pith. sign in

arxiv: 2602.09763 · v2 · submitted 2026-02-10 · 📡 eess.SP

Unsupervised Semi-Parametric Plug-in Likelihood-Ratio Detection for Covert Communications in the Presence of Disco Reconfigurable Intelligent Surfaces

Luyao Sun , Huan Huang , Yongxing Song , Zhongxing Tian , Hongliang Zhang , Weidong Mei , Dongdong Zou , Yi Cai This is my paper

Pith reviewed 2026-05-16 02:47 UTC · model grok-4.3

classification 📡 eess.SP
keywords covert communicationsdisco reconfigurable intelligent surfaceplug-in likelihood-ratio detectorunsupervised semi-parametric detectionnormalizing flowdetection error probabilityNeyman-Pearson detector
0
0 comments X p. Extension

The pith

The proposed unsupervised plug-in likelihood-ratio detector achieves monitoring performance close to its supervised counterpart for covert communications with a disco reconfigurable intelligent surface.

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

The paper develops an unsupervised semi-parametric plug-in likelihood-ratio detector for Willie to monitor covert communications between Alice and Bob in the presence of a disco reconfigurable intelligent surface. The DRIS makes constructing the optimal Neyman-Pearson detector analytically intractable, prompting the use of unlabeled data to learn the transmission distribution via a one-dimensional monotone normalizing flow while retaining a Gamma model for the silent case. The method exploits the structural prior that Willie's observations reduce to noise only under silence. This matters to a reader because it demonstrates how effective monitoring can be maintained without labeled training data or knowledge of noise statistics, even when surfaces aid the warden.

Core claim

The central claim is that the proposed unsupervised semi-parametric plug-in likelihood-ratio detector retains the parametric Gamma reference model under the silent hypothesis without requiring prior knowledge of noise, learns from unlabeled data a one-dimensional monotone normalizing flow model for the analytically intractable distribution under the transmission hypothesis, and achieves monitoring performance close to that of its supervised counterpart by exploiting the structural prior inherent in covert communications.

What carries the argument

The semi-parametric plug-in likelihood-ratio detector that pairs a parametric Gamma model for the silent hypothesis with a one-dimensional monotone normalizing flow learned from unlabeled data for the transmission hypothesis, exploiting the structural prior that observations reduce to noise only under silence.

If this is right

  • Willie can perform near-optimal detection without prior noise knowledge or labeled data.
  • The DRIS reduces Willie's detection error probability while also lowering the SJNR for Alice and Bob.
  • The detector works without channel state information at Willie or other parties.
  • Simulations confirm the unsupervised version performs close to the supervised one across various scenarios.

Where Pith is reading between the lines

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

  • This semi-parametric approach could generalize to other physical-layer detection tasks where one hypothesis distribution is simple and the other is complex.
  • In practice, the method's success would depend on how well the normalizing flow approximates the true distribution when the DRIS parameters vary dynamically.
  • It raises the possibility of combining such detectors with adaptive DRIS control to further optimize monitoring.

Load-bearing premise

The one-dimensional monotone normalizing flow accurately learns the analytically intractable distribution under the transmission hypothesis from unlabeled data, assuming the structural prior that observations reduce to noise only under silence holds exactly.

What would settle it

Running the detector on simulated data where the learned flow deviates significantly from the true transmission distribution, resulting in a detection error probability much higher than the supervised baseline.

Figures

Figures reproduced from arXiv: 2602.09763 by Dongdong Zou, Hongliang Zhang, Huan Huang, Luyao Sun, Weidong Mei, Yi Cai, Yongxing Song, Zhongxing Tian.

Figure 1
Figure 1. Figure 1: Covert communications in the presence of a disco reconfigurable intelligent surface (DRIS), where the warden Willie employs the masked autoregressive [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Detection error probability (DEP) at Willie (left y-axis) and achievable [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Detection error probability (DEP) at Willie (left y-axis) and achievable rate at Bob (right y-axis) vs. number of DRIS reflecting elements at (a) low [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Detection error probability (DEP) at Willie (left y-axis) and achievable rate at Bob (right y-axis) vs. number of DRIS phase quantization bits at (a) [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Detection error probability (DEP) at Willie (left y-axis) and achievable rate at Bob (right y-axis) vs. distance between Alice and DRIS at (a) low [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

Covert communications, also referred to as low probability of detection (LPD) communications, provide a higher level of privacy protection than cryptography and physical-layer security (PLS) by hiding transmissions in the ambient environment. In this work, we investigate covert communications in the presence of a disco reconfigurable intelligent surface (DRIS) deployed by the warden Willie, which reduces Willie's detection error probability (DEP), i.e., the sum of the false alarm rate (FAR) and the miss detection rate (MDR), and degrades the communication performance between Alice and Bob, without relying on either channel state information (CSI) or additional jamming power. However, the introduction of the DRIS makes it analytically intractable for Willie to construct the Neyman-Pearson (NP) detector, which is the optimal detector for monitoring potential covert transmissions between Alice and Bob. To this end, we develop an unsupervised semi-parametric plug-in likelihood-ratio detector for Willie. The proposed detector retains the parametric Gamma reference model under the silent hypothesis without requiring prior knowledge of noise, and learns from unlabeled data a one-dimensional monotone normalizing flow model for the analytically intractable distribution under the transmission hypothesis. In particular, it exploits the structural prior inherent in covert communications that Willie's observations reduce to noise only when Alice and Bob are silent. The monitoring performance at Willie is evaluated in terms of DEP, while the communication impact on Alice and Bob is quantified by the signal-to-jamming-plus-noise ratio (SJNR). Simulation results verify the analysis and show that the proposed unsupervised plug-in likelihood-ratio detector achieves monitoring performance close to that of its supervised counterpart.

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 develops an unsupervised semi-parametric plug-in likelihood-ratio detector for a warden (Willie) monitoring covert communications in the presence of a disco reconfigurable intelligent surface (DRIS). It retains a parametric Gamma model for the silent hypothesis (H0) that requires no noise knowledge and learns a one-dimensional monotone normalizing flow for the analytically intractable transmission hypothesis (H1) directly from unlabeled observations, exploiting the structural prior that observations reduce to noise only under silence. Performance is quantified by the warden's detection error probability (DEP) and the legitimate link's signal-to-jamming-plus-noise ratio (SJNR); simulations are stated to show the unsupervised detector achieves DEP close to its supervised counterpart.

Significance. If the central claim holds, the work is significant because it supplies a practical, label-free detector for an otherwise intractable monitoring problem created by the DRIS, thereby clarifying the limits of covert communications against this class of adversary. The semi-parametric construction that combines an exact structural prior for H0 with data-driven density estimation for H1 is a methodological strength that could transfer to other signal-detection settings where one hypothesis admits a simple parametric form while the other does not.

major comments (2)
  1. [§III and §IV] §III (Proposed Detector) and §IV (Unsupervised Training): the headline claim that the unsupervised plug-in LRT achieves DEP close to the supervised version rests on the unproven assertion that a 1D monotone normalizing flow trained on the unlabeled mixture recovers a density for H1 sufficiently accurate for the likelihood ratio; no consistency guarantee or separation argument is supplied showing that the unknown H1 proportion can be disentangled without biasing the ratio on the support that dominates the DEP, which is load-bearing for the result.
  2. [§V] §V (Numerical Results): the simulations that 'verify the analysis and show near-supervised DEP performance' report no error bars, no sensitivity sweeps over flow hyperparameters or mixture proportion, and no ablation on the Gamma reference fit, leaving the quantitative closeness claim only moderately supported and difficult to reproduce or stress-test.
minor comments (2)
  1. [Abstract] The abstract states that 'simulation results verify the analysis' yet the manuscript does not explicitly identify which closed-form expressions (if any) are being verified by the Monte-Carlo trials; a short clarifying sentence would help readers.
  2. [§III] Notation for the learned flow density (e.g., p̂_1) should be introduced once in §III and used consistently thereafter to avoid ambiguity with the true H1 density.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and insightful comments. We address each major comment point by point below, indicating the planned revisions.

read point-by-point responses

  1. Referee: [§III and §IV] §III (Proposed Detector) and §IV (Unsupervised Training): the headline claim that the unsupervised plug-in LRT achieves DEP close to the supervised version rests on the unproven assertion that a 1D monotone normalizing flow trained on the unlabeled mixture recovers a density for H1 sufficiently accurate for the likelihood ratio; no consistency guarantee or separation argument is supplied showing that the unknown H1 proportion can be disentangled without biasing the ratio on the support that dominates the DEP, which is load-bearing for the result.

    Authors: We acknowledge that the manuscript does not supply a formal consistency guarantee or separation argument for recovering the H1 density from the unlabeled mixture. The method exploits the structural prior that observations under H0 follow the fixed parametric Gamma distribution (with no noise knowledge required), so that the monotone normalizing flow trained on the mixture can capture the deviation attributable to H1. In the revised version we will expand the discussion in §IV to clarify this mechanism, including a qualitative argument based on the known form of the H0 density and the invertibility of the flow, together with additional controlled simulations that vary the H1 mixture proportion. A complete theoretical analysis of potential bias on the likelihood-ratio support is beyond the scope of the present work and is noted as future research. revision: partial

  2. Referee: [§V] §V (Numerical Results): the simulations that 'verify the analysis and show near-supervised DEP performance' report no error bars, no sensitivity sweeps over flow hyperparameters or mixture proportion, and no ablation on the Gamma reference fit, leaving the quantitative closeness claim only moderately supported and difficult to reproduce or stress-test.

    Authors: We agree that the simulation results would benefit from greater statistical rigor and robustness checks. In the revised manuscript we will add error bars computed from multiple independent Monte Carlo runs to all DEP curves, include sensitivity sweeps over normalizing-flow hyperparameters (number of layers, hidden dimension, learning rate) and over a range of H1 mixture proportions, and provide an ablation study on the Gamma reference-model fit. These additions will be placed in §V to strengthen support for the reported performance claims. revision: yes

standing simulated objections not resolved
  • A rigorous consistency proof establishing that the unsupervised 1D monotone normalizing flow recovers an H1 density sufficiently accurate for the likelihood ratio without additional assumptions on distribution separation.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper introduces a novel unsupervised semi-parametric plug-in LRT that retains an exact parametric Gamma model for the H0 (silent) hypothesis while training a 1D monotone normalizing flow on unlabeled mixture data to approximate the intractable H1 density, explicitly invoking the structural prior that observations equal noise under silence. No equation or claim reduces a performance prediction to a fitted parameter defined in terms of the target result, nor does any load-bearing step rely on a self-citation chain or imported uniqueness theorem. Simulation-based verification of DEP closeness to the supervised case is presented as empirical evidence rather than an algebraic identity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on a domain structural prior that observations equal noise under silence, a parametric Gamma model for that noise, and the assumption that a one-dimensional monotone normalizing flow can be learned unsupervised to approximate the transmission distribution; no free parameters are explicitly fitted beyond the flow training, and no new physical entities are postulated.

free parameters (1)
  • normalizing flow parameters
    Learned from unlabeled observations under the transmission hypothesis; no specific fitted values or hand-chosen constants are stated.
axioms (2)
  • domain assumption Willie's observations reduce to noise only when Alice and Bob are silent
    Invoked as the structural prior that enables the semi-parametric construction without labeled data.
  • domain assumption Noise under the silent hypothesis follows a Gamma distribution
    Retained as the parametric reference model; standard in wireless detection but not derived here.

pith-pipeline@v0.9.0 · 5622 in / 1391 out tokens · 111732 ms · 2026-05-16T02:47:53.501366+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

42 extracted references · 42 canonical work pages

  1. [1]

    Principles of physical layer security in multiuser wireless networks: A survey,

    A. Mukherjee, S. A. A. Fakoorian, J. Huang, and A. L. Swindlehurst, “Principles of physical layer security in multiuser wireless networks: A survey,”IEEE Commun. Surveys Tuts., vol. 16, no. 3, pp. 1550–1573, 3rd Quart. 2014

    work page 2014

  2. [2]

    Covert communications: A comprehensive survey,

    X. Chenet al., “Covert communications: A comprehensive survey,”IEEE Commun. Surveys Tuts., vol. 25, no. 2, pp. 1173–1198, 2nd Quart. 2023

    work page 2023

  3. [3]

    Covert communication in the presence of an uninformed jammer,

    T. V . Sobers, B. A. Bash, S. Guha, D. Towsley, and D. Goeckel, “Covert communication in the presence of an uninformed jammer,”IEEE Trans. Wireless Commun., vol. 16, no. 9, pp. 6193–6206, Sep. 2017

    work page 2017

  4. [4]

    Optimal power adaptation in covert communication with an uninformed jammer,

    K. Li, P. A. Kelly, and D. Goeckel, “Optimal power adaptation in covert communication with an uninformed jammer,”IEEE Trans. Wireless Commun., vol. 19, no. 5, pp. 3463–3473, May 2020

    work page 2020

  5. [5]

    Fundamental limits of covert commu- nication over MIMO AWGN channel,

    A. Abdelaziz and C. E. Koksal, “Fundamental limits of covert commu- nication over MIMO AWGN channel,” inProc. IEEE Conf. Commun. Netw. Secur . (CNS), Las Vegas, NV , USA, Oct. 2017, pp. 1–9

    work page 2017

  6. [6]

    Limits of reliable communi- cation with low probability of detection on AWGN channels,

    B. A. Bash, D. Goeckel, and D. Towsley, “Limits of reliable communi- cation with low probability of detection on AWGN channels,”IEEE J. Sel. Areas Commun., vol. 31, no. 9, pp. 1921–1930, Sep. 2013

    work page 1921

  7. [7]

    Multi-antenna covert communication via full-duplex jamming against a warden with uncertain locations,

    X. Chenet al., “Multi-antenna covert communication via full-duplex jamming against a warden with uncertain locations,”IEEE Trans. Wireless Commun., vol. 20, no. 8, pp. 5467–5480, Aug. 2021

    work page 2021

  8. [8]

    Wireless covert communications aided by distributed cooperative jamming over slow fading channels,

    T.-X. Zheng, Z. Yang, C. Wang, Z. Li, J. Yuan, and X. Guan, “Wireless covert communications aided by distributed cooperative jamming over slow fading channels,”IEEE Trans. Wireless Commun., vol. 20, no. 11, pp. 7026–7039, Nov. 2021

    work page 2021

  9. [9]

    Turbo covert channel: An iterative framework for covert communication over data networks,

    S. A. Ahmadzadeh and G. B. Agnew, “Turbo covert channel: An iterative framework for covert communication over data networks,” inProc. IEEE INFOCOM, Turin, Italy, Apr. 2013, pp. 2031–2039

    work page 2013

  10. [10]

    Covert com- munication in downlink NOMA systems with random transmit power,

    L. Tao, W. Yang, S. Yan, D. Wu, X. Guan, and D. Chen, “Covert com- munication in downlink NOMA systems with random transmit power,” IEEE Wireless Commun. Lett., vol. 9, no. 11, pp. 2000–2004, Nov. 2020

    work page 2000

  11. [11]

    Covert communication in coop- erative NOMA networks,

    O. A. Topal and G. Karabulut-Kurt, “Covert communication in coop- erative NOMA networks,” inProc. 2020 28th Signal Process. Commun. Appl. Conf. (SIU), Gaziantep, Turkey, Oct. 2020, pp. 1–4

    work page 2020

  12. [12]

    Covert commu- nication achieved by a greedy relay in wireless networks,

    J. Hu, S. Yan, X. Zhou, F. Shu, J. Li, and J. Wang, “Covert commu- nication achieved by a greedy relay in wireless networks,”IEEE Trans. Wireless Commun., vol. 17, no. 7, pp. 4766–4779, Jul. 2018

    work page 2018

  13. [13]

    Relay-assisted uplink covert communica- tion in the presence of multi-antenna warden and uninformed jamming,

    M. Lin, C. Liu, and W. Wang, “Relay-assisted uplink covert communica- tion in the presence of multi-antenna warden and uninformed jamming,” IEEE Trans. Commun., vol. 72, no. 4, pp. 2124–2137, Apr. 2024. 13

    work page 2024

  14. [14]

    Covert rate maximiza- tion in wireless full-duplex relaying systems with power control,

    R. Sun, B. Yang, S. Ma, Y . Shen, and X. Jiang, “Covert rate maximiza- tion in wireless full-duplex relaying systems with power control,”IEEE Trans. Commun., vol. 69, no. 9, pp. 6198–6212, Sep. 2021

    work page 2021

  15. [15]

    Covert communi- cations with a full-duplex receiver over wireless fading channels,

    J. Hu, K. Shahzad, S. Yan, X. Zhou, F. Shu, and J. Li, “Covert communi- cations with a full-duplex receiver over wireless fading channels,” inProc. IEEE Int. Conf. Commun. (ICC), Kansas City, MO, USA, May 2018, pp. 1–6

    work page 2018

  16. [16]

    Intelligent omni-surfaces for full-dimensional wire- less communications: Principles, technology, and implementation,

    H. Zhanget al., “Intelligent omni-surfaces for full-dimensional wire- less communications: Principles, technology, and implementation,”IEEE Commun. Mag., vol. 60, no. 2, pp. 39–45, Feb. 2022

    work page 2022

  17. [17]

    Holographic MIMO surfaces for 6G wireless networks: Opportunities, challenges, and trends,

    C. Huanget al., “Holographic MIMO surfaces for 6G wireless networks: Opportunities, challenges, and trends,”IEEE Wireless Commun., vol. 27, no. 5, pp. 118–125, Oct. 2020

    work page 2020

  18. [18]

    Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming,

    Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming,”IEEE Trans. Wireless Commun., vol. 18, no. 11, pp. 5394–5409, Nov. 2019

    work page 2019

  19. [19]

    Intelligent re- flecting surface aided wireless communications: A tutorial,

    Q. Wu, S. Zhang, B. Zheng, C. You, and R. Zhang, “Intelligent re- flecting surface aided wireless communications: A tutorial,”IEEE Trans. Commun., vol. 69, no. 5, pp. 3313–3351, May 2021

    work page 2021

  20. [20]

    Toward smart wireless communications via intelligent reflecting surfaces: A contemporary survey,

    S. Gonget al., “Toward smart wireless communications via intelligent reflecting surfaces: A contemporary survey,”IEEE Commun. Surveys Tuts., vol. 22, no. 4, pp. 2283–2314, 4th Quart. 2020

    work page 2020

  21. [21]

    Reconfigurable holo- graphic surface-enabled multi-user wireless communications: Amplitude- controlled holographic beamforming,

    R. Deng, B. Di, H. Zhang, Y . Tan, and L. Song, “Reconfigurable holo- graphic surface-enabled multi-user wireless communications: Amplitude- controlled holographic beamforming,”IEEE Trans. Wireless Commun., vol. 21, no. 8, pp. 6003–6017, Aug. 2022

    work page 2022

  22. [22]

    Coding metamaterials, digital metamaterials and programmable metamaterials,

    T. Cui, M. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,”Light Sci. Appl., vol. 3, Oct. 2014, Art. no. e218

    work page 2014

  23. [23]

    Reconfigurable intelligent surfaces for energy efficiency in wireless communication,

    C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, and C. Yuen, “Reconfigurable intelligent surfaces for energy efficiency in wireless communication,”IEEE Trans. Wireless Commun., vol. 18, no. 8, pp. 4157–4170, Aug. 2019

    work page 2019

  24. [24]

    Reconfigurable intelligent surface assisted multiuser MISO systems exploiting deep reinforcement learning,

    C. Huang, R. Mo, and C. Yuen, “Reconfigurable intelligent surface assisted multiuser MISO systems exploiting deep reinforcement learning,” IEEE J. Sel. Areas Commun., vol. 38, no. 8, pp. 1839–1850, Aug. 2020

    work page 2020

  25. [25]

    Covert communication in intelligent reflecting surface-assisted NOMA systems: Design, analysis, and optimization,

    L. Lv, Q. Wu, Z. Li, Z. Ding, N. Al-Dhahir, and J. Chen, “Covert communication in intelligent reflecting surface-assisted NOMA systems: Design, analysis, and optimization,”IEEE Trans. Wireless Commun., vol. 21, no. 3, pp. 1735–1750, Mar. 2022

    work page 2022

  26. [26]

    Covert communications via two-way IRS with noise power uncertainty,

    C. Wang, Z. Xiong, M. Zheng, N. Zhao, and D. Niyato, “Covert communications via two-way IRS with noise power uncertainty,”IEEE Trans. Commun., vol. 72, no. 8, pp. 4803–4815, Aug. 2024

    work page 2024

  27. [27]

    IRS-assisted covert communication with equal and unequal transmit prior probabilities,

    Y . Wuet al., “IRS-assisted covert communication with equal and unequal transmit prior probabilities,”IEEE Trans. Commun., vol. 72, no. 5, pp. 2897–2912, May 2024

    work page 2024

  28. [28]

    Covert communication assisted by UA V-IRS,

    C. Wanget al., “Covert communication assisted by UA V-IRS,”IEEE Trans. Commun., vol. 71, no. 1, pp. 357–369, Jan. 2023

    work page 2023

  29. [29]

    STAR-RIS aided covert communication in UA V air- ground networks,

    Q. Wanget al., “STAR-RIS aided covert communication in UA V air- ground networks,”IEEE J. Sel. Areas Commun., vol. 43, no. 1, pp. 245– 258, Jan. 2025

    work page 2025

  30. [30]

    DISCO might not be funky: Random intelligent reflective surface configurations that attack,

    H. Huanget al., “DISCO might not be funky: Random intelligent reflective surface configurations that attack,”IEEE Wireless Commun., vol. 31, no. 5, pp. 76–82, Oct. 2024

    work page 2024

  31. [31]

    Channel reciprocity attacks using intelligent surfaces with non-diagonal phase shifts,

    H. Wang, Z. Han, and A. L. Swindlehurst, “Channel reciprocity attacks using intelligent surfaces with non-diagonal phase shifts,”IEEE Open J. Commun. Soc., vol. 5, pp. 1469–1485, 2024

    work page 2024

  32. [32]

    Simultaneously exposing and jamming covert communications via disco reconfigurable intelligent surfaces,

    H. Huang, H. Zhang, Y . Cai, D. Niyato, A. L. Swindlehurst, and Z. Han, “Simultaneously exposing and jamming covert communications via disco reconfigurable intelligent surfaces,”IEEE J. Sel. Areas Commun., vol. 44, pp. 1708–1721, Feb. 2026

    work page 2026

  33. [33]

    Normalizing flows: An introduction and review of current methods,

    I. Kobyzev, S. J. D. Prince, and M. A. Brubaker, “Normalizing flows: An introduction and review of current methods,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 43, no. 11, pp. 3964–3979, Nov. 2021

    work page 2021

  34. [34]

    Density estimation using Real NVP,

    L. Dinh, J. Sohl-Dickstein, and S. Bengio, “Density estimation using Real NVP,” inProc. 5th Int. Conf. Learn. Represent. (ICLR), Toulon, France, Apr. 2017

    work page 2017

  35. [35]

    Neural spline flows,

    C. Durkan, A. Bekasov, I. Murray, and G. Papamakarios, “Neural spline flows,” inAdv. Neural Inf. Process. Syst. 32 (NeurIPS), Vancouver, BC, Canada, Dec. 2019, pp. 7509–7520

    work page 2019

  36. [36]

    Intelligent reflecting surface aided multi-user communication: Capacity region and deployment strategy,

    S. Zhang and R. Zhang, “Intelligent reflecting surface aided multi-user communication: Capacity region and deployment strategy,”IEEE Trans. Commun., vol. 69, no. 9, pp. 5790–5806, Sep. 2021

    work page 2021

  37. [37]

    Disco intelligent reflecting surfaces: Active channel aging for fully- passive jamming attacks,

    H. Huang, Y . Zhang, H. Zhang, Y . Cai, A. L. Swindlehurst, and Z. Han, “Disco intelligent reflecting surfaces: Active channel aging for fully- passive jamming attacks,”IEEE Trans. Wireless Commun., vol. 23, no. 1, pp. 806–819, Jan. 2024

    work page 2024

  38. [38]

    Anti-jamming precoding against disco intelligent reflecting surfaces based fully-passive jamming attacks,

    H. Huanget al., “Anti-jamming precoding against disco intelligent reflecting surfaces based fully-passive jamming attacks,”IEEE Trans. Wireless Commun., vol. 23, no. 8, pp. 9315–9329, Aug. 2024

    work page 2024

  39. [39]

    Non-stationary channel estimation for extremely large-scale MIMO,

    Y . Chen and L. Dai, “Non-stationary channel estimation for extremely large-scale MIMO,”IEEE Trans. Wireless Commun., vol. 23, no. 7, pp. 7683–7697, Jul. 2024

    work page 2024

  40. [40]

    Channel estimation for extremely large-scale MIMO: Far-field or near-field?

    M. Cui and L. Dai, “Channel estimation for extremely large-scale MIMO: Far-field or near-field?”IEEE Trans. Commun., vol. 70, no. 4, pp. 2663–2677, Apr. 2022

    work page 2022

  41. [41]

    On the product of indepen- dent complex Gaussians,

    N. O’Donoughue and J. M. F. Moura, “On the product of indepen- dent complex Gaussians,”IEEE Trans. Signal Process., vol. 60, no. 3, pp. 1050–1063, Mar. 2012. [42]Evolved Universal Terrestrial Radio Access (E-UTRA); Further Ad- vancements for E-UTRA Physical Layer Aspects, 3GPP TR 36.814, Mar. 2010

    work page 2012

  42. [42]

    Intelligent reflecting surface: Practical phase shift model and beamforming optimization,

    S. Abeywickrama, R. Zhang, Q. Wu, C. Yuen, “Intelligent reflecting surface: Practical phase shift model and beamforming optimization,” IEEE Trans. Commun., vol. 68, no. 9, pp. 5849–5863, Sept. 2020

    work page 2020