Learning-Based Multiuser Scheduling in MIMO-OFDM Systems with Hybrid Beamforming

Fran\c{c}ois Durand; Matthew Andrews; Pouya Agheli; Tugce Kobal

REVIEW 5 major objections 6 minor 18 references

Learning-Based Multiuser Scheduling in MIMO-OFDM Systems with Hybrid Beamforming

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

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Pith's one-line read A supervised neural network can act as a fast surrogate for greedy user scheduling in mmWave MIMO-OFDM systems with hybrid beamforming, trading a modest loss in proportional fairness for much shorter run times.

desk verdict Useful engineering extension of flat-fading scheduling to OFDM, but the DNN's PRB-averaged features leave a real representational gap that the paper never checks. read the letter →

arxiv 2506.08263 v2 pith:JZOIIPJE submitted 2025-06-09 cs.IT cs.LGeess.SPmath.IT

Pouya Agheli , Tugce Kobal , François Durand , Matthew Andrews This is my paper

classification cs.ITcs.LGeess.SPmath.IT

keywords multiuserschedulinghybridbeamformingMIMO-OFDMmillimeterwaveproportionalfairnesssupervisedlearningdeepneuralnetworkgreedyalgorithm

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

Multiuser scheduling in a millimeter-wave MIMO-OFDM downlink is hard because the number of RF chains caps how many users can be served at once, and choosing the wrong subset wastes the limited multiplexing gain. The paper's proposal is a two-timescale protocol that fixes each user's analog beam on a slow timescale and then, on a fast timescale, selects the user subset and designs a zero-forcing digital precoder. Against greedy incremental, greedy decremental, and sorting schedulers, the authors train a supervised deep neural network to imitate the greedy incremental scheduler's decisions. Their numerical results show the greedy incremental (decremental) scheduler achieves 1.76 (1.47) times higher proportional fairness at the cost of 2.3 (16.1) times longer run time than the learning-based one. The paper concludes that the right scheduler depends on whether the operator prioritizes fairness or speed, with the learning-based approach offering a favorable balance.

What carries the argument

The argument rests on two coupled mechanisms. First, the two-timescale protocol exploits the mmWave property that path angles change more slowly than path gains: analog beams are assigned from a codebook on a long timescale, and on each short timescale the base station forms an effective channel matrix, applies zero-forcing digital precoding, and schedules users. Second, the learning component is a supervised DNN whose normalized input features are the average effective-channel amplitudes and angles across PRBs, the angles of the assigned analog beams, and the user weights; its outputs are per-user selection decisions, and a cascade filter keeps the selected set within the RF-chain limit. The DNN is trained on labels from the greedy incremental scheduler, so the greedy algorithm acts as the teacher that defines what the network is trying to learn.

What would settle it

Take the trained DNN and evaluate it on channel realizations generated by a different, independently calibrated mmWave channel model, or on measured channels from a testbed, and compare the proportional fairness and the selected-user set against the greedy incremental scheduler. If the fairness gap grows substantially or the selected-user agreement collapses while the run-time advantage remains, the paper's claim that the learned scheduler is a dependable fast surrogate is falsified.

Watch

Extended reading notes

Core claim

Under the paper's synthetic mmWave channel model, supervised learning can reproduce the decisions of greedy incremental user scheduling closely enough to be practically useful. A fully connected DNN with three hidden layers, trained with cross-entropy loss on labels produced by the greedy incremental algorithm, predicts which users to serve; a selection filter enforces the RF-chain limit. In the evaluated scenario with 20 users and 8 RF chains, the incremental, decremental, and learning-based schedulers select 18.8%, 29.49%, and 16.62% of users on average, respectively, showing that all three avoid serving everyone to keep interference low. The paper reports that the incremental (decremental) method provides 1.76 (1.47) times higher PF at the cost of 2.3 (16.1) times longer run time compared to the learning-based method, and interprets this as evidence that learning-based scheduling is a fast surrogate for greedy scheduling in hybrid beamforming MIMO-OFDM systems with modest fairness loss.

Load-bearing premise

The learned scheduler is trained and evaluated on samples drawn from the same synthetic millimeter-wave channel generator, so the claimed speed-fairness trade-off is only shown for that channel distribution; if real deployment channels differ in user distribution, mobility, or scattering, the DNN's decisions may no longer track the greedy algorithm.

Editorial extensions

If this is right

In a deployment where scheduling decisions must be made within a slot, the learning-based approach keeps run time nearly constant as the maximum number of served users grows, unlike the greedy methods whose search cost increases with Imax.
Operators with a strict fairness target should use greedy incremental scheduling, while operators with a tight computation budget should use the learning-based scheduler; the decremental method's 16.1 times longer run time gives it little practical advantage in the tested regime.
Because the greedy and learning-based schedulers deliberately serve far fewer than the maximum number of users (around 17–29% on average), interference-aware subset selection matters as much as the RF-chain limit in these systems.
The learning-based scheduler's performance ceiling is set by the greedy incremental teacher that produced its labels, so it cannot be expected to exceed the fairness of the incremental algorithm in this setup.

Reading between the lines

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

The paper does not test transfer, but because the DNN's input features are generic effective-channel quantities, the same supervised pipeline could in principle be retrained for other mmWave deployments, codebooks, or antenna geometries without architectural changes.
A natural extension the authors do not run is to train the network with a loss that directly maximizes proportional fairness instead of imitating greedy labels; this could close the fairness gap while preserving the speed advantage.
The paper assumes one user per resource grid; extending to OFDMA, where multiple users share a PRB, would require a different output structure and is explicitly left for future work.

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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

Two things to know. First, this paper is a competent extension of the authors' prior flat-fading scheduler to frequency-selective MIMO-OFDM with hybrid beamforming, and it gives system designers a concrete menu of schedulers with a clear performance/runtime trade-off. Second, the central claim that the DNN is a fast surrogate for greedy scheduling in OFDM is weaker than it looks, because the DNN's input features discard all per-PRB information.

The system model and ZF precoding are standard and correctly stated. The two-timescale protocol is sensible, and the greedy incremental/decremental, sorting, and random baselines are fairly implemented. The numerical study is reasonably extensive, and Fig. 3(c)'s trade-off plot is a clean way to present the results. The concrete numbers—incremental gives 1.76x higher PF at 2.3x runtime, decremental 1.47x at 16.1x compared to the learning-based approach—are useful if they hold up.

Now the soft spots. The most serious is the PRB-averaged DNN input. As the stress-test note says, the first two input subvectors use (1/K)*sum_k u_{k,ij}, while the greedy labels are computed from per-PRB rates with per-PRB SINRs. Frequency-selective channels with 20 subpaths per cluster and K=12 PRBs can produce realizations with identical PRB averages but different greedy schedules; the DNN cannot distinguish them. The paper never reports imitation accuracy or compares against a variant with per-PRB features. This is an in-distribution representational gap, not a distribution-shift concern. The claim that the learning-based approach solves the OFDM scheduling problem is not supported by the evidence. The PF numbers may still be good for the simulated scenario, but that would be an artifact of the channel generator making the averages sufficiently informative.

Second, Table I sets NSB=1, meaning each long-time block equals one short-time block. That collapses the two-timescale protocol and means the long-timescale analog beam assignment is re-derived every slot. The paper never tries another value, so the two-timescale motivation is untested.

Third, there are missing experimental details: no error bars, no optimizer or learning rate for the DNN, no EMA smoothing factor eta_i, and no comparison with the closest baselines—the authors' own prior work [8] or the OFDM baseline [9]. These are minor-to-moderate gaps, but they make the quantitative trade-off claims hard to assess.

Overall, the paper is a solid engineering study with a plausible speed-fairness trade-off, but the PRB-averaging issue is a genuine flaw that needs addressing. It deserves peer review—an editor should send it out—but the reviewers should ask for per-PRB feature comparison, robustness tests across frequency selectivity, and the missing hyperparameters. I'd bring it to reading group if the goal is to discuss what makes a learned surrogate credible, but not as a finished result.

Referee Report

5 major / 6 minor

Summary. The paper studies downlink multiuser scheduling in a mmWave MIMO-OFDM system with hybrid beamforming. It adopts a two-timescale protocol in which analog beams are assigned on a long timescale, while user scheduling and ZF digital precoding are performed on a short timescale. The scheduling objective is formulated as a weighted-sum-rate proxy for proportional fairness. The authors propose greedy incremental and decremental user-selection algorithms, a sorting heuristic, random selection, and a supervised DNN scheduler trained to imitate the greedy incremental decisions. Numerical simulations for I=20 users, NRF=8 RF chains, and K=12 PRBs at 28 GHz show that the incremental and decremental algorithms achieve higher PF than the learning-based scheduler but require 2.3x and 16.1x longer run time, respectively; the paper concludes that the choice among approaches depends on whether PF or run time is the primary criterion.

Significance. The paper offers a clear system model and an empirical comparison of several scheduling algorithms plus a DNN surrogate in a realistic mmWave OFDM setup. The PF decomposition and the two-timescale protocol are standard and clearly stated, and the evaluation metric is computed externally from actual scheduling outcomes, which is appropriate. If it were firmly established that the DNN can imitate the greedy policy with a modest PF loss at much lower run time, the result would be practically useful for fast scheduling in hybrid beamforming systems. However, the central empirical claim is supported only by point estimates without uncertainty quantification, the nearest frequency-selective baseline [9] is not evaluated, and the DNN input is a PRB-averaged summary that may be insufficient for the frequency-selective scheduling task. The result is plausible but not yet established.

major comments (5)

[VI-A1 and Eqs. (6)-(7), (13)-(15)] The first two input subvectors of the DNN are built from the effective channel averaged over all PRBs, namely (1/K) * sum_k u_{k,ij}, whereas the greedy labels are computed from per-PRB rates r_i(t) = sum_k B_k log2(1 + SINR_{k,i}), where each SINR_{k,i} depends on the full per-PRB matrices U_k(M(t);t). Since a sum of logarithms across PRBs is not determined by the average effective channel, two channel realizations with identical PRB averages can lead to different greedy schedules. The paper reports neither the label accuracy of the DNN nor an ablation with per-PRB features, so the learning-based scheduler may be fitting a summary statistic rather than solving the OFDM scheduling problem. The authors should either include per-PRB features, demonstrate that the PRB average is sufficient for the adopted channel generator, or add a controlled experiment with stronger frequency selectivity.
[VI-B and VII-C] The DNN is trained on samples generated by the same greedy incremental algorithm against which it is evaluated. Consequently, the comparison in Fig. 3(a) measures how well the DNN approximates that greedy policy, not how close the learning-based scheduler is to the optimal PF. The paper also does not compare with the frequency-selective baseline [9], despite citing its limitations. Please add an independent reference point (exhaustive search for a reduced-size problem, an upper bound, or the algorithm of [9]) and report the DNN's selection accuracy over the test set.
[Table I and Figs. 3-4] All numerical experiments set NSB=1, so the analog beamformer is recomputed in every short-time block. This means the two-timescale structure presented in Section IV-A is never actually exercised in the evaluation, and the claimed benefit of separating long- and short-timescale decisions is not demonstrated. Experiments with NSB>1, or at least a sensitivity sweep over NSB, are needed to support the two-timescale protocol as a contribution.
[Section VII and Table I] The trade-off ratios quoted in Section VII-C (incremental provides 1.76x higher PF at 2.3x runtime; decremental provides 1.47x at 16.1x) are point estimates from a single set of simulations. No error bars, confidence intervals, or multiple training seeds are reported, and there is no sensitivity to the number of PRBs, number of subpaths per cluster, user mobility, or codebook size. Without this information, the headline conclusion that the learning-based approach strikes a favorable balance is not statistically grounded.
[Section VI-B and Table I] The training setup is not fully specified: the optimizer and learning rate are omitted, no regularization or initialization is described, the threshold converting continuous DNN outputs into the binary selection variables alpha_i is not given, and no random seeds or code/data are provided. Since the paper's main evidence is empirical, these omissions prevent replication and verification of the reported run-time and PF figures.

minor comments (6)

[Algorithm 1, line 3] The phrase 'weighted sum-rate user' should read 'user that offers the highest weighted sum-rate'; the decremental procedure in Section V-A2 is described only in prose and would benefit from being presented as a numbered algorithm for symmetry.
[Section II, Eq. (2)] The dimension should be typeset as C^{M(t) x M(t)}; the current 'CM (t) x M (t)' is ambiguous.
[Section VI-A1] The PRB-average should be written (1/K) * sum_{k=1}^K u_{k,ij}; as printed, 'sum_{k=1}^K u_{k,ij}/K' is ambiguous. The normalization applied to the four subvectors is also not specified.
[Section VI-A2] The rounding rule for obtaining alpha_i from the DNN output is not defined; please specify the threshold (e.g., 0.5) and how ties are broken.
[Section V-B] The sorting algorithm does not state how many users are selected; clarify whether it always selects Imax users.
[Section VII-A] Since Table I fixes NSB=1, the text in Section IV-A that describes NSB-1 repeated short-time blocks should explicitly note that the simulations do not exercise this long-timescale reuse.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: PF and run-time are measured externally, and the only self-citation is not load-bearing.

full rationale

The paper's derivation chain is self-contained at the level of the claimed result. The learning-based scheduler is trained by supervised imitation of the greedy incremental algorithm (Section VI-B: "A sample set is generated using greedy incremental user scheduling over N1 episodes"), and its PF is then computed from the rates of actually scheduled users via Eq. (8), not from the training labels. The run-time comparison is likewise measured externally in Figs. 3 and 4. No equation in the paper defines the predicted metric in terms of the training target, and no fitted parameter is renamed as a prediction. The only self-citation is [8] (J. Kim and M. Andrews, with M. Andrews as a co-author of the present paper), used in the introduction to motivate the extension to OFDM; the method and evaluation in Sections VI and VII do not rely on any theorem, parameter, or dataset from [8]. The PRB-averaged effective-channel input features (Section VI-A1) may be an information bottleneck, but that is an expressiveness or generalization issue rather than a circular definition: the DNN output is not equal to the PF input by construction.

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

No new physical entities are introduced. The central claim rests on standard system-model assumptions and on several hand-picked simulation or training parameters, the most notable being an unspecified EMA smoothing factor, NSB=1, and unreported DNN optimizer and learning rate. These choices affect the quantitative trade-off but not the qualitative conclusion that a fast learned scheduler exists.

free parameters (4)

EMA smoothing factor eta_i = not specified (0 <= eta <= 1)
The PF metric (8) uses an exponential moving average of user rates; the smoothing factor is introduced in Section III-A but never assigned a value in Table I, so the absolute PF values in Fig. 3 are not reproducible.
NSB (short-time blocks per long-time block) = 1
Set to 1 in Table I. This makes analog beams re-selected every slot, collapsing the two-timescale protocol into a one-timescale scheme and leaving the long-timescale analog beam assignment untested.
DNN hidden layer sizes (L1, L2, L3) = (1200, 500, 200)
Chosen by hand in Table I; the learning-based scheduler's performance, and therefore the trade-off claim, depends on them. Optimizer and learning rate are not reported.
DNN training hyperparameters (beta, N3, N4) = beta=0.8, N3=16, N4=300
Sample split, batch size, and epochs are chosen in Table I and affect the trained model's quality; no ablation is provided.

assumptions (5)

domain assumption Path angles are static over long-time blocks while path gains vary over shorter blocks
Invoked in Section IV-A to justify the two-timescale protocol; based on [13]-[15], not validated in this paper.
standard math The long-term PF objective can be decomposed into per-slot weighted sum-rate maximization with weights 1/R_i(t-1)
Taken from Stolyar [12]; the paper applies this decomposition without proof.
domain assumption Zero-forcing precoding is near-optimal in mmWave channels due to the small number of clusters
Used to compute digital precoders via (14) and (15), following [2], [13].
domain assumption One user is scheduled per resource grid, so OFDMA scheduling is excluded
Stated in Section II as a modeling choice, with OFDMA left for future work.
domain assumption The mmWave channel model of Akdeniz et al. [13, Eq. (9)] with 20 subpaths per cluster and the Doppler formula (19) is representative
All numerical results depend on this synthetic channel model; no real measurements are used.

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Cite this review

Pith. "Pith review of Learning-Based Multiuser Scheduling in MIMO-OFDM Systems with Hybrid Beamforming." pith.science (2026). https://pith.science/paper/JZOIIPJE

@misc{pith2026250608263,
  author       = {Pith},
  title        = {Pith review of: Learning-Based Multiuser Scheduling in MIMO-OFDM Systems with Hybrid Beamforming},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JZOIIPJE}},
  note         = {Machine review of arXiv:2506.08263}
}

read the original abstract

We investigate the multiuser scheduling problem in multiple-input multiple-output (MIMO) systems using orthogonal frequency division multiplexing (OFDM) and hybrid beamforming in which a base station (BS) communicates with multiple users over millimeter wave (mmWave) channels in the downlink. Improved scheduling is critical for enhancing spectral efficiency and the long-term performance of the system from the perspective of proportional fairness (PF) metric in hybrid beamforming systems due to its limited multiplexing gain. Our objective is to maximize PF by properly designing the analog and digital precoders within the hybrid beamforming and selecting the users subject to the number of radio frequency (RF) chains. Leveraging the characteristics of mmWave channels, we apply a two-timescale protocol. On a long timescale, we assign an analog beam to each user. Scheduling the users and designing the digital precoder are done accordingly on a short timescale. To conduct scheduling, we propose combinatorial solutions, such as greedy and sorting algorithms, followed by a machine learning (ML) approach. Our numerical results highlight the trade-off between the performance and complexity of the proposed approaches. Consequently, we show that the choice of approach depends on the specific criteria within a given scenario.

Figures

Figures reproduced from arXiv: 2506.08263 by the authors.

**Figure 2.** Structure of the two-timescale protocol for one resource grid. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** The impact of the maximum number of users served per slot on (a) the average PF and (b) the required run time of the algorithms, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Timing profiles of the main user scheduling components. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

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Pith tools

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

[1] [8]

Learning-based adaptive user selection in millimeter wave hybrid beamforming systems,

J. Kim and M. Andrews, “Learning-based adaptive user selection in millimeter wave hybrid beamforming systems,” in IEEE International Conference on Communications (ICC) , 2023

work page 2023

[2] [9]

Multi-user scheduling in hybrid millimeter wave massive MIMO systems,

S. M. Hosseini, S. Shahsavari, and C. Rosenberg, “Multi-user scheduling in hybrid millimeter wave massive MIMO systems,” in IEEE Wireless Communications and Networking Conference (WCNC) , 2022

work page 2022

[3] [1]

Scaling up MIMO: Opportunities and challenges with very large arrays,

F. Rusek et al. , “Scaling up MIMO: Opportunities and challenges with very large arrays,” IEEE Signal Processing Magazine , vol. 30, no. 1, pp. 40–60, 2012

work page 2012

[4] [2]

Limited feedback hybrid precoding for multi-user millimeter wave systems,

A. Alkhateeb, G. Leus, and R. W. Heath, “Limited feedback hybrid precoding for multi-user millimeter wave systems,” IEEE Transactions on Wireless Communications, vol. 14, no. 11, pp. 6481–6494, 2015

work page 2015

[5] [3]

Frequency selective hybrid precoding for limited feedback millimeter wave systems,

A. Alkhateeb and R. W. Heath, “Frequency selective hybrid precoding for limited feedback millimeter wave systems,” IEEE Transactions on Communications, vol. 64, no. 5, pp. 1801–1818, 2016

work page 2016

[6] [4]

Dynamic subarrays for hybrid precoding in wideband mmWave MIMO systems,

S. Park, A. Alkhateeb, and R. W. Heath, “Dynamic subarrays for hybrid precoding in wideband mmWave MIMO systems,” IEEE Transactions on Wireless Communications, vol. 16, no. 5, pp. 2907–2920, 2017

work page 2017

[7] [5]

Hybrid analog and digital beamforming for mmWave OFDM large-scale antenna arrays,

F. Sohrabi and W. Yu, “Hybrid analog and digital beamforming for mmWave OFDM large-scale antenna arrays,” IEEE Journal on Selected Areas in Communications , vol. 35, no. 7, pp. 1432–1443, 2017

work page 2017

[8] [6]

A joint scheduling and millimeter wave hybrid beamforming system with partial side information,

G. Kwon and H. Park, “A joint scheduling and millimeter wave hybrid beamforming system with partial side information,” in IEEE International Conference on Communications (ICC) , 2016

work page 2016