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REVIEW 5 major objections 6 minor 30 references

Heterogeneous Secure Transmissions in IRS-Assisted NOMA Communications: CO-GNN Approach

T0 review · 5 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A graph neural network can jointly set beamforming, power, and IRS phase shifts from received signals alone, beating alternating optimization in secure IRS-NOMA.

desk verdict Novel GNN for secure IRS-NOMA, but the CSI-free claim is undermined by a circular input-output dependence and a train-test mismatch. read the letter →

arxiv 2506.05381 v1 pith:HDOPYTJQ submitted 2025-06-03 cs.CR cs.ITeess.SPmath.IT

Linlin Liang , Zongkai Tian , Haiyan Huang , Xiaoyan Li , Zhisheng Yin , Dehua Zhang , Nina Zhang , Wenchao Zhai This is my paper
classification cs.CRcs.ITeess.SPmath.IT
keywords intelligentreflectingsurfacenon-orthogonalmultipleaccessphysicallayersecuritysecrecyrategraphneuralnetworksbeamformingoptimizationpowerallocation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that a graph neural network, called CO-GNN, can jointly choose the base-station beamforming, NOMA power split, and IRS phase shifts in an IRS-assisted NOMA system by reading the received signals directly, with no channel estimation. The setting includes two kinds of attackers: external eavesdroppers outside the NOMA pairing and internal ones that are legitimate users overhearing other users' signals. Training the network with the negative sum secrecy rate as the loss is claimed to maximize secrecy performance, and simulations are said to show CO-GNN reaching the highest secrecy rate among the compared schemes, roughly 40% above the alternating-optimization baseline for external eavesdropping and 30% for internal eavesdropping. If true, the result would offer a lower-complexity, CSI-free way to secure IRS-NOMA links in dynamic networks.

What carries the argument

The load-bearing mechanism is the CO-GNN graph representation and its end-to-end training loss. The IRS is node 0 and the $K$ users are nodes $1,\dots,K$; user-node features are the real and imaginary parts of the received signal $Y_k$, and the IRS node feature is their mean. Two message-passing layers update user nodes by mean-pooling neighbor messages and the IRS node by max-pooling across users, so that the IRS representation emphasizes the user most exposed to eavesdropping. A fully connected output layer maps the final representations to $\boldsymbol{\Phi}\in\mathbb{C}^N$ with unit-modulus entries, $\mathbf{w}\in\mathbb{C}^{M\times K}$ normalized to satisfy the power constraint, and $\mathbf{a}\in\mathbb{R}^K$ on the probability simplex. Training with $L=-\sum_k R_k^{\mathrm{sec}}$ as loss is what the paper argues lets the network jointly suppress both external and internal eavesdroppers without explicit channel estimation.

What would settle it

Train CO-GNN on channels drawn from one distribution, such as user coordinates inside the training box with a Rician factor of 10 dB, and evaluate it on channels from a clearly different distribution, such as users outside that box or a Rician factor of 5 dB, comparing against the alternating-optimization baseline; if the secrecy-rate advantage shrinks or reverses, the learned received-signal-to-parameter map does not generalize and the CSI-free claim fails.

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Extended reading notes

Core claim

The paper's central claim is that the non-convex joint optimization of beamforming vectors $\mathbf{w}$, NOMA power allocation $\mathbf{a}$, and IRS phase shifts $\boldsymbol{\Phi}$ for maximizing the sum secrecy rate can be replaced by a learned map $g(\cdot)$ from received signals $\mathbf{Y}$ to those parameters. CO-GNN represents the IRS as node 0 and the $K$ users as nodes $1,\ldots,K$, passes the received-signal features through two message-passing layers with mean-pooling for user nodes and max-pooling for the IRS node, and outputs unit-modulus phase shifts, a normalized beamforming matrix, and power factors summing to one. The loss is the negative sum secrecy rate $-\sum_k R_k^{\mathrm{sec}}$, where $R_k^{\mathrm{sec}}=[R_k-R_{\phi\to k}]^+$ with the eavesdropper rate taken from either an external or an internal node. Under this training, simulations show the sum secrecy rate increasing with transmit power, number of IRS elements, and number of antennas, with CO-GNN outperforming all benchmarks, including alternating optimization.

Load-bearing premise

The paper assumes that a user's received signal $y_k$, which is produced by the very beamforming, power allocation, and phase shifts the network must output, carries enough information for the network to recover the optimal $(\mathbf{w},\mathbf{a},\boldsymbol{\Phi})$ without channel estimation, and that this fixed-point-like mapping is learnable and stable.

Editorial extensions

If this is right

  • If CO-GNN works as claimed, secure IRS-NOMA operation no longer requires explicit channel estimation at deployment time, because the received signal itself is the network input.
  • The paper's curves imply that adding IRS elements, transmit antennas, or transmit power all improve the secrecy rate under both external and internal eavesdropping, with CO-GNN consistently above the compared schemes.
  • CO-GNN's online complexity of $O((3\times 3+L)d_{\mathrm{MLP}}T_R)$ is much lower than the AO baseline's $O(I_\lambda I_w K M^3+K^2N^2+P_o t)$, so the method is positioned for real-time resource allocation.
  • The permutation invariance and equivariance properties of the graph construction allow the same trained network to handle different numbers of users, easing scaling to larger NOMA groups.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural stress test the paper does not run is to train on one channel distribution and test on another, such as different user locations or a different Rician K-factor; the claim that the received signal encapsulates enough information would be falsified if the secrecy-rate gain over alternating optimization disappears out of distribution.
  • Because training still uses simulated channel realizations to compute the loss, the no-channel-estimation property holds only at inference; the cost of obtaining realistic training data is left unquantified.
  • The max-pooling aggregation at the IRS node encodes the assumption that the most exposed user dominates the eavesdropping risk; with colluding or multiple eavesdroppers this design choice may need to be revisited.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 6 minor

Summary. The manuscript proposes CO-GNN, a graph neural network that maps received signals directly to BS beamforming, NOMA power allocation, and IRS phase shifts in an IRS-assisted NOMA system with both external and internal eavesdroppers, with the objective of maximizing the sum secrecy rate. The paper claims that this approach eliminates the need for channel estimation, is scalable, and outperforms alternating optimization and several GNN-based ablations, and the claims are supported by simulations for K=2 users, M=5 antennas, and N=10-100 IRS elements. The core contribution is the end-to-end learned mapping g(·) from received-signal features to the optimization variables.

Significance. If the method worked as claimed, a CSI-free, low-complexity GNN for secure IRS-NOMA would be a useful alternative to alternating optimization in dynamic settings. The paper does formulate a relevant problem (joint beamforming, power allocation, and phase-shift optimization with two eavesdropping modes) and includes ablation studies and a complexity comparison, which are positive elements. However, the central claim rests on an input representation that depends on the very outputs the network must produce, and the training procedure uses full CSI while inference is claimed to be CSI-free; the reported secrecy-rate gains are therefore not established. A redefinition of the network input or a rigorous fixed-point formulation, together with a statistical evaluation, would be needed before the significance of the contribution can be assessed.

major comments (5)
  1. [Section III.B.1, Eq. (20)] The central claim of a CSI-free mapping g(·) is not well posed. Y_k in Eq. (12) is a scalar that depends on the current (w,a,Φ), on the random data symbols s_i, and on noise, not only on the channel; at inference time the network must output (w,a,Φ) before Y can be measured, yet Y is the input, and no initial configuration, iterative scheme, or fixed-point condition is specified. For K=2, M=5, N=100, each user node receives two real scalars while the output contains 2M beamforming entries, K power coefficients, and N phase shifts, so the claimed map is massively underdetermined without the structural assumptions that are never stated. This directly undermines the abstract's claim that CO-GNN 'eliminates the need for channel estimation.'
  2. [Algorithm 1, lines 15–17] The training procedure contradicts the CSI-free claim. The loss is computed as LIN(HR, HI, w, a, Φ) and LEX(HR, HI, w, a, Φ) using true channel matrices HR and HI, so full CSI is available during training, while the text claims that deployment requires no channel estimation; the paper provides no generalization argument that a network trained on H can operate from Y alone. In addition, Y is initialized to 0 and is not updated when w, a, and Φ change during the training loop, so the input distribution at training time is inconsistent with the closed-loop dependence expressed in Eq. (12).
  3. [Section III.C, Eqs. (30)–(32)] The convergence guarantee is not a valid proof. The Lipschitz condition in Eq. (31) together with the Adam optimizer does not imply monotonic decrease of the loss or convergence to a local minimum for a non-convex objective, and the [x]+ operator in Eq. (18) is non-differentiable at 0, so the assertion in Eq. (32) that the gradient 'always exists' is false as written. The training section should either provide a rigorous convergence argument or explicitly state that only empirical convergence is observed.
  4. [Problem (19) and Eq. (30)] The constraint Rsec ≥ Rmin is part of the optimization problem but is absent from the loss function and from Algorithm 1. The text in Section II.B claims that CO-GNN 'dynamically adjusts' resources to meet Rmin, but no penalty term, projection, or constraint handling mechanism is described, so the fairness guarantee is unsupported.
  5. [Section IV.B, Figs. 4–9] The performance claims are based on single-trial point estimates with no confidence intervals, error bars, or multiple-seed reporting, so the statements that CO-GNN 'significantly outperforms' and the quantitative improvements of 40% and 30% are not statistically supported. Moreover, there is no comparison against an upper bound or a known near-optimal solution, so the gains could reflect the weakness of the chosen benchmarks rather than the quality of the learned policy.
minor comments (6)
  1. [Eq. (2)] The Rician model uses sqrt(κ/(1+κ)) for both the LOS and NLOS components; the NLOS coefficient should normally be sqrt(1/(1+κ)), otherwise the channel power normalization is inconsistent.
  2. [Table II] The entry 'Number of message passing la' is truncated and should read 'layers'.
  3. [Section IV.C] Figure 11 is referenced in the text before the figure is introduced; the figure order should be adjusted.
  4. [Section IV.D] The complexity expression O((3×3+L)dMLPTR) uses T_R without defining it, and the notation 'PTR' is unclear; the authors should define all symbols.
  5. [Conclusion] The conclusion mentions 'hardware impairments' although no hardware impairment model appears in the system model or simulations; either add such a model or remove the mention.
  6. [Section I.A] The first paragraph contains the typo 'IRS-assited-NOMA' and should read 'IRS-assisted-NOMA'.

Circularity Check

2 steps flagged · score 6.0 of 10

The CO-GNN 'CSI-free received-signal-to-parameters' mapping is self-referential: by Eq. (12) the input Y is defined as a function of the outputs (w,a,Φ) that g(Y) must produce, and the training loss (Eq. 30) is the exact secrecy-rate metric evaluated with true CSI, so the headline performance is not an independent prediction.

  1. self definitional [Section II.B Eq. (19) and Section III.B.1 Eq. (20), with Eq. (12)]
    "By mapping the received signals directly to the optimized beamforming, power allocation and phase shifts for utility maximization, we can bypass the channel estimation ... we can get the optimal beamforming w, power allocation a and phase shifts Φ based directly on the received signals Y by a function g(·). ... yk = PK i=1(hb,k + GΦhr,k)T wk sqrt(Ptak)sk + nk ... the received signal encapsulates ample information pertaining to beamforming, power allocation, and phase shifts."

    Eq. (19) defines the network output as (w,a,Φ)=g(Y), and Eq. (20) uses Y_k as the sole input feature. But Eq. (12) defines Y_k as a function of the beamforming vector w_k, the power allocation a_k, and the IRS phases Φ, together with random symbols s_k and noise. Thus the mapping's input is defined in terms of its own output: one must know (w,a,Φ) to receive the Y from which (w,a,Φ) are to be produced. No initial configuration, iterative update, or fixed-point condition is given, and Algorithm 1 never recomputes Y after w,a,Φ change inside training. The claimed 'ample information pertaining to beamforming, power allocation, and phase shifts' is therefore the circular statement that Y contains the parameters that are defined to produce Y.

  2. fitted input called prediction [Section III.C Eq. (30) and Algorithm 1 (lines 16-17)]
    "The loss function of CO-GNN is defined as the negative value of the sum secrecy rate: L = − PK k=1 Rsec k (w, a, Φ) ... EIN : Calculate loss function LIN (HR, HI, w, a, Φ) using (18); EEX : Calculate loss function LEX (HR, HI, w, a, Φ)."

    The metric reported in Figs. 4-9 (sum secrecy rate) is exactly the negative of the training loss L in Eq. (30), and Algorithm 1 computes that loss from the true channel matrices HR, HI while the model claims to operate without channel estimation. The network is therefore fitted to maximize the very quantity later presented as the result; the 'prediction' that CO-GNN achieves the highest secrecy rate is a fitted value of its own objective. Because the input Y is not recomputed with the output parameters (step 1), the held-out evaluation is not an independent test of the claimed CSI-free mapping.

full rationale

Two linked issues make the central claim circular rather than merely hard to verify. First, the optimization problem Eq. (19) posits a function g that maps received signals Y to (w,a,Φ), while Eq. (12) defines the received signal as a function of those same (w,a,Φ); no fixed-point or initialization procedure is specified, and Algorithm 1 keeps Y fixed during training. The 'CSI-free' claim also depends on this self-referential mapping. Second, the training loss Eq. (30) is the exact negative of the reported sum secrecy rate and is computed with true CSI (HR, HI) in Algorithm 1, so the headline secrecy-rate curves are the optimized objective rather than an independent prediction. No load-bearing self-citations or imported uniqueness theorems appear; the circularity is internal to the problem formulation. Because the input-output self-reference makes the proposed mapping ill-posed, the central performance claim is not supported as a prediction, though the complexity analysis and benchmark comparisons are not themselves circular.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The free parameters are standard neural network hyperparameters chosen by hand. The main load-bearing assumptions are the sufficiency of received signals as input and the convergence behavior of the training procedure, both of which are asserted rather than established.

free parameters (5)
  • Learning rate = 1e-4
    Chosen by hand and tuned in Fig. 3; affects convergence and final secrecy rate.
  • Batch size = 32
    Selected after experiments in Fig. 3; affects training dynamics.
  • Number of message passing layers = 1
    Listed in Table II as 'Number of message passing la'; no ablation shown.
  • Linear embedding dimension d_MLP = 512
    Used in the complexity expression in Section IV.D; chosen without justification.
  • Pooling choices = mean for users, max for IRS
    Mean-pooling and max-pooling are chosen in Eqs. (22)-(25) with heuristic motivations, not derived.
assumptions (5)
  • ad hoc to paper The received signal y_k contains sufficient information to determine the optimal beamforming, power allocation, and phase shifts without explicit channel estimation.
    Asserted in Section III.A ('the received signal encapsulates ample information'). No proof or information-theoretic argument is given, and the signal depends on the network's own outputs.
  • domain assumption The SIC decoding order is based on the combined channel's equivalent channel gain, and users decode in descending channel gain order.
    Standard NOMA assumption invoked in Section II.A; the SINR expressions in Eq. (13) rely on it.
  • domain assumption Channel models: BS-user links follow Rayleigh fading, and IRS-involved links follow Rician fading with a known K-factor.
    Standard channel modeling assumptions in Eqs. (1)-(3); the results are simulation-specific but common in the field.
  • domain assumption Gradient descent with Adam converges to a local minimum of the non-convex loss function.
    Section III.C claims this as a guarantee, but the argument is not a rigorous proof and the loss function includes non-smooth [x]+ operations.
  • domain assumption The internal eavesdropper f, a legitimate user with weaker channel condition, can decode other users' signals via SIC as described by Eq. (17) and the analogous SINR.
    The behavior of the internal Eve is assumed without validation, and the interaction with the legitimate secrecy rate of f is not clearly modeled.

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Pith. "Pith review of Heterogeneous Secure Transmissions in IRS-Assisted NOMA Communications: CO-GNN Approach." pith.science (2026). https://pith.science/paper/HDOPYTJQ

@misc{pith2026250605381,
  author       = {Pith},
  title        = {Pith review of: Heterogeneous Secure Transmissions in IRS-Assisted NOMA Communications: CO-GNN Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HDOPYTJQ}},
  note         = {Machine review of arXiv:2506.05381}
}
read the original abstract

Intelligent Reflecting Surfaces (IRS) enhance spectral efficiency by adjusting reflection phase shifts, while Non-Orthogonal Multiple Access (NOMA) increases system capacity. Consequently, IRS-assisted NOMA communications have garnered significant research interest. However, the passive nature of the IRS, lacking authentication and security protocols, makes these systems vulnerable to external eavesdropping due to the openness of electromagnetic signal propagation and reflection. NOMA's inherent multi-user signal superposition also introduces internal eavesdropping risks during user pairing. This paper investigates secure transmissions in IRS-assisted NOMA systems with heterogeneous resource configuration in wireless networks to mitigate both external and internal eavesdropping. To maximize the sum secrecy rate of legitimate users, we propose a combinatorial optimization graph neural network (CO-GNN) approach to jointly optimize beamforming at the base station, power allocation of NOMA users, and phase shifts of IRS for dynamic heterogeneous resource allocation, thereby enabling the design of dual-link or multi-link secure transmissions in the presence of eavesdroppers on the same or heterogeneous links. The CO-GNN algorithm simplifies the complex mathematical problem-solving process, eliminates the need for channel estimation, and enhances scalability. Simulation results demonstrate that the proposed algorithm significantly enhances the secure transmission performance of the system.

Figures

Figures reproduced from arXiv: 2506.05381 by the authors.

Figure 1
Figure 1. System Model in real-world scenarios. C. Paper Organization The rest of the paper is given as follows. Section II pro￾poses the system model, hardware impairments and problem formulation. Section III gives the designed CO-GNN network for joint optimization. Section IV presents the performance results and the analysis and Section V draws the conclusion. II. SYSTEM MODEL AND PROBLEM FORMULATION A. System Model In this… view at source ↗
Figure 2
Figure 2. Proposed Deep Learning Framework: CO-GNN [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. The convergence of the proposed CO-GNN networks [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: The sum secrecy rate versus transmit power [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: The sum secrecy rate versus the number of reflecting [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: The sum secrecy rate versus the number of reflecting [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 11
Figure 11. Figure 11: The visual simulation setup of experimental configu [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 10
Figure 10. Figure 10: Array response of IRS obtained from CO-GNN over two users with [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 12
Figure 12. Figure 12: Computing time of different schemes. in the T ′′ R in these schemes, leading to slight variations in computational complexity. • As for the AO algorithm, the complexity of the WMMSE algorithm is O (IλIwKM3 ), where Iλ and Iw are the iter￾ation numbers of searching λ a…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.