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Joint Precoding and AP Selection for Energy Efficient RIS-aided Cell-Free Massive MIMO Using Multi-agent Reinforcement Learning

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims a fuzzy-logic multi-agent reinforcement learning scheme that selects a subset of access points per user improves energy efficiency over full coverage and zero forcing, with faster convergence.

desk verdict Promising algorithmic idea, but the simulated EE values are about three times higher than the paper's own model allows, so the headline gains are not trustworthy as reported. read the letter →

arxiv 2411.11070 v1 pith:XBO2MYSX submitted 2024-11-17 cs.IT eess.SPmath.IT

Enyu Shi , Jiayi Zhang , Ziheng Liu , Yiyang Zhu , Chau Yuen , Derrick Wing Kwan Ng , Marco Di Renzo , Bo Ai This is my paper · ORCID
classification cs.ITeess.SPmath.IT
keywords reconfigurableintelligentsurfacecell-freemassiveMIMOenergyefficiencyaccesspointselectionmulti-agentreinforcementlearningfuzzylogicprecodinguser-centricnetworks
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

The paper tries to establish that, in a reconfigurable-intelligent-surface (RIS) aided cell-free massive MIMO network, letting each user be served by a selected subset of access points rather than by all of them is both practical and energy-efficient when the joint choice of precoding, AP selection, and RIS phase shifts is made by a double-layer multi-agent reinforcement learning scheme. The scheme uses an adaptive power threshold to choose which APs serve which users and a fuzzy-logic layer to compress the agents' state space and speed up training. The authors report that, in their simulated configuration, this raises energy efficiency by about 10% at the peak over full coverage and up to 85% over zero-forcing precoding when each AP has 10 antennas, while converging in about 45% of the training time of plain MARL. They also show that increasing transmit power or RIS element count improves spectral efficiency but eventually degrades EE, so the design exposes a trade-off.

What carries the argument

The carrying object is the double-layer fuzzy-logic-based MADDPG architecture. In the first layer, each AP is an agent whose action space is the joint precoding vectors and a per-UE binary selection; the selection is produced by an adaptive power threshold that compares each precoding vector's power to a threshold updated toward a target average. In the second layer, the same agents choose RIS phase-shift actions. Fuzzy logic sits between the environment and the agents: membership functions cluster observed states into a smaller number of fuzzy states, and defuzzification maps fuzzy actions back to actual actions, so the network trains on F fuzzy agents instead of L physical APs. This compression is what carries the claimed reduction in convergence time and complexity.

What would settle it

Reproduce the simulation with B = 180 kHz and the stated static powers; with the plotted sum SE near 14 bps/Hz, Eq. (13) caps EE at about 5×$10^{5}$ bit/J. If the code produces the plotted ~1.8×$10^{6}$ bit/J values, the published system model differs from the simulation, and the gains must be re-evaluated under the stated parameters.

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Extended reading notes

Core claim

The central claim is that the EE maximization problem, which is a non-concave mixed-integer program, can be approximated by decoupling it into two coordinated learning layers: a first MADDPG layer that jointly designs precoding and, through an adaptive power threshold, the AP-UE selection matrix; and a second layer that designs the RIS phase shifts given that selection. Fuzzy logic reduces the number of effective agents by mapping the original agent states to a smaller set of fuzzy states through membership functions, cutting computational complexity from exponential to linear in the number of APs at a reported cost of 2.5–3.6% in EE performance. The paper argues that the gain over zero forcing and over full-coverage MADDPG, as well as the faster convergence, support user-centric AP selection and fuzzy acceleration as effective tools for green RIS-aided cell-free networks.

Load-bearing premise

The EE and SE curves rest on the bandwidth and power-consumption parameters stated in Section V-A and Table III; if the simulator actually used different values, the reported percentage improvements are unanchored.

Editorial extensions

If this is right

  • If the reported gains hold, serving each user by a small learned subset of APs outperforms full-coverage precoding in energy efficiency, especially when transmit power is high.
  • The fuzzy-logic state compression makes the MARL approach practical at larger AP counts, since complexity scales linearly with the number of APs instead of exponentially.
  • EE peaks at a moderate transmit power and a moderate number of RIS elements; beyond those points the additional power consumption outweighs the SE gains.
  • The 2.5–3.6% EE loss of FL-MARL relative to plain MARL is a small price for a 45% reduction in convergence time, so fuzzy compression is a viable deployment trade-off.

Reading between the lines

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

  • The paper's quantitative EE results are hard to reconcile with its stated 180 kHz bandwidth and power model: plugging the reported SE and static power into Eq. (13) gives an EE ceiling of roughly 5×10^5 bit/J, while the plots reach about 1.8×10^6 bit/J, implying the simulator may use a wider bandwidth or a different power model than stated.
  • The adaptive power threshold acts like a learned sparsification regularizer on the precoding matrix; a similar threshold mechanism could transfer to other massive MIMO resource allocation tasks such as pilot assignment or user scheduling.
  • The fuzzy-layer idea generalizes: any multi-agent wireless optimization with large state/action spaces could compress agents through membership functions, at a known cost in precision.
  • The trade-off between RIS element count and element power suggests a design rule: the optimal N decreases as Pelement increases, which could guide hardware choices without full simulation.
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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 manuscript considers a downlink RIS-aided cell-free massive MIMO system and formulates a joint precoding, RIS phase-shift, and binary AP-selection optimization problem to maximize energy efficiency. It proposes a double-layer multi-agent deep deterministic policy gradient (MADDPG) architecture, an adaptive power-threshold AP-selection algorithm, and a fuzzy-logic (FL) strategy to reduce the number of agents and accelerate convergence. A complexity comparison is provided, and simulations report that the proposed scheme improves EE by about 10% over full AP coverage at the peak, by 16% and 85% over full-coverage FL-MADDPG and ZF at M=10, and converges in about 45% of the time of plain MADDPG.

Significance. If the numerical results are reliable, the paper would offer a scalable MARL-based solution to a relevant problem in RIS-aided cell-free massive MIMO and a useful complexity reduction. The double-layer decomposition and the explicit complexity comparison in Table I are clear strengths. However, the central quantitative claims are currently undermined by an internal inconsistency between the stated power model/bandwidth and the plotted EE magnitudes, and by missing training details that make the experiments irreproducible. The contribution is therefore not yet established.

major comments (4)
  1. [V-A, Table III, Eq. (13), Figs. 6-10] The plotted EE magnitudes are inconsistent with the stated parameters and with Eq. (13). With B=180 kHz, a maximum observed sum SE of about 22 bps/Hz (Figs. 7/9/11), and the static powers in Table III (P_CPU=5 W, L*P_static=0.4 W, K*P_k=0.06 W, L*P_0=0.8 W, N*P_element=0.64 W), Eq. (13) gives P_total at least 6.9 W and EE at most B*SE/P_total ~ 5.8e5 bit/J. The EE curves in Figs. 6, 8, and 10 reach about 1.8e6 bit/J, roughly 3.1 times higher. Matching the plots would require B ~ 1.8 MHz, P_CPU ~ 0.5 W, or a different power/unit model, none of which is stated. Because the reported 10%, 16%, and 85% improvements are read from these curves, the numerical claims are not validated by the written model.
  2. [IV-B, Algorithm 2, Table II] The MARL training details needed for reproducibility are missing: learning rates, batch size, number of training episodes/steps, number of fuzzy agents N_F, membership width d_a, and initialization/update rate tau_threshold. The results are reported without seeds or confidence intervals. Since the paper's claims rest entirely on simulations, these omissions prevent independent verification; please provide a complete hyperparameter table and, if possible, code or data.
  3. [Abstract, V-D, Fig. 8] The abstract states a general '85% enhancement over the zero-forcing (ZF) method,' but the text reports this figure only at M=10 in Fig. 8, while the peak improvement over full coverage in Fig. 6 is 10% and the conclusion repeats only the 10% figure. The headline claim should be restricted to the configuration actually simulated and should be accompanied by the variability across the settings shown in Figs. 6-12.
  4. [IV-B and constraint (14d)] The mapping from the continuous MADDPG action to the binary AP-selection matrix satisfying (14d) is under-specified. Algorithm 1 uses a power threshold, but Eqs. (15)-(18) treat A as a given matrix, and no discretization step or feasibility-repair mechanism is described. Please specify how binary integer feasibility is enforced during training and execution.
minor comments (5)
  1. [III-C, Eq. (14b)] Constraint (14b) is written with 'for all k in K' even though it bounds a sum over k; the universal quantifier should be over l (one per AP). In addition, constraint (14c) is called a 'sparse constraint' but it is a phase-shift constraint.
  2. [IV-A] The text says 'the concept of Federated Learning (FL) was proposed in [46]', but reference [46] is a book on fuzzy logic and the algorithm subsequently uses FL to mean fuzzy logic. Please correct the terminology and the citation.
  3. [V-A and Table III] The maximum AP transmit power is stated as '5 dB' in the text and '3.2 W' in Table III; please use consistent units (e.g., 5 dBW). Similarly, the figure captions give Pelement = -20 dB, which should be specified as -20 dBW or as 10 mW to match Table III.
  4. [IV-B] The AP-level action space is stated as AAP in L; since the action is an L x K AP-selection matrix, this notation should be corrected to avoid confusion.
  5. [Figs. 3-5] The convergence figures have unlabeled axes except for the caption text; please specify what is plotted (e.g., normalized reward versus training episode) and include multiple-seed curves or error bars.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the EE metric, the learning objective, and the baselines are defined independently, and the reported gains are simulation comparisons rather than derived identities.

full rationale

The derivation chain starts from an independently stated system model (Eqs. (1)-(7)), a power consumption model adopted from the literature (Eqs. (8)-(13)), and a well-defined EE objective (Eq. (13)); none of these quantities is defined in terms of the proposed FL-based MARL solution or its outputs. The fuzzy-logic membership functions and the adaptive power threshold in Algorithm 1 are hand-specified design heuristics, not parameters fitted to the EE curves that are then relabeled as predictions. The RL reward functions in Eqs. (16) and (18) are defined directly from the EE metric, which is standard for an optimization-oriented algorithm and does not make the resulting EE comparison circular. The baselines (ZF, APFC-MADDPG, APS-MADDPG, and FL variants) are distinct schemes evaluated under the same metric, so the 10%, 16%, and 85% EE improvements are comparative simulation results with external grounding. The paper contains self-citations ([16], [20], [33], [35]) but they are used as related-work context or as a starting point for the fuzzy-logic design; no load-bearing claim is justified solely by an author-overlapping citation, and no uniqueness theorem is imported from the authors' prior work. The complexity reduction attributed to fuzzy logic is additionally supported by the paper's own complexity expressions in Table I. The noted inconsistency between the plotted EE magnitudes and Eq. (13) with the stated B = 180 kHz and P_CPU = 5 W is a reproducibility or correctness issue, not a circularity: it indicates a possible mismatch between the implemented and written models, but it does not show that any reported result is equivalent to its input by construction. Accordingly, no circular step is identified.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The numerical results rest on a stack of untested modeling choices: a borrowed channel model, a borrowed power model, an unspecified continuous-to-binary action mapping, an unquantified fuzzy approximation error, and single-trial convergence observations. No new physical entities are introduced; the fuzzy agents are an algorithmic device whose complexity-reduction claim is asserted, not proved.

free parameters (3)
  • Adaptive power threshold P_threshold and update rate τ_threshold = not reported
    Algorithm 1 uses the precoding-power threshold to decide which AP serves which UE; the threshold and its update rate are hand-set and never listed in Table III. The AP selection they produce is the paper's claimed source of EE gain.
  • Number of fuzzy agents N_F and membership width d_a = not reported
    The complexity reduction and convergence speedup claims depend on how many fuzzy agents replace the L actual agents and on the width d_a in the membership function ξ = exp(-|S-Ŝ|/(d_a n)); neither is specified.
  • Reward contribution weights ξ_lk = unspecified function of distance
    The AP-level reward Eq. (16) weights each agent's EE contribution by ξ_lk, described only as 'closely related to distance'; the actual weighting is unstated and directly shapes the learned policy.
assumptions (5)
  • domain assumption The adopted channel and path-loss model 'similar to [21]' is sufficient.
    Invoked in Section V-A; the simulation evidence for all claims inherits this model, which is not validated against measurements or a second model.
  • domain assumption Power consumption model of [42] (Eqs. 8-11), including SE-dependent fronthaul power, applies to the user-centric RIS system.
    Extended without modification in Section III-B; the SE-dependent fronthaul term couples EE to SE and affects all reported EE curves.
  • ad hoc to paper The continuous MARL action can realize the binary AP-selection matrix of constraint (14d).
    Algorithm 1 and Section IV-B never specify the quantization or feasibility step; without it the simulated system is not the one formulated in (14).
  • ad hoc to paper Fuzzy-agent aggregation preserves near-optimal policies (approximation error is negligible).
    Remark 1 and Section IV-A assert the fuzzy mapping reduces complexity 'by sacrificing a certain degree of precision' but provide no bound on the induced performance loss; the 2.5-3.6% gap is only measured in one simulation configuration.
  • ad hoc to paper The MARL training converges to a policy whose quality is representative.
    Convergence is asserted from Figs. 3-5 without theoretical guarantee, seeds, or replication statistics.

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Cite this review

Pith. "Pith review of Joint Precoding and AP Selection for Energy Efficient RIS-aided Cell-Free Massive MIMO Using Multi-agent Reinforcement Learning." pith.science (2026). https://pith.science/paper/XBO2MYSX

@misc{pith2026241111070,
  author       = {Pith},
  title        = {Pith review of: Joint Precoding and AP Selection for Energy Efficient RIS-aided Cell-Free Massive MIMO Using Multi-agent Reinforcement Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XBO2MYSX}},
  note         = {Machine review of arXiv:2411.11070}
}
read the original abstract

Cell-free (CF) massive multiple-input multiple-output (mMIMO) and reconfigurable intelligent surface (RIS) are two advanced transceiver technologies for realizing future sixth-generation (6G) networks. In this paper, we investigate the joint precoding and access point (AP) selection for energy efficient RIS-aided CF mMIMO system. To address the associated computational complexity and communication power consumption, we advocate for user-centric dynamic networks in which each user is served by a subset of APs rather than by all of them. Based on the user-centric network, we formulate a joint precoding and AP selection problem to maximize the energy efficiency (EE) of the considered system. To solve this complex nonconvex problem, we propose an innovative double-layer multi-agent reinforcement learning (MARL)-based scheme. Moreover, we propose an adaptive power threshold-based AP selection scheme to further enhance the EE of the considered system. To reduce the computational complexity of the RIS-aided CF mMIMO system, we introduce a fuzzy logic (FL) strategy into the MARL scheme to accelerate convergence. The simulation results show that the proposed FL-based MARL cooperative architecture effectively improves EE performance, offering a 85\% enhancement over the zero-forcing (ZF) method, and achieves faster convergence speed compared with MARL. It is important to note that increasing the transmission power of the APs or the number of RIS elements can effectively enhance the spectral efficiency (SE) performance, which also leads to an increase in power consumption, resulting in a non-trivial trade-off between the quality of service and EE performance.

Figures

Figures reproduced from arXiv: 2411.11070 by the authors.

Figure 1
Figure 1. Illustration of two representative RIS-aided CF mMI [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Illustration of a double-layer FL-based MARL networ [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Convergence rate of MADDGP for AP selection or AP full [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Convergence rate of FL-based MADDGP for AP selection [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Convergence time of MADDPG and FL-MADDPG algorithm w [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Energy efficiency versus the transmission power cons [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 9
Figure 9. Figure 9: Spectral efficiency versus the number of AP antennas w [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Energy efficiency versus the number of RIS elements w [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

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Forward citations

Cited by 2 Pith papers

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.