Neural Channel Knowledge Map Assisted Scheduling Optimization of Active IRSs in Multi-User Systems

Jiangbin Lyu; Liqun Fu; Xintong Chen; Zhenyu Jiang

REVIEW 3 major objections 5 minor 18 references

Neural Channel Knowledge Map Assisted Scheduling Optimization of Active IRSs in Multi-User Systems

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that a Transformer-based channel knowledge map trained on position-tagged historical measurements can predict ergodic spectral efficiency accurately enough for a low-complexity matching scheduler to reach near-optimal max-

desk verdict Useful learned-CKM scheduling framework for multi-AIRS systems, but the 'near-optimal' headline is only proven against the same neural surrogate, so the true gap to optimality remains open. read the letter →

arxiv 2508.07009 v1 pith:NPDN47AT submitted 2025-08-09 cs.IT cs.AIcs.LGmath.IT

Xintong Chen , Zhenyu Jiang , Jiangbin Lyu , Liqun Fu This is my paper · ORCID

classification cs.ITcs.AIcs.LGmath.IT

keywords neuralchannelknowledgemapactiveIRSergodicspectralefficiencypredictionmax-minthroughputschedulingstablematchingiterativebalancingTransformermulti-userOFDMA

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 tries to remove the need for real-time channel state information when scheduling many users across multiple active IRSs. It builds a neural channel knowledge map that learns, from historical measurements tagged with user positions, the distribution of each link's received power and then the resulting ergodic spectral efficiency under any candidate association. On top of that predictor it runs a low-complexity scheduler, SM-IB, to maximize the minimum achievable ergodic throughput subject to each IRS serving one user per slot. The paper demonstrates in simulation that the predictor is more accurate than MLP and LSTM baselines, and that the scheduler comes close to the exact solver's upper bound in max-min throughput while running in milliseconds to a few tenths of a second. A sympathetic reader would see this as making cell-level multi-AIRS scheduling a matter of cheap position-based inference rather than expensive instantaneous CSI acquisition.

What carries the argument

The central object is the neural channel knowledge map, split into two learned maps. LPS-Net is a Transformer encoder with piecewise-linear encoded scalar features and learnable target tokens; it maps a UE position plus AIRS configuration to a vector of 16-quantile CDFs for direct, cascaded, scattered, and dynamic-noise link powers. SE-Net is a Transformer encoder whose input tokens are the CDFs of the direct, serving, non-serving, and noise links for a given association, with a category position embedding, and whose output token is regressed to the ergodic SE. The scheduling machinery is SM-IB: constrained K-Means clusters UEs, Gale-Shapley stable matching forms UE-to-AIRS associations, ite

What would settle it

Train the neural CKM on samples whose user positions lie within a small central region of a cell, then evaluate it for users spread across the full cell or a different cell layout; if predicted ergodic SE drifts from Monte Carlo averages (substantial mean-relative-error growth) at unvisited positions, the spatial-generalization premise fails. A deployment test does the same with live channel measurements: compare the CKM's predicted link-power CDFs against measured ones at positions never seen in training, and check whether the SM-IB schedule computed from them still attains the predicted max-

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Extended reading notes

Core claim

The paper claims that in a single-cell downlink network with multiple active IRSs, the difficult job of scheduling users across IRSs and resource blocks can be separated from instantaneous channel state acquisition. It trains two cascaded Transformer-based networks on historical, position-tagged channel and throughput measurements: LPS-Net predicts per-link power statistics (quantized CDFs of direct, cascaded, scattered, and noise powers) from a UE position and the AIRS configuration, and SE-Net composes those link statistics, under a candidate UE-to-AIRS association, into an ergodic spectral efficiency estimate. On these predicted efficiencies, a three-stage SM-IB scheduler performs stable

Load-bearing premise

The load-bearing premise is spatial generalization: a regression model trained on one dataset of simulated channel samples at known positions is assumed to predict the ergodic spectral efficiency for any user position and system configuration the optimizer will meet; if that learned map is biased outside its training distribution, the scheduler optimizes a wrong objective and the near-optimality result collapses.

Editorial extensions

If this is right

Under the paper's assumptions, cell-level multi-AIRS scheduling can be run from position fixes and historical measurements, so channel-state acquisition delay no longer makes scheduling decisions obsolete.
The cascaded LPS-Net and SE-Net decomposition means the same link-power statistics can be reused for many candidate associations, cutting the cost of evaluating schedules from channel simulation to milliseconds.
SM-IB's hierarchy gives max-min throughput close to the exact solver's upper bound with runtime that stays around a tenth of a second even at 210 users, while the exact solver's runtime grows to tens of minutes.
Since the predictor is trained on link-power CDFs rather than raw channels, the same architecture can adapt to other AIRS phase optimization schemes without retraining the whole stack.
Max-min fairness becomes tractable at cell scale: the paper's numbers suggest that 6 AIRSs and 210 users can be scheduled in about a third of a second, enabling dynamic re-scheduling as users move.

Reading between the lines

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

Because LPS-Net outputs link-power CDFs rather than a single rate, the same trained network could support objectives beyond max-min throughput, such as outage-constrained or delay-sensitive scheduling, by re-designing only the SE-Net head; the paper does not explore this.
The reported near-optimality is demonstrated for a particular inner loop with equal transmit-power allocation and a fixed MCCM beamforming scheme; extending the same neural-CKM predictor to jointly optimize power and phase would require re-running the gap analysis, not just retraining the networks.
A natural testable extension is mobility-aware scheduling: since the map is position-conditioned, predicted SEs for predicted future locations could drive proactive association and slot assignment, sidestepping the latency of fresh CSI at every reposition.
The SE-Net architecture treats link CDFs as a variable-length token set, so the same framework could scale to more or fewer AIRSs than the 2 to 6 shown, provided the training set covers the enlarged configuration space.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The core idea here is genuinely useful: replace per-scheduling CSI acquisition with a learned map from UE positions to ergodic SE, then schedule on top of that map. The cascaded LPS-Net/SE-Net design is new in this context, and the SM-IB heuristic is a sensible, low-complexity matching/balancing scheme. The prediction accuracy numbers (MRE ~8.65% for SE, quantile errors under 1 dB for link power CDFs) beat the MLP/LSTM baselines, and the running-time advantage over Gurobi is dramatic. On the strengths, this paper does a credible job of formulating a hard scheduling problem and showing that a learned surrogate plus a tailored heuristic can make it tractable.

But the central claim—near-optimal max-min throughput—is not actually substantiated. The Gurobi upper bound in Fig. 4 solves (P2) using the same trained neural CKM predictions, not true Monte Carlo ergodic SEs. So the gap shown is the scheduling suboptimality under the surrogate model, and it says nothing about how close SM-IB is to the true optimum under actual channel statistics. The paper never evaluates the final schedules with true MC ergodic SE, nor computes a true upper bound. That is a load-bearing omission. Even in the tested scenario, the optimized objective is the surrogate's, and max-min fairness is exactly the kind of objective where small prediction biases on bottleneck UEs can be exploited.

Other soft spots are more minor but still matter: no error bars on the key scheduling plot, no code or data release, a single QuaDRiGa scenario, and convergence arguments for SM-IB that are heuristic (monotonic improvement, not optimality). The loss weights and hyperparameters look hand-picked rather than systematically tuned. None of this kills the proposal, but it does mean the paper's strongest claim is conditional.

The paper is written coherently, and I don't see internal contradictions. It deserves a serious referee: the problem is real, the architecture is novel enough, and the empirical evidence for prediction quality is decent. But it needs revision before publication: evaluate the final schedules with true MC ergodic SE, add error bars, release the artifacts, and temper the 'near-optimal' language until it's actually measured. I'd bring it to a reading group if the discussion is about learning-based resource allocation; I wouldn't cite it yet for the scheduling result.

Referee Report

3 major / 5 minor

Summary. The paper proposes a scheduling framework for multi-user downlink systems with multiple active IRSs. Because instantaneous CSI acquisition is costly, the authors introduce a neural Channel Knowledge Map (CKM) composed of two cascaded Transformer-based networks: LPS-Net, which predicts per-link power statistics (CDF quantiles) from user position and system configuration, and SE-Net, which maps these statistics and the UE-to-IRS association to an ergodic spectral efficiency. The ergodic SE predictions are then used as the objective in a max-min throughput scheduling problem (P2), solved by a three-stage Stable Matching-Iterative Balancing (SM-IB) algorithm. Numerical results on QuaDRiGa-generated channels report that the neural CKM improves prediction accuracy over MLP/LSTM baselines and that SM-IB closely approaches a Gurobi-based upper bound while reducing runtime.

Significance. If the claims hold, the paper offers a practical way to avoid instantaneous CSI in IRS scheduling, with a modular learning architecture (predict link statistics, then compose them into SE) and a low-complexity heuristic for a difficult mixed-integer problem. The problem is timely and the proposed decomposition is sensible. The paper also provides explicit complexity expressions and a comparison against Gurobi. However, the central validation is incomplete: the reported near-optimality is measured against an upper bound computed on the same neural-network surrogate, not on true channel statistics, and the spatial generalization of the learned CKM is not tested beyond a random split of the same 10,000-sample QuaDRiGa dataset. These gaps are load-bearing for the paper's headline claims.

major comments (3)

[§VI-C, Eq. (17), Fig. 4] The 'near-optimal' claim compares SM-IB only against a Gurobi solution of (P2) in which the objective Ru is computed from SE-Net predictions (Eq. (17)), not from true ergodic spectral efficiency. The paper never evaluates the true Monte-Carlo ergodic throughput of the final schedules, nor does it compute a true upper bound. In a max-min problem, systematic overestimation of the bottleneck UE's SE can make the heuristic appear near-optimal even when actual fairness is poor. The authors should report the actual ergodic throughput of the schedules produced by SM-IB and by Gurobi using the channel model (Eq. (5)), ideally with confidence intervals, and, for small instances, compare against exhaustive search or a valid true upper bound.
[§IV-B, §VI-B] The spatial-generalization premise is not validated. LPS-Net and SE-Net are trained on 10,000 QuaDRiGa samples and evaluated on a random 8:1:1 split of the same dataset. Since SM-IB is later applied to arbitrary UE positions and scheduling configurations, prediction bias outside the training distribution could make the algorithm optimize a systematically wrong objective. The authors should add cross-scenario validation, e.g., testing on UE positions, AIRS locations/orientations, or shadowing maps not seen in training, and report prediction error as a function of distance from the training positions. Without this, the scheduling results in Fig. 4 are only valid under the untested assumption that the learned mapping generalizes.
[§VI-C, Fig. 4, Table II] No error bars, confidence intervals, or multiple random trials are reported for the key scheduling comparison. Given the stochasticity of QuaDRiGa large-scale parameters, small-scale fading, and neural-network training, the statement that the proposed algorithm 'achieves a max-min ergodic throughput close to that of the upper bound' is not statistically supported. The authors should report means with confidence intervals over multiple independent dataset/training/scheduling runs, or at least over multiple random UE drops.

minor comments (5)

[Eq. (20)] The loss function for SE-Net is denoted fδLPS(η̄, η̂), but the parameter used is δSE. This notation likely refers to the same smooth L1 loss, but should be renamed (e.g., fδSE) to avoid confusion.
[Table I] The table header 'NetworkNpara.' is unclear; define Npara as the number of trainable parameters in the caption or main text.
[§V-B] The complexity of the Iterative Balancing algorithm is given as O(log2(1/ϵ)) without derivation. Since the throughput gap may not shrink geometrically in all cases, a brief justification or reference would strengthen the claim.
[§VI-A] The comparison of phase optimization schemes reports single-point values (3.233 versus 3.357 bps/Hz) without variance or confidence intervals; please add error bars or note if these are means over the 50 realizations.
[General] No code or data is provided. Given the reliance on a simulated dataset and deep learning, releasing code/data or at least detailed experiment seeds would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the neural CKM is a supervised regressor validated on held-out data, and the SM-IB vs. Gurobi comparison is an internal scheduling-optimization benchmark, not a circular reduction.

full rationale

The paper's derivation chain is not circular. LPS-Net and SE-Net are trained with supervised labels generated by Monte Carlo simulations in QuaDRiGa (Section VI-B), and their prediction accuracy is evaluated on a held-out test set (Table I), providing external validation of the surrogate. The scheduling optimization in SM-IB uses the neural-CKM-predicted ergodic SE as an objective function, but this is a standard surrogate-based optimization: the predictions are not constructed from the scheduling output, and no parameter is fitted to the max-min throughput that is later reported. The Gurobi upper bound solves the same problem (P2) using the same neural-CKM SE predictions, so the gap in Fig. 4 measures scheduling suboptimality under the surrogate model rather than against true channel statistics. This is a limitation of the evaluation—the true Monte-Carlo max-min throughput and a true upper bound are never computed—but it is not a circularity in the logical sense: the claim 'near-optimal' is conditional on the surrogate objective, and the surrogate itself is independently tested. There is no load-bearing self-citation, no imported uniqueness theorem, and no ansatz smuggled in via citation. Therefore the circularity score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its load-bearing machinery is a learned regression (neural network weights) plus a set of channel modeling and scheduling assumptions. All free parameters are either neural weights or hand-tuned hyperparameters; no independent evidence is given for spatial generalizability beyond the training set.

free parameters (4)

LPS-Net weights = 3,648,004 parameters
Fitted to 10,000 QuaDRiGa MC samples to predict link power CDFs (Eq. 16).
SE-Net weights = 3,237,377 parameters
Fitted to map link power CDFs to ergodic SE (Eq. 17).
Loss weights and thresholds = gamma=0.2, eta=20.0, delta_LPS=0.5, delta_SE=1.0; epsilon, xi unreported
Chosen by hand in Eqs. (19)-(20) without sensitivity analysis; algorithm thresholds in Section V are not quantified.
Transformer hyperparameters = 4 layers, 4 heads, 256-dim token
Set without a reported systematic search; these choices affect both accuracy and complexity claims.

assumptions (5)

domain assumption Channel statistics and UE positions are obtainable via statistical channel measurements and positioning (Section III-B).
The whole CKM premise assumes such historical data can be collected for training the networks.
domain assumption QuaDRiGa 3GPP channel models represent the physical environment (Section II-A).
All numerical evaluations rely on this synthetic channel generator; real-world validity is untested.
domain assumption Ergodic SE is statistically identical across RBs under statistical CSI (Section III-A).
This justifies replacing per-RB discrete allocation with continuous per-slot RB ratio rho_u,q in (P2).
domain assumption Equal power allocation and MCCM-based beamforming are adopted (Section III-A).
The problem (P2) is formulated under these fixed schemes; the claimed generality to other beamforming is stated but not demonstrated.
domain assumption Each IRS serves at most one UE per time slot (Section II).
Adopted from [2] to maximize beamforming gain; this assumption drives the time-sharing constraints (9).

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Cite this review

Pith. "Pith review of Neural Channel Knowledge Map Assisted Scheduling Optimization of Active IRSs in Multi-User Systems." pith.science (2026). https://pith.science/paper/NPDN47AT

@misc{pith2026250807009,
  author       = {Pith},
  title        = {Pith review of: Neural Channel Knowledge Map Assisted Scheduling Optimization of Active IRSs in Multi-User Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NPDN47AT}},
  note         = {Machine review of arXiv:2508.07009}
}

read the original abstract

Intelligent Reflecting Surfaces (IRSs) have potential for significant performance gains in next-generation wireless networks but face key challenges, notably severe double-pathloss and complex multi-user scheduling due to hardware constraints. Active IRSs partially address pathloss but still require efficient scheduling in cell-level multi-IRS multi-user systems, whereby the overhead/delay of channel state acquisition and the scheduling complexity both rise dramatically as the user density and channel dimensions increase. Motivated by these challenges, this paper proposes a novel scheduling framework based on neural Channel Knowledge Map (CKM), designing Transformer-based deep neural networks (DNNs) to predict ergodic spectral efficiency (SE) from historical channel/throughput measurements tagged with user positions. Specifically, two cascaded networks, LPS-Net and SE-Net, are designed to predict link power statistics (LPS) and ergodic SE accurately. We further propose a low-complexity Stable Matching-Iterative Balancing (SM-IB) scheduling algorithm. Numerical evaluations verify that the proposed neural CKM significantly enhances prediction accuracy and computational efficiency, while the SM-IB algorithm effectively achieves near-optimal max-min throughput with greatly reduced complexity.

Figures

Figures reproduced from arXiv: 2508.07009 by the authors.

**Figure 1.** Multi-AIRS assisted multi-user systems. link power statistics based on given UE positions and system configurations; and 2) composing the link power statistics to infer the ergodic SE under given UE-to-AIRS association, respectively. To capture the highly nonlinear function mappings associated with these two sub-tasks, we choose Transformer [13] as the core building blocks for flexible input encoding and output mapp… view at source ↗

**Figure 2.** Neural CKM to predict link power statistics and ergodic SE. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Ergodic throughput under different number of AIRS elements. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Minimum ergodic throughput per UE under different schemes. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

Intelligent surfaces empowered wireless network: Recent advances and the road to 6G,

Q. Wu, B. Zheng, C. You et al., “Intelligent surfaces empowered wireless network: Recent advances and the road to 6G,” Proc. IEEE , vol. 112, no. 7, pp. 724–763, 2024

work page 2024

[2] [2]

Intelligent reflecting surface-assisted multiple access with user pairing: NOMA or OMA?

B. Zheng, Q. Wu, and R. Zhang, “Intelligent reflecting surface-assisted multiple access with user pairing: NOMA or OMA?” IEEE Commun. Lett., vol. 24, no. 4, pp. 753–757, Apr. 2020

work page 2020

[3] [3]

Active RIS vs. passive RIS: Which will prevail in 6G?

Z. Zhang, L. Dai, X. Chen, C. Liu, F. Yang, R. Schober, and H. V . Poor, “Active RIS vs. passive RIS: Which will prevail in 6G?” IEEE Trans. Commun., vol. 71, no. 3, pp. 1707–1725, 2022

work page 2022

[4] [4]

Active-IRS-aided wireless communica- tion: Fundamentals, designs and open issues,

Z. Kang, C. You, and R. Zhang, “Active-IRS-aided wireless communica- tion: Fundamentals, designs and open issues,” IEEE Wireless Commun., vol. 31, no. 3, pp. 368–374, 2024

work page 2024

[5] [5]

Multi-pair D2D communications aided by an active RIS over spatially correlated channels with phase noise,

Z. Peng, X. Liu, C. Pan et al. , “Multi-pair D2D communications aided by an active RIS over spatially correlated channels with phase noise,” IEEE Wireless Commun. Lett. , vol. 11, no. 10, pp. 2090–2094, 2022

work page

[6] [6]

Site-specific deployment optimization of intelligent reflect- ing surface for coverage enhancement,

D. Fu et al., “Site-specific deployment optimization of intelligent reflect- ing surface for coverage enhancement,” in VTC-Spring, 2024, pp. 01–07

work page 2024

[7] [7]

IRS-enhanced OFDMA: Joint re- source allocation and passive beamforming optimization,

Y . Yang, S. Zhang, and R. Zhang, “IRS-enhanced OFDMA: Joint re- source allocation and passive beamforming optimization,” IEEE Wireless Commun. Lett., vol. 9, no. 6, pp. 760–764, 2020

work page 2020

[8] [8]

Intelligent resource allocation for IRS-enhanced OFDM communication systems: A hybrid deep reinforcement learning approach,

W. Wu, F. Yang, F. Zhou, Q. Wu, and R. Q. Hu, “Intelligent resource allocation for IRS-enhanced OFDM communication systems: A hybrid deep reinforcement learning approach,” IEEE Trans. Wireless Commun., vol. 22, no. 6, pp. 4028–4042, 2023

work page 2023