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REVIEW 4 major objections 5 minor 50 references

Joint Optimization based on Two-phase GNN in RIS- and DF-assisted MISO Systems with Fine-grained Rate Demands

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A two-phase GNN learns RIS phase shifts, beamforming, and relay selection directly from CSI, while a penalty term balances sum rate against per-user rate demands.

desk verdict The fine-grained rate penalty loss is a reasonable idea, but the GNN as described cannot perform the relay selection or inter-group optimization the paper claims. read the letter →

arxiv 2506.02642 v1 pith:RVP6UR7M submitted 2025-06-03 cs.IT eess.SPmath.IT

Huijun Tang , Jieling Zhang , Zhidong Zhao , Huaming Wu , Hongjian Sun , Pengfei Jiao This is my paper
classification cs.ITeess.SPmath.IT
keywords reconfigurableintelligentsurfacedecode-and-forwardrelaygraphneuralnetworkfine-grainedratedemandsselectionjointbeamformingMISOsystems
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

Users in real networks are clustered and have different rate needs, but most RIS-relay optimization treats them as uniform individuals and maximizes only total throughput. The paper tries to close that gap by proposing a joint optimization model for a RIS- and DF-assisted MISO downlink with grouped users and per-user rate thresholds. It claims that a two-phase graph neural network, fed only channel state information, can simultaneously learn base-station beamforming, RIS phase shifts, relay beamforming, and relay selection, and that a penalty term in the loss lets the network trade sum rate against the fraction of users whose rate demands are met. If right, this would give a low-complexity, unsupervised way to run fine-grained quality-of-service control in RIS-relay networks without solving hard nonconvex problems per channel realization.

What carries the argument

The named central object is the two-phase GNN, a message-passing network with one RIS node and $K$ user nodes in each phase. In phase one, user-node features are built from the BS-to-user and BS-to-RIS channel matrices, the RIS node aggregates them with a mean operation, user nodes aggregate one another with a max operation to capture worst-case interference, and readout layers map the final features to the BS beamforming vectors $g_k$ and quantized RIS phases $\theta_i^1$. Phase two repeats the same structure on the relay-to-user and relay-to-RIS channels to produce relay beamforming $f_k$ and $\theta_i^2$. The carrying mechanism is the penalty-augmented loss: negative sum rate plus $\beta \min(0, \gamma^R_{j,k} - \gamma^R_{th})$ and $\lambda \min(0, R_{i,k} - R^{th}_{i,k})$, which is what makes the satisfaction ratio tunable. As defined, the graph contains no relay nodes, group nodes, or relay-selection variable, so relay selection is performed as a separate step after the GNN readouts rather than as a message-passing output.

What would settle it

Extend the graph with explicit relay nodes and optionally group nodes carrying relay- and group-specific channel features, retrain under the same loss, and compare relay-selection decisions, sum rate, and satisfaction ratios with the original architecture; unchanged performance would indicate the reported relay-selection gains do not come from learned message passing.

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Extended reading notes

Core claim

The paper's central claim is that jointly optimizing both transmission phases of a RIS- and DF-assisted MISO system—active beamforming at the BS and relays, passive phase shifts at the RISs, and the choice of which relay forwards—can be learned end-to-end by a two-phase GNN from CSI, while fine-grained rate demands are enforced through a penalty-augmented loss. The authors define the JOFD-TG algorithm: a first-phase graph outputs the BS beamforming matrix and the first-phase RIS phase shifts, a second-phase graph outputs the relay beamforming matrix and the second-phase phase shifts, and the loss subtracts the sum rate plus penalty terms that activate when a relay SINR or a user rate falls below its threshold. Simulations compare against random phase shifts, particle swarm optimization, and a DNN, and report that the GNN achieves higher sum rate and higher satisfaction ratios, that the fine-grained user-level granularity outperforms coarse- and group-level granularity, and that adjusting the penalty weight can drive the satisfaction ratio toward 100%.

Load-bearing premise

The load-bearing premise is that a message-passing graph containing only one RIS node and $K$ user nodes is enough to represent multiple relays, multiple groups, inter-group competition, and relay selection; the paper specifies no mechanism by which relay identity or group membership enters the learned variables.

Editorial extensions

If this is right

  • If the central claim holds, the same two-phase GNN can be retrained for new deployments without per-realization optimization, since it learns from CSI in an unsupervised way.
  • The penalty parameter $\lambda$ provides a single dial for fairness: increasing it raises the fraction of users meeting their rate thresholds, at some cost in raw sum rate.
  • Fine-grained, per-user thresholds should dominate group-level or coarse thresholds in both sum rate and satisfaction, because the network can allocate resources to individual needs.
  • Relay placement and selection can matter more than RIS phase tuning in this two-phase topology, so system designers should prioritize relay positioning and the relay-selection rule.
  • The model's permutation-invariant aggregation should let it generalize to different numbers of users, with graceful degradation as the training and testing user counts diverge.

Reading between the lines

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

  • Not pursued in the paper: making relay selection an explicit part of the learned graph by adding relay nodes and edges would test whether the reported relay-selection gains actually come from message passing or from the separate post-training selection rule.
  • The penalty-loss idea transfers naturally to other constrained resource-allocation problems where a hard requirement can be softened into a tunable penalty, such as latency or energy constraints in network slicing.
  • One could probe the fairness-optimal operating point by plotting the full trade-off curve of sum rate against satisfaction ratio as the penalty weight varies, and then choosing the weight from an operator-defined service objective.
  • If the graph were extended with group nodes, the claimed inter-group competition might become representable as a learned resource-allocation mechanism rather than an emergent effect of relay selection.
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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

4 major / 5 minor

Summary. The paper considers a downlink MISO system with a multi-antenna base station, multiple RISs, multiple half-duplex DF relays, and users clustered into groups with fine-grained rate thresholds. It formulates a sum-rate maximization problem P1 with power, DF-decoding, rate-threshold, and discrete-phase constraints, and proposes an unsupervised two-phase graph neural network that takes CSI as input and outputs RIS phase shifts, BS beamforming vectors, and relay beamforming vectors. A penalty-based loss is introduced to trade off sum rate against fine-grained rate-demand satisfaction. Simulations compare the method with DNN, PSO, and random baselines and report higher sum rates and satisfaction ratios, plus generalization across different numbers of users.

Significance. If the architecture actually realized the claimed joint optimization, the paper would be a useful contribution: it is among the first in the reviewed comparison to combine group-level inter/intra trade-offs with per-user fine-grained rate demands, and the unsupervised penalty formulation is a simple way to control satisfaction ratio. Strengths include an explicit permutation-invariant feature design, a generalization study in Table IV, and comparison against several baselines. However, the central architectural claim is not supported by the described graph, and there are dimensional errors in the signal model; the experimental results therefore cannot be interpreted as validating the claimed method until these issues are fixed.

major comments (4)
  1. [§IV.A, §IV.B, Algorithm 1] The message-passing graph in both phases is explicitly described as fully connected with K+1 nodes: one RIS node and K user nodes (e.g., 'comprising K+1 nodes... one node dedicated to the RIS... along with K nodes assigned to the users'). There are no relay nodes and no group nodes, and the readouts produce θ_i, g_k, and f_k with no relay index. Since the system model in §III includes J DF relays and I groups, and P1 constraint C2 in (10b) sums over j=1..J of tr(F_j F_j^H), the network cannot represent distinct relay beamforming matrices, relay-selection decisions, or group-level competition. Algorithm 1 line 16 instructs to 'Select the appropriate relay' without specifying a selection variable, node, or output. Consequently the abstract's claim of simultaneously and autonomously learning 'phase shifts, beamforming, and relay selection' is not supported by the described architecture.
  2. [§III.C, §IV.A, §IV.B] No mechanism in the GNN encodes grouping. The graph has one RIS node and K user nodes; no node or aggregation is indexed by group i. The loss functions (29)–(31) include sums over i and group-threshold penalties, but the architecture has no group-level representation, so the claimed modelling of 'intra-group cooperation' and 'inter-group competition' (Section III, Section V.B.3) is not realized by the network. The text states 'inter-group competition is dynamically balanced through relay selection,' but relay selection itself is absent from the graph.
  3. [§III.A, Eqs. (3)–(4)] Equation (3) is dimensionally invalid: H_i θ_i^1 is an M×1 vector while (H^B_{i,k})^T is a 1×M row vector, so the sum and the outer transpose are undefined. This error propagates into the SINR expression (4) and into the input definitions (11) for the first-phase GNN, and it prevents the model from being unambiguously instantiated. All expressions involving (H^B_{i,k})^T need to be corrected, presumably to use H^B_{i,k} or its conjugate transpose in the appropriate inner product.
  4. [§III.A, Eqs. (5)–(8), (29)–(31)] The relay-dependent quantities are not consistently defined. The second-phase SINR γ^(2)_{i,k} in (8) depends only on f_k and has no relay index j, while γ^R_{j,k} in (6) depends on α_k, which itself depends on j; the notation in (6) mixes j and k indices in the denominator. The loss functions sum β over j=1..J of min(0,γ^R_{j,k}−γ^R_th), which either adds the same penalty J times if γ^R_{j,k} does not depend on j, or requires J distinct relay beamformers that the network does not output. The power constraint C2 in (10b) uses F_j while the phase-2 readout outputs f_k ∈ C^L; the relationship between F_j and f_k is never defined. These inconsistencies make the training objective not well matched to P1.
minor comments (5)
  1. [Eq. (30)] The group-granularity loss is written with weight λ, but the following sentence refers to μ as the weight coefficient; the notation should be aligned.
  2. [Fig. 5, Section V.B] The label 'JOFG-Random' appears to be a typo for 'JOFD-Random', and the names JOGD-TG/JOCD-TG are used inconsistently across the text and figures.
  3. [Abstract] The abstract contains 'low date rates', which should be 'low data rates'.
  4. [Table III, Fig. 9] The penalty weights β and λ are fixed at 1000, and only λ is swept in Fig. 9; a similar sweep or ablation for β would better support the claim that the satisfaction ratio is tunable via the penalty parameter.
  5. [Algorithm 1, line 7] The neighbor set N(k) is used, but the graph is fully connected for user nodes; clarifying that N(k) denotes all other users in the fully connected setting would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim is an empirical performance comparison against explicit baselines, and no load-bearing result reduces to its own inputs or to a self-citation chain.

full rationale

The paper's central contribution is an unsupervised GNN trained with an explicit objective in equations (29)-(31), and its claim is that this trained model outperforms random, PSO, and DNN baselines in simulation. That claim is an empirical comparison, not a derivation forced by construction. The penalty terms in the loss functions are defined directly in terms of the same rate thresholds used in the satisfaction-ratio evaluation; this is the intended mechanism of a Lagrangian-style penalty method, and reporting higher satisfaction as lambda increases is a validation that the optimizer enforces its own constraint, not a circular prediction. The GNN architecture in Sections IV.A and IV.B is fully specified by the paper's own equations (17)-(28), and no unverified external result is imported to make the derivation work. The paper cites prior work ([30], [31], [34], [44]) for training setups and system configurations, but these citations are incidental and not load-bearing; none of them supplies a uniqueness theorem or a premise that already contains the paper's conclusion. The most notable gap—Algorithm 1 line 16 states "Select the appropriate relay to calculate the sum rate" without specifying a selection mechanism, and the graph has no relay nodes or relay-indexed outputs—is a representational completeness and correctness concern, not a circularity of the kind defined in this analysis. Accordingly, no circular step is identified.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The central method relies on standard quasi-static Rayleigh/Rician channels, perfect DF decoding, and an unverified assumption that a user-and-RIS-only graph can encode relay selection and inter-group competition. The penalty weights beta and lambda are tuned by inspection of simulation curves, so they are free parameters of the method rather than derived constants.

free parameters (4)
  • penalty weight lambda = 1000 (default), 2000 for near-100% satisfaction
    Chosen by empirical observation in Section V.B.6 and Figure 9 to balance sum rate and constraint satisfaction.
  • relay SINR penalty weight beta = 1000
    Set in Table III; no sensitivity analysis is provided.
  • feature dimension q = 128
    Tunable network parameter selected in Table III.
  • number of node update layers D = 3
    Adjustable parameter set in Table III.
assumptions (3)
  • domain assumption Channels are quasi-static Rician (RIS links) and Rayleigh (other links), and remain constant during the two phases.
    Stated after equation (1) and used throughout the system model.
  • domain assumption DF relays decode all user signals perfectly in the first phase.
    Stated in Section III.A, but this is internally inconsistent with constraint C3 which imposes a relay SINR threshold.
  • ad hoc to paper A graph with one RIS node and K user nodes can represent multiple relays, multiple groups, and relay selection.
    Introduced in Sections IV.A and IV.B without justification; no relay or group nodes appear in the graph.

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Cite this review

Pith. "Pith review of Joint Optimization based on Two-phase GNN in RIS- and DF-assisted MISO Systems with Fine-grained Rate Demands." pith.science (2026). https://pith.science/paper/RVP6UR7M

@misc{pith2026250602642,
  author       = {Pith},
  title        = {Pith review of: Joint Optimization based on Two-phase GNN in RIS- and DF-assisted MISO Systems with Fine-grained Rate Demands},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RVP6UR7M}},
  note         = {Machine review of arXiv:2506.02642}
}
read the original abstract

Reconfigurable intelligent Surfaces (RIS) and half-duplex decoded and forwarded (DF) relays can collaborate to optimize wireless signal propagation in communication systems. Users typically have different rate demands and are clustered into groups in practice based on their requirements, where the former results in the trade-off between maximizing the rate and satisfying fine-grained rate demands, while the latter causes a trade-off between inter-group competition and intra-group cooperation when maximizing the sum rate. However, traditional approaches often overlook the joint optimization encompassing both of these trade-offs, disregarding potential optimal solutions and leaving some users even consistently at low date rates. To address this issue, we propose a novel joint optimization model for a RIS- and DF-assisted multiple-input single-output (MISO) system where a base station (BS) is with multiple antennas transmits data by multiple RISs and DF relays to serve grouped users with fine-grained rate demands. We design a new loss function to not only optimize the sum rate of all groups but also adjust the satisfaction ratio of fine-grained rate demands by modifying the penalty parameter. We further propose a two-phase graph neural network (GNN) based approach that inputs channel state information (CSI) to simultaneously and autonomously learn efficient phase shifts, beamforming, and relay selection. The experimental results demonstrate that the proposed method significantly improves system performance.

Figures

Figures reproduced from arXiv: 2506.02642 by the authors.

Figure 1
Figure 1. Classify device rate demands into three granularities: coarse-grained, [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The proposed downlink communication for RIS-DF assisted MISO systems with multiple user groups, in which a group communicates through an [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. (a) The graph neural network architecture in different phases. Aggregation and combination operations of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The sum rate of different designs with or without [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: The sum rate of different locations of RIS, relays and users [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: The sum rate of different numbers of BS antennas and relay antennas [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: The sum rate of different numbers of RIS elements [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: The sum rate, satisfaction rate and loss of different epochs [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: The sum rate and satisfaction rate of different weight coefficients [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

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Pith tools

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