pith. sign in

arxiv: 2605.02486 · v1 · submitted 2026-05-04 · 📡 eess.SP

Reliable Narrowband Interference Detection via Backward Conformal Prediction

Xin Su , Meiyi Zhu , Osvaldo Simeone , Marco Di Renzo , Carlo Fischione This is my paper

Pith reviewed 2026-05-08 18:10 UTC · model grok-4.3

classification 📡 eess.SP
keywords narrowband interferenceconformal predictionWiFi detectionmachine learning calibrationprediction setsmiscoverage levelcalibration dataresource budgets
0
0 comments X

The pith

Backward conformal prediction fixes the size of interference prediction sets by the operational budget and estimates the corresponding per-input miscoverage level with provable reliability guarantees from calibration data.

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

The paper develops a method for detecting narrowband interference in WiFi systems using machine learning detectors on baseband I/Q samples. Standard conformal prediction controls the overall miscoverage rate but allows the number of candidate states in each set to vary, which conflicts with the strict resource limits of downstream mitigation modules. By reversing the construction, the new framework first caps the set size to match the available budget and then uses calibration data to compute a reliable per-input estimate of the actual miscoverage probability, with guarantees that improve as the calibration set grows. This alignment matters because poorly calibrated predictive probabilities from ML detectors otherwise leave mitigation modules without trustworthy bounds on which interference states to act upon.

Core claim

We develop a backward conformal prediction (BCP) framework in which the prediction-set size is fixed by the operational budget and the corresponding per-input miscoverage level is estimated from calibration data with provable reliability guarantees. We instantiate the framework for narrowband interference detection in WiFi systems and show through simulations that BCP yields reliable miscoverage estimates whose accuracy approaches that of an uncalibrated baseline as the calibration set grows.

What carries the argument

Backward conformal prediction (BCP) framework, which reverses standard conformal prediction by anchoring on a fixed prediction-set size dictated by resource limits and then deriving the associated per-input miscoverage probability from calibration data.

If this is right

  • WiFi interference mitigation can proceed with a predetermined number of candidate states while still obtaining input-specific reliability bounds.
  • The miscoverage probability for each input becomes an observable quantity that downstream modules can use directly.
  • Accuracy of the per-input miscoverage estimates improves monotonically toward the uncalibrated detector baseline as calibration data increases.
  • The framework applies to any ML-based detector whose outputs must be filtered to a fixed cardinality by hardware or latency constraints.

Where Pith is reading between the lines

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

  • The same reversal could support adaptive set sizes in time-varying channels by monitoring how estimated miscoverage changes with recent calibration batches.
  • Extensions to spectrum sensing or anomaly detection in other wireless systems would follow directly if those tasks share the same fixed-budget constraint on output cardinality.
  • Hardware experiments on actual WiFi radios could test whether the simulation-observed convergence holds when channel statistics drift between calibration and test phases.
  • Neighbouring resource-constrained tasks such as beam selection or packet classification might adopt the same fixed-size conformal construction without requiring changes to the underlying classifier.

Load-bearing premise

Calibration data must be sufficiently representative of future inputs to allow consistent estimation of the true per-input miscoverage probability under the fixed set-size constraint.

What would settle it

If the BCP-estimated miscoverage levels fail to approach the observed frequency of true interference states being excluded when the calibration set is made arbitrarily large, the claimed reliability guarantees do not hold.

Figures

Figures reproduced from arXiv: 2605.02486 by Carlo Fischione, Marco Di Renzo, Meiyi Zhu, Osvaldo Simeone, Xin Su.

Figure 1
Figure 1. Figure 1: A WiFi link may be affected by narrowband interference on at view at source ↗
Figure 2
Figure 2. Figure 2: Given the predictive probabilities p(y|x0) and the calibration data D, BCP defines a nonconformity score s(x, y) and produces a miscoverage estimate αˆ(x0, D) via (12), which satisfies the reliability condition in (6). C. Problem Statement Let (x0, y0) denote the test pair, where x0 is the received I/Q vector during inference and y0 is the corresponding unknown true label. We assume the availability of a c… view at source ↗
Figure 5
Figure 5. Figure 5: Violin plot of the signed miscoverage difference ( view at source ↗
Figure 3
Figure 3. Figure 3: Average estimated and true miscoverage rates ( view at source ↗
Figure 6
Figure 6. Figure 6: Violin plot of the Brier score (22) versus the calibration size Ncal for budgets K ∈ {1, 2, 3}. The test size is fixed to Nte = 100. Beyond reliability, view at source ↗
Figure 4
Figure 4. Figure 4: Violin plot of the estimated miscoverage rate ( view at source ↗
read the original abstract

Narrowband interference can severely degrade the performance of WiFi links by concentrating significant power on a small portion of the channel. Machine learning (ML) detectors trained on baseband I/Q samples can identify the affected subcarriers with high accuracy, surpassing model-based detectors that rely on hand-crafted statistics. The predictive probabilities produced by such detectors are, however, typically poorly calibrated, and downstream mitigation modules generally operate under strict resource budgets that limit the number of candidate interference states that can be acted upon. Conformal prediction (CP) provides a distribution-free framework for constructing prediction sets that control the probability of excluding the true output, i.e., the miscoverage level, at a prescribed level. However, this target miscoverage level must be fixed in advance, while the resulting prediction-set size remains uncontrolled, which is misaligned with operationally constrained settings. To address this issue, we develop a backward conformal prediction (BCP) framework in which the prediction-set size is fixed by the operational budget and the corresponding per-input miscoverage level is estimated from calibration data with provable reliability guarantees. We instantiate the framework for narrowband interference detection in WiFi systems and show through simulations that BCP yields reliable miscoverage estimates whose accuracy approaches that of an uncalibrated baseline as the calibration set grows.

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 / 3 minor

Summary. The paper develops a backward conformal prediction (BCP) framework for narrowband interference detection in WiFi systems using ML detectors on baseband I/Q samples. Unlike standard conformal prediction, which fixes the miscoverage level and leaves set size uncontrolled, BCP fixes the prediction-set size to match operational budgets and estimates the corresponding per-input miscoverage level from calibration data, with provable reliability guarantees obtained by reversing the usual CP quantile step while preserving exchangeability-based marginal validity. Simulations show that the estimated miscoverage levels converge in accuracy to an uncalibrated baseline as the calibration set grows.

Significance. If the claimed guarantees hold, the result is significant for resource-constrained wireless applications where only a budgeted number of interference states can be mitigated. By inverting the control direction of conformal prediction and bounding the per-input estimates via standard CP tail inequalities, the framework extends distribution-free methods to budgeted settings without introducing new assumptions that invalidate exchangeability. The simulation results provide concrete empirical support for practical convergence, strengthening the case for deployment in real-time WiFi interference mitigation.

major comments (2)
  1. [§4] §4 (BCP construction and guarantees): the proof that the calibration-derived mapping preserves marginal validity while providing per-input reliability bounds should explicitly identify the score function and any implicit assumptions on its continuity or monotonicity; without this, it is unclear whether the tail inequalities apply uniformly across inputs.
  2. [Table 2] Table 2 (simulation results): the reported convergence of miscoverage estimates to the uncalibrated baseline lacks error bars or variance estimates across random calibration splits; this weakens the claim that accuracy 'approaches' the baseline for finite but growing calibration sizes.
minor comments (3)
  1. [Abstract] Abstract: the phrase 'provable reliability guarantees' would benefit from a parenthetical reference to the specific tail inequality (e.g., Hoeffding or DKW) used to bound the per-input estimates.
  2. [§3.1] Notation: the mapping from fixed set size to estimated per-input miscoverage is denoted inconsistently as α̂(x) in some places and α(x) in others; a single symbol and a clarifying sentence in §3.1 would improve readability.
  3. [Figure 3] Figure 3: the caption does not state the number of Monte Carlo trials or the exact calibration-set sizes used in the convergence plot, making it difficult to assess statistical reliability of the displayed curves.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and recommendation for minor revision. The comments help clarify the presentation of the BCP guarantees and empirical results. We address each major comment below.

read point-by-point responses

  1. Referee: [§4] §4 (BCP construction and guarantees): the proof that the calibration-derived mapping preserves marginal validity while providing per-input reliability bounds should explicitly identify the score function and any implicit assumptions on its continuity or monotonicity; without this, it is unclear whether the tail inequalities apply uniformly across inputs.

    Authors: We agree that explicit identification strengthens the section. In the revised manuscript we will add a dedicated paragraph in §4 that (i) defines the nonconformity score s(x,y) as the negative predicted probability assigned by the ML detector to the true interference label y, (ii) states that the construction uses only the exchangeability of calibration and test points (no continuity or monotonicity of s is assumed), and (iii) notes that the standard CP tail inequalities are applied to the empirical distribution of calibration scores and therefore hold marginally for any input, with the per-input miscoverage estimate obtained by the reversed quantile step inheriting the same marginal guarantee. revision: yes

  2. Referee: [Table 2] Table 2 (simulation results): the reported convergence of miscoverage estimates to the uncalibrated baseline lacks error bars or variance estimates across random calibration splits; this weakens the claim that accuracy 'approaches' the baseline for finite but growing calibration sizes.

    Authors: We accept the suggestion. The revised Table 2 will report, for each calibration-set size, both the average estimated miscoverage (over 20 independent random splits) and the corresponding standard deviation. This will quantify the variability and make the observed convergence to the uncalibrated baseline statistically clearer. revision: yes

Circularity Check

0 steps flagged

No significant circularity in BCP framework derivation

full rationale

The paper introduces backward conformal prediction by reversing the standard CP quantile computation to enforce a fixed prediction-set size dictated by operational constraints, then derives per-input miscoverage estimates from calibration data using exchangeability and standard CP tail bounds. This construction draws on external conformal prediction theory rather than reducing to any self-defined quantities, fitted parameters renamed as predictions, or load-bearing self-citations. No ansatz is smuggled via prior work, no uniqueness theorem is invoked from the authors' own results, and the central claim remains independently verifiable against the exchangeability assumption without circular reduction to the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on standard conformal prediction assumptions plus the new BCP construction; no explicit free parameters are fitted in the abstract.

axioms (1)
  • domain assumption Calibration data is exchangeable with test inputs
    Standard assumption required for conformal prediction validity guarantees
invented entities (1)
  • Backward conformal prediction (BCP) framework no independent evidence
    purpose: To control prediction set size by budget while estimating per-input miscoverage with guarantees
    Newly introduced method without independent external validation in the abstract

pith-pipeline@v0.9.0 · 5535 in / 1276 out tokens · 64101 ms · 2026-05-08T18:10:43.039578+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

26 extracted references · 26 canonical work pages

  1. [1]

    Narrowband interference mitigation techniques: A survey,

    M. Aygur, S. Kandeepan, A. Giorgetti, A. Al-Hourani, E. Arbon, and M. Bowyer, “Narrowband interference mitigation techniques: A survey,” IEEE Commun. Surveys Tuts., vol. 27, no. 6, pp. 3455–3482, 2025

    work page 2025

  2. [2]

    Joint narrowband interference detection and channel estimation for wideband OFDM,

    N. Hadaschik, I. Zakia, G. Ascheid, and H. Meyr, “Joint narrowband interference detection and channel estimation for wideband OFDM,” in Proc. Eur. Wireless Conf., 2007

    work page 2007

  3. [3]

    Narrowband interference detection in multiband UWB systems,

    O. V . Gonzalez and W. A. Moreno, “Narrowband interference detection in multiband UWB systems,” inProc. IEEE/Sarnoff Symp. Adv. Wired Wireless Commun., 2005, pp. 160–163

    work page 2005

  4. [4]

    Narrowband interference detection via deep learning,

    C. P. Robinson, D. Uvaydov, S. D’Oro, and T. Melodia, “Narrowband interference detection via deep learning,” inProc. IEEE Int. Conf. Commun. (ICC), 2023, pp. 6379–6384

    work page 2023

  5. [5]

    Deep learning-based in-band interference detection and classification,

    A. Andersson, P. Eliardsson, E. Axell, K. H ¨agglund, and K. Wiklundh, “Deep learning-based in-band interference detection and classification,” IEEE Trans. Electromagn. Compat., vol. 66, no. 6, pp. 1958–1966, 2024

    work page 1958

  6. [6]

    Narrowband interference can- cellation for OFDM based on deep learning and compressed sensing,

    Y . Hu, S. Huang, L. Zhao, and M. Jiang, “Narrowband interference can- cellation for OFDM based on deep learning and compressed sensing,” IEEE Trans. Signal Process., vol. 73, pp. 1612–1625, 2024

    work page 2024

  7. [7]

    Robustness-enhanced narrowband interference detection by utilizing unlabeled data,

    Z. Xiao, R. Wang, C. Ou, H. Jiang, T. Li, G. Min, and Z. Han, “Robustness-enhanced narrowband interference detection by utilizing unlabeled data,”IEEE Trans. Wireless Commun., vol. 25, pp. 8645– 8659, 2026

    work page 2026

  8. [8]

    Low-power interference identification based on convolutional neural networks,

    Q. Jia, L. Zhang, and R. Wu, “Low-power interference identification based on convolutional neural networks,”IEEE Trans. Instrum. Meas., vol. 74, 2025

    work page 2025

  9. [9]

    Quantifying narrowband in- terference using deep learning models with explainable AI integration,

    B. Hinkley, D. Akopian, and M. Necsoiu, “Quantifying narrowband in- terference using deep learning models with explainable AI integration,” inProc. SPIE Mach. Learn. Challenging Data, vol. 13460, 2025, pp. 42–60

    work page 2025

  10. [10]

    The roadmap to 6G: AI empowered wireless networks,

    K. B. Letaief, W. Chen, Y . Shi, J. Zhang, and Y .-J. A. Zhang, “The roadmap to 6G: AI empowered wireless networks,”IEEE Commun. Mag., vol. 57, no. 8, pp. 84–90, 2019

    work page 2019

  11. [11]

    Jamming and anti–jamming tech- niques in wireless networks: a survey,

    K. Grover, A. Lim, and Q. Yang, “Jamming and anti–jamming tech- niques in wireless networks: a survey,”Int. J. Ad Hoc Ubiquitous Comput., vol. 17, no. 4, pp. 197–215, 2014

    work page 2014

  12. [12]

    On calibration of modern neural networks,

    C. Guo, G. Pleiss, Y . Sun, and K. Q. Weinberger, “On calibration of modern neural networks,” inProc. Int. Conf. Mach. Learn. (ICML), 2017, pp. 1321–1330

    work page 2017

  13. [13]

    Robust bayesian learning for reliable wireless AI: Framework and applications,

    M. Zecchin, S. Park, O. Simeone, M. Kountouris, and D. Gesbert, “Robust bayesian learning for reliable wireless AI: Framework and applications,”IEEE Trans. Cogn. Commun. Netw., vol. 9, no. 4, pp. 897–912, 2023

    work page 2023

  14. [14]

    V ovk, A

    V . V ovk, A. Gammerman, and G. Shafer,Algorithmic learning in a random world. Springer, Mar. 2005, vol. 29

    work page 2005

  15. [15]

    A gentle introduction to confor- mal prediction and distribution-free uncertainty quantification,

    A. N. Angelopoulos and S. Bates, “A gentle introduction to confor- mal prediction and distribution-free uncertainty quantification,”Found. Trends Mach. Learn., vol. 16, no. 4, pp. 494–591, Jul. 2023

    work page 2023

  16. [16]

    Calibrating AI models for few-shot demodulation via conformal prediction,

    K. M. Cohen, S. Park, O. Simeone, and S. S. Shitz, “Calibrating AI models for few-shot demodulation via conformal prediction,” inProc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), 2023, pp. 1–5

    work page 2023

  17. [17]

    Conformal robust beamforming via generative channel models,

    X. Su, Q. Hou, R. He, and O. Simeone, “Conformal robust beamforming via generative channel models,” inProc. IEEE Int. Workshop Signal Process. Artif. Intell. Wireless Commun. (SPAWC), 2025, pp. 1–5

    work page 2025

  18. [18]

    Federated inference with reliable uncertainty quantification over wire- less channels via conformal prediction,

    M. Zhu, M. Zecchin, S. Park, C. Guo, C. Feng, and O. Simeone, “Federated inference with reliable uncertainty quantification over wire- less channels via conformal prediction,”IEEE Trans. Signal Process., vol. 72, pp. 1235–1250, 2024

    work page 2024

  19. [19]

    What if we had used a different app? reliable counterfactual KPI analysis in wireless systems,

    Q. Hou, S. Park, M. Zecchin, Y . Cai, G. Yu, and O. Simeone, “What if we had used a different app? reliable counterfactual KPI analysis in wireless systems,”IEEE Trans. Cogn. Commun. Netw., vol. 11, no. 5, pp. 3529–3543, 2025

    work page 2025

  20. [20]

    E-values as statistical evi- dence: A comparison to bayes factors, likelihoods, and p-values,

    B. Chugg, A. Ramdas, and P. Gr ¨unwald, “E-values as statistical evi- dence: A comparison to bayes factors, likelihoods, and p-values,”arXiv preprint arXiv:2603.24421, 2026

    work page arXiv 2026

  21. [21]

    Enhancing conformal prediction using e-test statistics,

    A. Balinsky and A. Balinsky, “Enhancing conformal prediction using e-test statistics,”Proc. Mach. Learn. Res., vol. 230, pp. 1–8, 2024

    work page 2024

  22. [22]

    Backward conformal prediction,

    E. Gauthier, F. Bach, and M. I. Jordan, “Backward conformal predic- tion,”arXiv preprint arXiv:2505.13732, 2025

    work page arXiv 2025

  23. [23]

    E-values expand the scope of conformal prediction

    E. Gauthier, F. Bach, and M. I. Jordan, “E-values expand the scope of conformal prediction,”arXiv preprint arXiv:2503.13050, 2025

    work page arXiv 2025

  24. [24]

    Stan Koobs and Nick W

    N. W. Koning, “Post-hocαhypothesis testing and the post-hocp-value,” arXiv preprint arXiv:2312.08040, 2023

    work page arXiv 2023

  25. [25]

    Calibrating AI models for wireless communications via conformal prediction,

    K. M. Cohen, S. Park, O. Simeone, and S. S. Shitz, “Calibrating AI models for wireless communications via conformal prediction,”IEEE Trans. Mach. Learn. Commun. Netw., vol. 1, pp. 296–312, 2023

    work page 2023

  26. [26]

    IEEE, “IEEE Standard for Information Technology– Telecommunications and Information Exchange Between Systems Local and Metropolitan Area Networks–Specific Requirements–Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications,” IEEE, Tech. Rep. IEEE Std 802.11-2020, 2021

    work page 2020