Pith. sign in

REVIEW 1 major objections 7 minor 51 references

Three signal views beat one for cross-domain modulation recognition

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · glm-5.2

2026-07-10 01:17 UTC pith:PP5HBXEG

load-bearing objection Solid engineering contribution with one real gap in the prior-selection validation the 1 major comments →

arxiv 2607.08031 v1 pith:PP5HBXEG submitted 2026-07-09 eess.SP cs.AI

DKDNet: Dual Knowledge and Data-Driven Network for Cross-Domain Automatic Modulation Classification

classification eess.SP cs.AI
keywords automatic modulation classificationunsupervised domain adaptationsignal prior knowledgemulti-representation learningfeature fusioncross-domain generalizationautocorrelation functionamplitude-phase representation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Deep-learning models that classify radio modulation types degrade badly when channel conditions change between training and deployment. Existing domain-adaptation methods try to fix this by aligning feature distributions statistically, but they treat the signal as generic data and ignore the physical structure that distinguishes one modulation type from another. This paper argues that feeding the network three complementary representations of each received signal—raw in-phase/quadrature samples, amplitude–phase trajectories, and the autocorrelation function—gives the model prior knowledge that is both modulation-discriminative and relatively stable across channel conditions, so that domain alignment has better material to work with. The authors analyze five candidate representations, select these three based on discriminability, cross-domain stability, and complementarity, and design a dual-branch fusion module that adaptively weights them before adversarial domain alignment. On both self-generated and public benchmarks, the approach improves target-domain accuracy by 8–15 percentage points over source-only baselines and by several points over existing domain-adaptation methods.

Core claim

The central claim is that the choice of input representation matters as much as the domain-alignment strategy: raw IQ samples alone preserve waveform detail but are domain-sensitive; amplitude–phase dynamics make modulation structure explicit but still carry channel artifacts; the autocorrelation function cancels constant phase rotation and suppresses additive noise, providing a more domain-stable statistical view. Combining all three through a lightweight adaptive fusion unit, then applying adversarial domain alignment on the fused features, yields consistent accuracy gains that cannot be reproduced by simply scaling up a single-IQ model or by adding arbitrary extra input branches. Ablation

What carries the argument

The mechanism is a three-stage pipeline: (1) each of the three signal representations (IQ, AP, ACF) is independently encoded by parallel 1D-convolution-plus-LSTM branches that share architecture but not parameters, producing same-dimensional embeddings in a unified feature space; (2) a Dynamic Lightweight Fusion Unit combines a global additive branch with an adaptive importance-weighting branch that uses pooled descriptors and sigmoid gating to emphasize informative representation components, then fuses both via element-wise multiplication; (3) the fused features are optimized by a standard classification loss on labeled source data and a gradient-reversal-based adversarial loss for source–t

Load-bearing premise

The theoretical argument for selecting the autocorrelation function as a domain-stable prior relies on simplified channel models—flat fading, constant phase rotation, and white noise—while the authors' own derivation shows that carrier frequency offset is not fully removed but merely transformed into a lag-dependent phase factor. The empirical validation that these three representations provide the best balance of discriminability, stability, and complementarity is conducted,

What would settle it

If replacing AP and ACF with two arbitrary projected IQ views of the same dimensionality were to match or exceed DKDNet's cross-domain accuracy, or if scaling a single-IQ model to equivalent parameter count were to close the performance gap, the central claim that domain-stable signal priors (rather than model capacity or input dimensionality) drive the improvement would be falsified.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Share X Bluesky LinkedIn Reddit HN

If this is right

  • The principle that domain-stable structural priors should be selected and fused before domain alignment, rather than relying on alignment alone, could transfer to other signal-classification tasks where physical invariants exist—radar waveform identification, sonar, or biomedical signal classification.
  • The systematic evaluation of candidate representations by discriminability, domain discrepancy, and complementarity provides a template for prior selection in other cross-domain learning problems where multiple sensor views or feature transforms are available.
  • If the autocorrelation function's domain-stability advantages generalize beyond the tested channel models, it could become a standard auxiliary input for robust signal recognition in dynamic environments.
  • The framework's compatibility with different backbone architectures and domain-adaptation objectives suggests that prior-guided representation selection is an orthogonal improvement layer that can stack on top of future UDA advances.

Where Pith is reading between the lines

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

  • If the autocorrelation function's noise-suppression and phase-cancellation properties are the main source of its domain stability, then representations based on higher-order cyclostationary statistics—which capture periodicity at multiple orders—might offer even stronger invariance and could be tested as additional or replacement priors.
  • The finding that simply adding input branches with projected IQ data (information-matched controls) does not improve performance suggests that the benefit is genuinely from the signal-domain priors, not from increased representation dimensionality—a distinction that could guide feature engineering in other multi-view learning settings.
  • The authors' prior selection is validated primarily on their own simulated datasets with configurable impairments; if real-world channel impairments (e.g., nonlinear hardware effects, impulsive noise, time-varying multipath) break the simplified assumptions underlying ACF's stability, the gap between the three-prior combination and simpler baselines may narrow.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 7 minor

Summary. The paper proposes DKDNet, a dual knowledge- and data-driven framework for cross-domain automatic modulation classification (AMC). The central idea is to select three signal representations—IQ, AP, and ACF—as prior-guided inputs, motivated by their discriminability, domain stability, and complementarity, and to fuse them via a Multi-Representation Feature Encoder (MRFE) and a Dynamic Lightweight Fusion Unit (DLFU) under an adversarial domain alignment objective. The authors construct a new simulated dataset series (RML2025) with progressively intensified channel impairments and also evaluate on the public RML22 benchmark. The experimental evaluation is thorough, including ablations isolating prior quality from model capacity, backbone compatibility, UDA-method compatibility, and sample-efficiency analyses.

Significance. The work addresses a practically important problem: cross-domain generalization of AMC under channel-induced distribution shifts. The key conceptual contribution—using physically grounded signal priors to complement data-driven feature alignment—is reasonable and well-motivated. The controlled study in Table V is a notable strength: the IQ+P1+P2 baseline (33.04%) versus IQ+AP+ACF (48.93%) at matched input dimensionality provides strong evidence that the gain comes from meaningful signal priors rather than mere capacity increase. The release of the RML2025 Series datasets and code is a positive step for reproducibility. The framework's compatibility with multiple backbones (Table VIII) and UDA methods (Table IX) demonstrates practical flexibility.

major comments (1)
  1. The empirical justification for selecting IQ, AP, and ACF (Table II) is conducted under a single adaptation setting: AWGN→Ri1. This is load-bearing because the entire architecture is built around these three representations, and the theoretical analysis in §III-B uses simplified channel models (Eq. 7 assumes flat fading; Eq. 12 assumes white noise; Eq. 13 explicitly shows CFO is not removed from ACF but transformed into a lag-dependent phase factor). The RML22 experiment (Table IV) validates the full DKDNet pipeline but does not re-run the prior comparison on that external benchmark. To strengthen the central claim that IQ+AP+ACF is the optimal prior combination, the authors should either (a) re-run the Table II comparison on at least one additional adaptation setting with different channel statistics (e.g., AWGN→Ray3 or Ri1→Ray3), or (b) explicitly acknowledge in §III-B or §IV-C that A1
minor comments (7)
  1. Table I: The 'CFO / SRO' column lists '50 (std 0.01)' for Ri2, Ri3, Ray2, and Ray3, but the text in §IV-B states SRO is set to 50 Hz relative to the 200 kHz sampling rate. It would help to clarify whether the table values refer to CFO, SRO, or both, and to state the units explicitly in the table.
  2. §III-D: The MRFE description mentions 'four one-dimensional convolutional layers with kernel size 1×3, stride 1, and padding 1, producing feature maps with 16, 32, 64, and 2 channels, respectively.' The final channel count of 2 seems unusually small; please confirm this is correct and not a typo.
  3. §III-E, Eq. (23): The fusion output is F = F_global ⊙ F_refined. Since F_global is an element-wise sum of three feature vectors and F_refined is a 1×1 convolution output, please clarify whether the element-wise multiplication is intended as a gating mechanism and briefly justify this design choice.
  4. Fig. 2: The y-axis labels and legend are small. Please ensure font sizes are adequate for print.
  5. Table II: The 'All reps.' row (IQ+AP+DFT+ACF+CD) achieves the highest H-score (0.437) but lower adapted accuracy (45.61%) than IQ+AP+ACF (47.58%). This is discussed in the text, but it would strengthen the narrative to explicitly note that H-score alone is not a sufficient selection criterion.
  6. §IV-A: The GRL coefficient λ is listed as a free parameter but its value is not stated in the experimental setup. Please state the value used.
  7. The paper uses 'compact' to describe the selected prior set and 'lightweight' for DLFU. Given that DKDNet has 237.24K parameters and 29.66M FLOPs (Table V), it would be helpful to contextualize these against typical AMC model sizes to substantiate the 'lightweight' claim.

Circularity Check

0 steps flagged

No significant circularity: prior selection uses independent metrics (H-score, MMD) and theoretical analysis derived from first principles, not fitted to final accuracy.

full rationale

The paper's derivation chain is largely self-contained. The prior selection (IQ, AP, ACF) is justified through two independent mechanisms: (1) theoretical analysis in Section III-B deriving representation properties from the signal model in Eq. (1) using standard signal processing identities (e.g., ACF canceling constant phase rotation in Eq. (10), suppressing white noise in Eq. (12), CFO transforming to a lag-dependent phase factor in Eq. (13)); and (2) empirical evaluation in Table II using H-score (class discriminability) and MMD (domain discrepancy) as selection criteria—neither of which is the final classification accuracy being optimized. The controlled study in Table V (IQ+P1+P2 at 33.04% vs. IQ+AP+ACF at 48.93%) further confirms the gain comes from meaningful signal priors rather than mere capacity increase. The RML2025 Series datasets are author-generated, and prior selection is validated on only one setting (AWGN→Ri1), which is a generalization concern but not a circularity issue—the selection metrics are structurally independent of the final performance metric. No self-citation chain is load-bearing for the central claim. The theoretical derivations use standard signal processing results, not the authors' own prior theorems. The only minor self-citation is the authors' prior work [21], [23], [45] on related AMC methods, but these are cited for context, not as the mathematical foundation for the present claims. The derivation does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

6 free parameters · 4 axioms · 2 invented entities

No new physical entities or forces are postulated. The invented entities are architectural components and datasets, both with falsifiable handles.

free parameters (6)
  • GRL coefficient λ = not specified
    Controls the strength of gradient reversal in the domain discriminator (§III-F). Value or schedule not stated in the paper.
  • DLFU MLP hidden dimensions = not specified
    Architecture of the MLPs in Eq. (21) for importance estimation is not detailed.
  • Dropout rate = 0.5
    Applied after each linear layer in the classifier (§IV-A). Standard choice, not tuned.
  • Learning rate = 5e-4
    Fixed learning rate for Adam optimizer (§IV-A).
  • LSTM hidden size = 128
    Hidden size of the final LSTM layer in each MRFE branch (§III-D).
  • Conv channel sizes = [16, 32, 64, 2]
    Output channels of the four 1D conv layers in MRFE (§III-D). The final 2-channel output seems unusually small and may be a typo for 128 or 256.
axioms (4)
  • domain assumption Source and target domains share the same modulation label space (closed-set assumption)
    Stated in §III-A: Y_s = Y_t = Y. This excludes open-set or partial-set domain adaptation scenarios.
  • domain assumption The signal model in Eq. (1) captures the dominant sources of distribution shift
    The model includes amplitude scaling, timing offset, CFO, phase offset, multipath fading, and AWGN. Other impairments (e.g., nonlinear distortion, interference) are not modeled.
  • ad hoc to paper Flat-fading approximation is sufficient to illustrate ACF stability
    Eq. (7) neglects timing offset and noise to derive Eq. (10). The paper acknowledges this is 'for illustration' but uses it to support the ACF selection.
  • domain assumption H-score and MMD are adequate proxies for discriminability and domain discrepancy
    Used in §III-B and Table II to justify prior selection. Alternative metrics (e.g., Wasserstein distance, mutual information) might yield different rankings.
invented entities (2)
  • RML2025 Series datasets independent evidence
    purpose: Controlled cross-domain AMC benchmark with progressively intensified channel impairments
    Publicly released on GitHub with full configuration parameters in Table I. Can be independently regenerated and evaluated.
  • DLFU (Dynamic Lightweight Fusion Unit) independent evidence
    purpose: Adaptive fusion of multi-representation features via global additive + attention-weighted branches
    Ablation in Table VI compares against simpler fusion strategies, showing DLFU outperforms concatenation, addition, and attention-only fusion.

pith-pipeline@v1.1.0-glm · 24037 in / 4038 out tokens · 166846 ms · 2026-07-10T01:17:35.748730+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of DKDNet: Dual Knowledge and Data-Driven Network for Cross-Domain Automatic Modulation Classification." pith.science (2026). https://pith.science/paper/PP5HBXEG

@misc{pith2026260708031,
  author       = {Pith},
  title        = {Pith review of: DKDNet: Dual Knowledge and Data-Driven Network for Cross-Domain Automatic Modulation Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PP5HBXEG}},
  note         = {Machine review of arXiv:2607.08031}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

The dynamics of communication environments induce significant distribution shifts across domains, challenging the generalization of deep learning-based automatic modulation classification (AMC) models. While existing UDA methods alleviate this problem by aligning source and target features, they give limited consideration to modulation-specific structures that remain informative across domain conditions. In this paper, we consider signal prior knowledge, grounded in communication protocols and physical principles, as a potential way to enhance cross-domain representation learning. Given that different priors may vary in modulation discriminability, domain stability, and complementarity, this paper first analyzes five commonly adopted signal representations that instantiate different signal priors. From them, in-phase/quadrature (IQ), amplitude--phase (AP), and autocorrelation function (ACF) are selected as compact prior-guided inputs. Based on that, a dual knowledge and data-driven network (DKDNet) is proposed for cross-domain AMC. The multi-representation feature encoder (MRFE) and dynamic lightweight fusion unit (DLFU) are designed to achieve unified representation learning and adaptive feature fusion, and the resulting fused features are optimized with modulation classification and adversarial domain alignment objectives. Experiments on both simulated and public datasets validate the rationality of the prior selection and demonstrate the superiority of the proposed method.

Figures

Figures reproduced from arXiv: 2607.08031 by Chenxu Wang, Hanlin Mo, Hantong Xing, Licheng Jiao, Lirong Han, Shuang Wang.

Figure 1
Figure 1. Figure 1: Framework of the proposed DKDNet. Source samples [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Confusion matrices of DKDNet under the AWGN [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Performance comparison between DKDNet and baseline methods [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Class-level t-SNE visualization of target-domain features under the [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Domain-level t-SNE visualization before and after adaptation under [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Evaluation of sample efficiency for DKDNet and the IQ-only baseline [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

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

51 extracted references · 51 canonical work pages

  1. [1]

    Robust generative defense against adversarial attacks in intelligent modulation recognition,

    Z. Zhang, L. Ma, M. Liu, Y . Chen, N. Zhao, and A. Nallanathan, “Robust generative defense against adversarial attacks in intelligent modulation recognition,”IEEE Transactions on Cognitive Communications and Networking, vol. 11, no. 2, pp. 1041–1052, 2025

  2. [2]

    Edge-learning-based col- laborative automatic modulation classification for hierarchical cognitive radio networks,

    P. Dong, C. He, S. Gao, F. Zhou, and Q. Wu, “Edge-learning-based col- laborative automatic modulation classification for hierarchical cognitive radio networks,”IEEE Internet of Things Journal, vol. 11, no. 21, pp. 34 443–34 454, 2024

  3. [3]

    A spatiotemporal multi-channel learning framework for automatic modulation recognition,

    J. Xu, C. Luo, G. Parr, and Y . Luo, “A spatiotemporal multi-channel learning framework for automatic modulation recognition,”IEEE Wire- less Communications Letters, vol. 9, no. 10, pp. 1629–1632, 2020

  4. [4]

    Learn- ing the unknown: Improving modulation classification performance in unseen scenarios,

    E. Perenda, S. Rajendran, G. Bovet, S. Pollin, and M. Zheleva, “Learn- ing the unknown: Improving modulation classification performance in unseen scenarios,” inIEEE INFOCOM 2021 - IEEE Conference on Computer Communications, 2021, pp. 1–10

  5. [5]

    Deep learning models for wireless signal classification with distributed low- cost spectrum sensors,

    S. Rajendran, W. Meert, D. Giustiniano, V . Lenders, and S. Pollin, “Deep learning models for wireless signal classification with distributed low- cost spectrum sensors,”IEEE Transactions on Cognitive Communica- tions and Networking, vol. 4, no. 3, pp. 433–445, 2018

  6. [6]

    Real-time radio technology and modulation classification via an lstm auto-encoder,

    Z. Ke and H. Vikalo, “Real-time radio technology and modulation classification via an lstm auto-encoder,”IEEE Transactions on Wireless Communications, vol. 21, no. 1, pp. 370–382, 2022

  7. [7]

    Survey of automatic mod- ulation classification techniques: classical approaches and new trends,

    O. Dobre, A. Abdi, Y . Bar-Ness, and W. Su, “Survey of automatic mod- ulation classification techniques: classical approaches and new trends,” IET Communications, vol. 1, pp. 137–156, 2007

  8. [8]

    Online hybrid likelihood based modulation classification us- ing multiple sensors,

    B. Dulek, “Online hybrid likelihood based modulation classification us- ing multiple sensors,”IEEE Transactions on Wireless Communications, vol. 16, no. 8, pp. 4984–5000, 2017

  9. [9]

    Cooperative mod- ulation classification for multipath fading channels via expectation- maximization,

    J. Zhang, D. Cabric, F. Wang, and Z. Zhong, “Cooperative mod- ulation classification for multipath fading channels via expectation- maximization,”IEEE Transactions on Wireless Communications, vol. 16, no. 10, pp. 6698–6711, 2017

  10. [10]

    Automatic composite-modulation classification using cyclic-paw-print features for cognitive aerospace communications,

    X. Yan, X. Zhong, H.-C. Wu, P. Yang, Q. Wang, and Y . Chen, “Automatic composite-modulation classification using cyclic-paw-print features for cognitive aerospace communications,”IEEE Transactions on Communications, vol. 72, no. 9, pp. 5486–5502, 2024

  11. [11]

    Generalized automatic modulation classification for ofdm systems under unseen synthetic channels,

    S. Huang, J. He, Z. Yang, Y . Chen, S. Chang, Y . Zhang, and Z. Feng, “Generalized automatic modulation classification for ofdm systems under unseen synthetic channels,”IEEE Transactions on Wireless Com- munications, vol. 23, no. 9, pp. 11 931–11 941, 2024. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, JUNE 2026 13

  12. [12]

    A front end for discriminative learning in automatic modulation classification,

    F. C. B. F. Muller, C. Cardoso, and A. Klautau, “A front end for discriminative learning in automatic modulation classification,”IEEE Communications Letters, vol. 15, no. 4, pp. 443–445, 2011

  13. [13]

    Automatic modula- tion classification based on constellation density using deep learning,

    Y . Kumar, M. Sheoran, G. Jajoo, and S. K. Yadav, “Automatic modula- tion classification based on constellation density using deep learning,” IEEE Communications Letters, vol. 24, no. 6, pp. 1275–1278, 2020

  14. [14]

    M-ary frequency shift keying signal classification based-on discrete fourier transform,

    Z. Yu, Y . Shi, and W. Su, “M-ary frequency shift keying signal classification based-on discrete fourier transform,” inIEEE Military Communications Conference, 2003. MILCOM 2003., vol. 2, 2003, pp. 1167–1172 V ol.2

  15. [15]

    A hybrid approach for cross-dataset modulation recognition of wireless inter- ference,

    Z. Zhang, H. Li, Y . Li, Z. Chen, S. Wang, and T. Luo, “A hybrid approach for cross-dataset modulation recognition of wireless inter- ference,”IEEE Transactions on Communications, vol. 73, no. 12, pp. 13 677–13 690, 2025

  16. [16]

    Automatic modulation classification using combination of genetic programming and knn,

    M. W. Aslam, Z. Zhu, and A. K. Nandi, “Automatic modulation classification using combination of genetic programming and knn,”IEEE Transactions on Wireless Communications, vol. 11, no. 8, pp. 2742– 2750, 2012

  17. [17]

    End-to-end learning from spectrum data: A deep learning approach for wireless signal identification in spectrum monitoring applications,

    M. Kulin, T. Kazaz, I. Moerman, and E. De Poorter, “End-to-end learning from spectrum data: A deep learning approach for wireless signal identification in spectrum monitoring applications,”IEEE Access, vol. 6, pp. 18 484–18 501, 2018

  18. [18]

    Modulation classification based on signal constellation diagrams and deep learning,

    S. Peng, H. Jiang, H. Wang, H. Alwageed, Y . Zhou, M. M. Sebdani, and Y .-D. Yao, “Modulation classification based on signal constellation diagrams and deep learning,”IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 3, pp. 718–727, 2019

  19. [19]

    Exploitation of spectral redundancy in cyclostationary signals,

    W. Gardner, “Exploitation of spectral redundancy in cyclostationary signals,”IEEE Signal Processing Magazine, vol. 8, no. 2, pp. 14–36, 1991

  20. [20]

    Convolutional radio mod- ulation recognition networks,

    T. J. O’Shea, J. Corgan, and T. C. Clancy, “Convolutional radio mod- ulation recognition networks,” inEngineering Applications of Neural Networks: 17th International Conference, EANN 2016, Aberdeen, UK, September 2-5, 2016, Proceedings 17. Springer, 2016, pp. 213–226

  21. [21]

    Psrnet: Few-shot automatic modulation classification under potential domain differences,

    H. Xing, S. Wang, J. Wang, L. Mei, Y . Xu, H. Zhou, H. Xu, and L. Jiao, “Psrnet: Few-shot automatic modulation classification under potential domain differences,”IEEE Transactions on Wireless Communications, vol. 24, no. 1, pp. 371–384, 2025

  22. [22]

    Goldsmith,Wireless communications

    A. Goldsmith,Wireless communications. Cambridge university press, 2005

  23. [23]

    Sigda: A superimposed domain adaptation framework for automatic modulation classification,

    S. Wang, H. Xing, C. Wang, H. Zhou, B. Hou, and L. Jiao, “Sigda: A superimposed domain adaptation framework for automatic modulation classification,”IEEE Transactions on Wireless Communications, vol. 23, no. 10, pp. 13 159–13 172, 2024

  24. [24]

    A contrastive learner for automatic modu- lation classification,

    M. Du, J. Pan, and D. Bi, “A contrastive learner for automatic modu- lation classification,”IEEE Transactions on Wireless Communications, vol. 24, no. 4, pp. 3575–3589, 2025

  25. [25]

    Open set domain adaptation for automatic modulation classification in dynamic communication environments,

    M. Zhang, P. Tang, G. Wei, X. Ni, G. Ding, and H. Wang, “Open set domain adaptation for automatic modulation classification in dynamic communication environments,”IEEE Transactions on Cognitive Com- munications and Networking, vol. 10, no. 3, pp. 852–865, 2024

  26. [26]

    Deep modulation recognition in an unknown environment,

    L. Li, Q. Peng, P. C. Cosman, and L. B. Milstein, “Deep modulation recognition in an unknown environment,” in2019 53rd Asilomar Con- ference on Signals, Systems, and Computers, 2019, pp. 1045–1048

  27. [27]

    A survey of deep transfer learning in automatic modulation classification,

    X. Wang, Y . Zhao, and Z. Huang, “A survey of deep transfer learning in automatic modulation classification,”IEEE Transactions on Cognitive Communications and Networking, vol. 11, no. 3, pp. 1357–1381, 2025

  28. [28]

    S. S. Haykin,Digital communications. Wiley New York, 1988

  29. [29]

    Attentive siamese networks for automatic modulation classification based on multitiming constellation diagrams,

    Y . Mao, Y .-Y . Dong, T. Sun, X. Rao, and C.-X. Dong, “Attentive siamese networks for automatic modulation classification based on multitiming constellation diagrams,”IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 9, pp. 5988–6002, 2023

  30. [30]

    Multi-view discriminant framework for automatic modulation open set recognition,

    J. Hou, D. Xu, F. Song, Z. Chen, Q. Xuan, S. Zheng, Y . Lin, and X. Yang, “Multi-view discriminant framework for automatic modulation open set recognition,”IEEE Transactions on Communications, vol. 73, no. 6, pp. 4378–4393, 2025

  31. [32]

    Data and knowledge dual-driven automatic modulation classification for 6g wire- less communications,

    R. Ding, F. Zhou, Q. Wu, C. Dong, Z. Han, and O. A. Dobre, “Data and knowledge dual-driven automatic modulation classification for 6g wire- less communications,”IEEE Transactions on Wireless Communications, vol. 23, no. 5, pp. 4228–4242, 2024

  32. [33]

    A survey of modulation classification using deep learning: Signal representation and data preprocessing,

    S. Peng, S. Sun, and Y .-D. Yao, “A survey of modulation classification using deep learning: Signal representation and data preprocessing,”IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 12, pp. 7020–7038, 2022

  33. [34]

    Revolution of wireless signal recognition for 6g: Recent advances, challenges and future directions,

    H. Zhang, F. Zhou, H. Du, Q. Wu, and C. Yuen, “Revolution of wireless signal recognition for 6g: Recent advances, challenges and future directions,”IEEE Communications Surveys & Tutorials, vol. 28, pp. 3521–3563, 2026

  34. [35]

    Automatic modulation classification: A deep learning enabled approach,

    F. Meng, P. Chen, L. Wu, and X. Wang, “Automatic modulation classification: A deep learning enabled approach,”IEEE Transactions on Vehicular Technology, vol. 67, no. 11, pp. 10 760–10 772, 2018

  35. [36]

    Statistical spectral analysis—a nonprobabilistic theory,

    W. A. Gardner and E. A. Robinson, “Statistical spectral analysis—a nonprobabilistic theory,” 1989

  36. [37]

    Toward next-generation signal intelligence: A hybrid knowledge and data-driven deep learning framework for radio signal classification,

    S. Zheng, X. Zhou, L. Zhang, P. Qi, K. Qiu, J. Zhu, and X. Yang, “Toward next-generation signal intelligence: A hybrid knowledge and data-driven deep learning framework for radio signal classification,” IEEE Transactions on Cognitive Communications and Networking, vol. 9, no. 3, pp. 564–579, 2023

  37. [38]

    Automatic modulation identification based on the probability density function of signal phase,

    Q. Shi and Y . Karasawa, “Automatic modulation identification based on the probability density function of signal phase,”IEEE Transactions on Communications, vol. 60, no. 4, pp. 1033–1044, 2012

  38. [39]

    Deep neural network architectures for modulation classification,

    X. Liu, D. Yang, and A. E. Gamal, “Deep neural network architectures for modulation classification,” in2017 51st Asilomar Conference on Signals, Systems, and Computers, 2017, pp. 915–919

  39. [40]

    Multitask-learning- based deep neural network for automatic modulation classification,

    S. Chang, S. Huang, R. Zhang, Z. Feng, and L. Liu, “Multitask-learning- based deep neural network for automatic modulation classification,” IEEE Internet of Things Journal, vol. 9, no. 3, pp. 2192–2206, 2022

  40. [41]

    Data-driven deep learning for automatic modulation recognition in cognitive radios,

    Y . Wang, M. Liu, J. Yang, and G. Gui, “Data-driven deep learning for automatic modulation recognition in cognitive radios,”IEEE Transac- tions on Vehicular Technology, vol. 68, no. 4, pp. 4074–4077, 2019

  41. [42]

    Automatic modulation classification based on joint feature map and convolutional neural network,

    F. Wang, C. Yang, S. Huang, and H. Wang, “Automatic modulation classification based on joint feature map and convolutional neural network,”IET Radar, Sonar & Navigation, vol. 13, no. 6, pp. 998–1003, 2019

  42. [43]

    Domain adaptation-based automatic modulation recognition,

    T. Li and Y . Xiao, “Domain adaptation-based automatic modulation recognition,”Scientific Programming, vol. 2021, no. 1, p. 4277061, 2021

  43. [44]

    Adversarial transfer learning for deep learning based automatic modulation classification,

    K. Bu, Y . He, X. Jing, and J. Han, “Adversarial transfer learning for deep learning based automatic modulation classification,”IEEE Signal Processing Letters, vol. 27, pp. 880–884, 2020

  44. [45]

    Imbalanced domain adaptation for automatic modulation classification,

    L. Mei, S. Wang, H. Xing, C. Wang, Y . Xu, and H. Zhou, “Imbalanced domain adaptation for automatic modulation classification,”IEEE Wire- less Communications Letters, vol. 13, no. 11, pp. 3172–3176, 2024

  45. [46]

    Rml22: Realistic dataset generation for wireless modulation classification,

    V . Sathyanarayanan, P. Gerstoft, and A. E. Gamal, “Rml22: Realistic dataset generation for wireless modulation classification,”IEEE Trans- actions on Wireless Communications, vol. 22, no. 11, pp. 7663–7675, 2023

  46. [47]

    Radio machine learning dataset generation with gnu radio,

    T. J. O’shea and N. West, “Radio machine learning dataset generation with gnu radio,” inProceedings of the GNU radio conference, vol. 1, no. 1, 2016

  47. [48]

    Domain generalization via invariant feature representation,

    K. Muandet, D. Balduzzi, and B. Sch ¨olkopf, “Domain generalization via invariant feature representation,” inProceedings of the 30th International Conference on Machine Learning, ser. Proceedings of Machine Learning Research, S. Dasgupta and D. McAllester, Eds., vol. 28, no. 1. Atlanta, Georgia, USA: PMLR, 17–19 Jun 2013, pp. 10–18

  48. [49]

    A kernel two-sample test,

    A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Sch ¨olkopf, and A. Smola, “A kernel two-sample test,”The journal of machine learning research, vol. 13, no. 1, pp. 723–773, 2012

  49. [50]

    Adversarial dis- criminative domain adaptation,

    E. Tzeng, J. Hoffman, K. Saenko, and T. Darrell, “Adversarial dis- criminative domain adaptation,” in2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017, pp. 2962–2971

  50. [51]

    Deep architectures for modulation recog- nition,

    N. E. West and T. O’Shea, “Deep architectures for modulation recog- nition,” in2017 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN), 2017, pp. 1–6

  51. [52]

    Over-the-air deep learning based radio signal classification,

    T. J. O’Shea, T. Roy, and T. C. Clancy, “Over-the-air deep learning based radio signal classification,”IEEE Journal of Selected Topics in Signal Processing, vol. 12, no. 1, pp. 168–179, 2018