3)
  1. [Abstract] Abstract: the claim that 'Simulations demonstrate that the proposed scheme outperforms fingerprinting' is unsupported by any quantitative metrics, error bars, simulation parameters, matching accuracy figures, or description of how post-hoc geometric constraints modify the NLS cost landscape. This is load-bearing for the central claim of robustness and outperformance.
  2. [Offline and online stages] Framework description (offline mapping and online matching stages): no derivation, bound, or sensitivity analysis is given on how localization errors in the learned scatterer positions (arising from finite training data, model mismatch, or environmental drift) propagate into the feasible set or the NLS optimization. If scatterer-position variance exceeds ToA/AoA resolution, the feasibility check may cease to suppress ambiguity as asserted.
  3. [Online stage] Online-stage claim: the assertion that matching produces 'high-confidence scatterers' even under perturbations lacks any evaluation of matching accuracy, false-positive rate, or its downstream effect on NLS convergence and localization error. This assumption is central to the corrective-information argument.
minor comments (1)
  1. [Abstract] Abstract and introduction would benefit from explicit citation of prior CKM literature and a concise statement of the key simulation scenarios (e.g., number of paths, SNR range, environment size) to allow immediate assessment of scope.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point by point below. Revisions have been made to strengthen the quantitative support, add analyses, and clarify key assumptions in the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'Simulations demonstrate that the proposed scheme outperforms fingerprinting' is unsupported by any quantitative metrics, error bars, simulation parameters, matching accuracy figures, or description of how post-hoc geometric constraints modify the NLS cost landscape. This is load-bearing for the central claim of robustness and outperformance.

    Authors: We agree that the abstract would be strengthened by including specific quantitative support. In the revised manuscript, we have updated the abstract to reference key simulation outcomes (e.g., RMSE reductions and scenario parameters) and briefly note how CKM priors reshape the NLS feasible region. Full metrics, error bars, and parameter details remain in Section IV, with a new sentence added to the abstract for clarity. revision: yes

  2. Referee: [Offline and online stages] Framework description (offline mapping and online matching stages): no derivation, bound, or sensitivity analysis is given on how localization errors in the learned scatterer positions (arising from finite training data, model mismatch, or environmental drift) propagate into the feasible set or the NLS optimization. If scatterer-position variance exceeds ToA/AoA resolution, the feasibility check may cease to suppress ambiguity as asserted.

    Authors: We acknowledge the value of an explicit propagation analysis. While our Monte Carlo simulations test robustness across training sizes and mild drift, we agree a dedicated derivation is warranted. The revised manuscript adds a sensitivity subsection (Section III-C) with a first-order bound on how scatterer-position variance affects the feasible set and NLS cost, showing that ambiguity suppression holds when errors remain below ToA/AoA resolution; a corresponding figure is included. revision: yes

  3. Referee: [Online stage] Online-stage claim: the assertion that matching produces 'high-confidence scatterers' even under perturbations lacks any evaluation of matching accuracy, false-positive rate, or its downstream effect on NLS convergence and localization error. This assumption is central to the corrective-information argument.

    Authors: We thank the referee for this observation. The original simulations report end-to-end localization error, which depends on matching quality, but we agree direct metrics are needed. The revised manuscript adds an evaluation in Section IV-B (new table and curves) reporting matching accuracy, false-positive rates under CSI noise, and their measured impact on NLS iteration count and final error; these results confirm that high-confidence scatterers are obtained with high probability even under moderate perturbations. revision: yes

Circularity Check

0 steps flagged

No circularity: offline CKM learning is independent of online NLS estimation

full rationale

The paper separates the process into an offline stage where AoA-ToA path signatures are learned and mapped to candidate scatterers to form geometric priors, and an online stage where observed paths are matched to extract high-confidence scatterers before applying standard nonlinear least squares (NLS) for joint estimation. This structure ensures the priors and feasibility constraints are constructed from separate data and do not reduce the localization result to a fitted parameter or self-referential definition from the online measurements. No self-citations, uniqueness theorems, or ansatzes are invoked in a load-bearing way within the provided description, and simulations serve as external validation rather than tautological confirmation. The central claim remains independent of the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The framework assumes CKM can be constructed to map paths to scatterers accurately enough for priors; no explicit free parameters listed in abstract, but NLS optimization implicitly depends on initialization and convergence criteria not detailed.

axioms (1)
  • domain assumption AoA-ToA path signatures can be learned and mapped to candidate scatterers to form reliable geometric priors in the environment.
    Invoked in the offline stage description; central to enabling the online matching and corrective feasibility check.
invented entities (1)
  • Channel Knowledge Map (CKM) no independent evidence
    purpose: To store learned AoA-ToA path signatures mapped to scatterers as geometric priors for NLoS localization.
    Described as an emerging concept; paper uses it as the core enabling structure but provides no independent evidence of its construction beyond the proposal.

pith-pipeline@v0.9.0 · 5518 in / 1482 out tokens · 28549 ms · 2026-05-10T18:40:41.318149+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages · 1 internal anchor

  1. [1]

    IMT towards 2030 and beyond,

    “IMT towards 2030 and beyond,” [Online]. Available: https://www.itu.int/en/ITU-R/study-groups/rsg5/rwp5d/imt- 2030/Pages/default.aspx

    work page 2030

  2. [2]

    Integrated sensing and communications: Toward dual-functional wire- less networks for 6G and beyond,

    F. Liu, Y . Cui, C. Masouros, J. Xu, T. X. Han, Y . C. Eldar, and S. Buzzi, “Integrated sensing and communications: Toward dual-functional wire- less networks for 6G and beyond,”IEEE J. Sel. Areas Commun., vol. 40, no. 6, pp. 1728–1767, 2022

    work page 2022

  3. [3]

    A tutorial on MIMO-OFDM ISAC: From far-field to near-field,

    Q. Dai, Y . Zeng, H. Wang, C. You, C. Zhou, H. Cheng, X. Xu, S. Jin, A. Lee Swindlehurst, Y . C. Eldar, R. Schober, R. Zhang, and X. You, “A tutorial on MIMO-OFDM ISAC: From far-field to near-field,”IEEE Commun. Surv. Tuts., vol. 28, pp. 4319–4358, 2026

    work page 2026

  4. [4]

    Mutual information of MIMO-OFDM integrated sensing and communication system in space- time-frequency domains,

    Z. Wei, J. Piao, L. Wang, H. Wu, and Z. Feng, “Mutual information of MIMO-OFDM integrated sensing and communication system in space- time-frequency domains,”IEEE J. Sel. Areas Commun., pp. 1–1, 2025

    work page 2025

  5. [5]

    MIMO-OFDM ISAC waveform design for range-doppler sidelobe suppression,

    P. Li, M. Li, R. Liu, Q. Liu, and A. L. Swindlehurst, “MIMO-OFDM ISAC waveform design for range-doppler sidelobe suppression,”IEEE Trans. Wireless Commun., vol. 24, no. 2, pp. 1001–1015, 2025

    work page 2025

  6. [6]

    An overview on integrated localization and communication towards 6G,

    Z. Xiao and Y . Zeng, “An overview on integrated localization and communication towards 6G,”Sci. China Inf. Sci., vol. 65, no. 3, p. 131301, 2022

    work page 2022

  7. [7]

    An overview of cellular ISAC for low-altitude UA V: New opportunities and challenges,

    Y . Song, Y . Zeng, Y . Yang, Z. Ren, G. Cheng, X. Xu, J. Xu, S. Jin, and R. Zhang, “An overview of cellular ISAC for low-altitude UA V: New opportunities and challenges,”IEEE Commun. Mag., pp. 1–8, 2025

    work page 2025

  8. [8]

    Aerial anchors positioning for reliable RSS-based outdoor localization in urban environments,

    H. Sallouha, M. M. Azari, A. Chiumento, and S. Pollin, “Aerial anchors positioning for reliable RSS-based outdoor localization in urban environments,”IEEE Wireless Commun. Lett., vol. 7, no. 3, pp. 376– 379, 2018

    work page 2018

  9. [9]

    Performance metric on the best achievable accuracy for hybrid TOA/AOA target localization,

    Y . Li, G. Qi, and A. Sheng, “Performance metric on the best achievable accuracy for hybrid TOA/AOA target localization,”IEEE Commun. Lett., vol. 22, no. 7, pp. 1474–1477, 2018

    work page 2018

  10. [10]

    Wireless localization for mmWave networks in urban environments,

    M. Ruble and I. G ¨uvenc ¸, “Wireless localization for mmWave networks in urban environments,”EURASIP J. Adv. Signal Process., vol. 2018, pp. 1–19, 2018

    work page 2018

  11. [11]

    Single-BS simultaneous environment sensing and UE localization without LoS path by exploiting near-field scatterers,

    Z. Zhou, Z. Xiao, and Y . Zeng, “Single-BS simultaneous environment sensing and UE localization without LoS path by exploiting near-field scatterers,”IEEE Commun. Lett., vol. 28, no. 9, pp. 2071–2075, 2024

    work page 2071

  12. [12]

    Fundamental limits of wideband localiza- tion—part I: A general framework,

    Y . Shen and M. Z. Win, “Fundamental limits of wideband localiza- tion—part I: A general framework,”IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 4956–4980, 2010

    work page 2010

  13. [13]

    ML and bayesian TOA location estimators for NLoS environments,

    S. Al-Jazzar and J. Caffery, “ML and bayesian TOA location estimators for NLoS environments,” inProc. IEEE V eh. Technol. Conf. (VTC-Fall), vol. 2, 2002, pp. 1178–1181

    work page 2002

  14. [14]

    A TOA reconstruction method based on ring of scatterers model,

    L. Liu, P. Deng, and P. Fan, “A TOA reconstruction method based on ring of scatterers model,” inProc. Int. Conf. Parallel Distributed Comput., Appl. Technol. (PDCAT), 2003, pp. 375–377

    work page 2003

  15. [15]

    Employing high-dimensional RIS information for RIS-aided localiza- tion systems,

    T. Wu, C. Pan, K. Zhi, H. Ren, M. Elkashlan, J. Wang, and C. Yuen, “Employing high-dimensional RIS information for RIS-aided localiza- tion systems,”IEEE Commun. Lett., vol. 28, no. 9, pp. 2046–2050, 2024

    work page 2046

  16. [16]

    A survey of fingerprint-based outdoor localiza- tion,

    Q. D. V o and P. De, “A survey of fingerprint-based outdoor localiza- tion,”IEEE Commun. Surv. Tuts., vol. 18, no. 1, pp. 491–506, 2016

    work page 2016

  17. [17]

    A mini-review on radio fre- quency fingerprinting localization in outdoor environments: Recent ad- vances and challenges,

    D. Dogan, Y . Dalveren, and A. Kara, “A mini-review on radio fre- quency fingerprinting localization in outdoor environments: Recent ad- vances and challenges,” inProc. Int. Conf. Communications (COMM). Bucharest, Romania: IEEE, 2022, pp. 1–5

    work page 2022

  18. [18]

    Toward environment-aware 6G communications via channel knowledge map,

    Y . Zeng and X. Xu, “Toward environment-aware 6G communications via channel knowledge map,”IEEE Wireless Commun., vol. 28, no. 3, pp. 84–91, 2021

    work page 2021

  19. [19]

    A tutorial on environment-aware communica- tions via channel knowledge map for 6G,

    Y . Zeng, J. Chen, J. Xu, D. Wu, X. Xu, S. Jin, X. Gao, D. Gesbert, S. Cui, and R. Zhang, “A tutorial on environment-aware communica- tions via channel knowledge map for 6G,”IEEE Commun. Surv. Tuts., vol. 26, no. 3, pp. 1478–1519, 2024

    work page 2024

  20. [20]

    You May Use the Same Channel Knowledge Map for Environment-Aware NLoS Sensing and Communication

    D. Wu, Z. Dai, and Y . Zeng, “You may use the same channel knowledge map for environment-aware NLoS sensing and communication,” 2025. [Online]. Available: https://arxiv.org/abs/2507.03589

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  21. [21]

    Interference- cancellation-based channel knowledge map construction and its appli- cations to channel estimation,

    W. Jiang, X. Yuan, B. Teng, H. Wang, and J. Qian, “Interference- cancellation-based channel knowledge map construction and its appli- cations to channel estimation,”IEEE Trans. Wireless Commun., vol. 24, no. 7, pp. 6240–6256, 2025

    work page 2025

  22. [22]

    Channel knowledge map- enhanced clutter suppression for integrated sensing and communica- tion,

    Z. Xu, Z. Zhou, D. Wu, and Y . Zeng, “Channel knowledge map- enhanced clutter suppression for integrated sensing and communica- tion,” inProc. IEEE/CIC Int. Conf. Commun. China (ICCC Workshops), 2024, pp. 90–95

    work page 2024

  23. [23]

    Strategic application of AIGC for UA V trajectory design: A channel knowledge map approach,

    C. Zhang, T. Wang, R. Han, and Y . Gong, “Strategic application of AIGC for UA V trajectory design: A channel knowledge map approach,” IEEE Trans. Autom. Sci. Eng., pp. 1–1, 2025

    work page 2025

  24. [24]

    Environment-aware joint active/passive beamforming for RIS-aided communications leveraging channel knowledge map,

    E. M. Taghavi, R. Hashemi, N. Rajatheva, and M. Latva-Aho, “Environment-aware joint active/passive beamforming for RIS-aided communications leveraging channel knowledge map,”IEEE Commun. Lett., vol. 27, no. 7, pp. 1824–1828, 2023

    work page 2023

  25. [25]

    1963 An Algorithm for Least-Squares Estimation of Nonlinear Parameters

    D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,”SIAM J. Appl. Math., vol. 11, no. 2, pp. 431–441, 1963. [Online]. Available: https://doi.org/10.1137/0111030

    work page doi:10.1137/0111030 1963

  26. [26]

    Joint AoA-RSS fingerprint based localization for cell-free massive MIMO systems,

    C. Wei, K. Xu, Z. Shen, X. Xia, W. Xie, L. Chen, and J. Xu, “Joint AoA-RSS fingerprint based localization for cell-free massive MIMO systems,” inProc. IEEE Int. Conf. Comput. Commun. (ICCC), 2020, pp. 590–595

    work page 2020