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REVIEW 3 major objections 5 minor 1 cited by

Federated Learning Strategies for Coordinated Beamforming in Multicell ISAC

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Federated learning coordinates multi-cell ISAC beamforming without sharing channel data.

desk verdict A useful FL-for-ISAC idea undermined by an undisclosed HFL weighting and a sensing SINR scaling error; fixable. read the letter →

arxiv 2501.16951 v1 pith:E744SZLX submitted 2025-01-28 eess.SP

Lai Jiang , Kaitao Meng , Murat Temiz , Jiaming Hu , Christos Masouros This is my paper · ORCID
classification eess.SP
keywords federatedlearningintegratedsensingandcommunications(ISAC)coordinatedbeamforminginter-cellinterferenceleakagemulti-cellnetworksdeepvertical
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 works on multi-cell integrated sensing and communications (ISAC), where base stations share spectrum for both communication and radar sensing. The problem is that beamforming from local channel knowledge alone creates inter-cell interference that hurts both users and neighboring-cell sensing receivers, while centralized beamforming needs global channel information and costly backhaul exchange. The authors propose two federated-learning designs that train deep networks for beamforming across base stations: a vertical-federated-learning (VFL) scheme in which a central server computes a global loss from locally designed beamformers, and a horizontal-federated-learning (HFL) scheme in which each base station trains solely on its own channel data using a loss that penalizes interference leakage. The central claim is that these distributed designs can reach performance comparable to centralized methods while keeping channel data local, cutting communication overhead and latency. If true, coordinated multi-cell ISAC beamforming becomes feasible in dense and latency-sensitive deployments.

What carries the argument

The load-bearing objects are the local loss functions in equations (21) and (22): the communication loss $L_c(W_m)$ adds a weighted penalty $\alpha$ on the total power leaked from base station $m$ toward all unintended users in other cells, and the sensing loss $L_s(W_m)$ adds a weighted penalty $\beta$ on the power leaked toward neighboring base stations' sensing receivers. Because each station can compute these leakage terms from its own channel estimates, the global problem splits into per-cell problems that FedAvg (averaging model parameters across stations) combines into a shared network. This leakage-based formulation is what lets the authors claim a fully decentralized training phase with no channel-data exchange.

What would settle it

Train the HFL framework in an interference-limited cell-edge scenario with the leakage weights $\alpha$ and $\beta$ swept from zero to large values, and compare the resulting global communication-plus-sensing rate against centralized WMMSE; if no setting of $\alpha$ and $\beta$ reproduces centralized performance, the claim that local loss minimization controls global interference is falsified.

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Extended reading notes

Core claim

The paper's central claim is that global interference control in multi-cell ISAC does not require global channel state information. The VFL framework trains each base station's local network branch while a central server evaluates the true global communication and sensing losses and feeds them back, so the stations learn to shape beams that suppress interference to other cells without exchanging channel data online. The HFL framework goes further: each station minimizes a local loss composed of its own achievable rates plus penalty terms for communication interference leakage and sensing interference leakage, defined via local channel estimates to neighboring receivers. With FedAvg-style aggregation of the model weights, the paper argues that minimizing these per-cell losses drives the global network objective to a near-optimal point, and numerical results show the HFL design closing most of the gap to centralized WMMSE while outperforming per-cell deep-learning and closed-form beamformers, especially in interference-limited regimes.

Load-bearing premise

The framework assumes that independently minimizing each base station's local loss, with its unreported leakage weights, pushes the global network objective to a near-optimal point, and that averaging the locally trained model weights converges to that solution.

Editorial extensions

If this is right

  • In interference-limited deployments, the HFL design should deliver most of the interference-nulling gain of centralized coordination while requiring only local channel estimates.
  • Communication overhead during training drops from uploading channel samples and beamformers (VFL) to uploading only model parameters (HFL), enabling fine-tuning or retraining in dense networks.
  • The same local leakage-penalty idea can be applied when the served users or targets move, since each station can recompute its leakage terms from its own updated channels.
  • Model pruning can remove 50–60% of network parameters while keeping performance near the unpruned model, making the beamforming network light enough for practical base stations.

Reading between the lines

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

  • Inference: extending the leakage-loss idea to time-varying channels, one could periodically recompute the penalty terms from fresh local CSI and retrain only the affected base station, a possibility the paper does not explore.
  • Inference: because the leakage penalties only suppress power leaked along known interfering directions, the HFL performance should degrade when the interfering channels are estimated with error; a robustness study would test this boundary.
  • Inference: the same local-loss construction could transfer to other coordinated radio problems, such as pilot assignment or power control in dense cell-free networks, wherever inter-node interference can be expressed as leaked power.
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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

3 major / 5 minor

Summary. The paper proposes two federated-learning-based beamforming frameworks for multi-cell ISAC systems. The first, VFL-based, has base stations train local DNNs while a central server computes the global communication and sensing loss and feeds it back for local model updates. The second, HFL-based, is fully decentralized: each BS trains a shared model locally using a newly proposed interference-leakage-based loss function (21)-(22), with FedAvg aggregation. The authors claim both methods can manage inter-cell interference using only local channel information and achieve performance comparable to centralized WMMSE while significantly reducing communication overhead and computational complexity. Numerical simulations compare the proposed schemes against WMMSE, per-cell deep learning, MRT, IMT, and CBF benchmarks under various SNRs, antenna counts, and S&C tradeoff weights, and also study model pruning.

Significance. If validated, the paper would provide a practical low-overhead alternative to centralized coordinated beamforming in multi-cell ISAC, and the HFL interference-leakage loss is an interesting and potentially useful construction. The paper also gives a detailed complexity and communication-overhead analysis and includes pruning experiments, which are valuable for deployment considerations. However, the current manuscript has several load-bearing technical gaps: the VFL training procedure as described is not implementable, the sensing SINR in Eq. (7) appears inconsistent with Eq. (6), and the HFL surrogate-to-global equivalence relies on undisclosed hyperparameters. These issues must be resolved before the central claims can be considered established.

major comments (3)
  1. [Section II-B, Eq. (7)] The sensing SINR in Eq. (7) appears to have a factor-N_R inconsistency relative to Eq. (6). After MRC combining with v_m = b(θ_m), the signal component in Eq. (6) is N_R α_m a^H(θ_m) W_m s_m, so the signal power in the SINR expression should scale as N_R^2 ∑_k |g^H_{m,m} w_{m,k}|^2 (with g_{m,m} = α_m a(θ_m)), whereas Eq. (7) uses only a single factor N_R in the numerator and keeps σ_s^2 in the denominator. This changes the numerical radar information rates by a factor of N_R (about 7.8 dB for N_R=6) and may therefore alter the reported sensing performance and the conclusions drawn from Figs. 5(b) and 8.
  2. [Section III-C, Step 4 and Eq. (18)] The VFL backward-propagation step is not well-defined. The paper states that each BS receives the global loss scalar and then performs individual backpropagation using the chain rule (Eq. (18)). However, the gradient ∂ℓ/∂ω_m of the global loss with respect to local parameters depends on ∂ℓ/∂W_m, which requires knowledge of all cross-cell channels (e.g., h_{n,m,k} for n≠m) and the beamformers of other BSs. A scalar global loss value does not provide this derivative information. To make the VFL procedure implementable, the server would need to transmit the gradient of the global loss with respect to each local output matrix W_m (or an equivalent error signal) to each BS, or the paper must explain how the local BS can compute the gradient without this information.
  3. [Section IV-B, Eqs. (21)-(22) and (25)] The central claim for the HFL framework rests on the assertion in Section IV-B that minimizing the local losses (21)-(22) leads to the minimization of the global loss (25), and hence solves the original problem (9). The local losses replace the actual SINR expressions, which contain inter-cell interference, with interference-free local SINRs plus leakage penalties weighted by α and β. There is no analytical characterization of the relationship between the surrogate (25) and the original objective (9); the paper only states that simulations verify the effectiveness. Moreover, the values of α and β used in Section V are never disclosed, and no sensitivity analysis is provided. Without these, the reported 'performance comparable to centralized methods' could be a tuning artifact of unreported hyperparameters rather than a robust property of the proposed method.
minor comments (5)
  1. [Section IV-A, Eq. (21)] In Eq. (21), the CIL penalty term is written as ∑_{n≠m} ∑_{i=1}^K |h^H_{m,n,i} w_{m,k}|^2, which is inconsistent with the definition of CIL in Eq. (19) where the beamforming matrix W_m appears. As written, the index k is free and the sum over k is missing. Please correct the expression, for example to ∑_{n≠m} ∑_{i=1}^K ∑_{k=1}^K |h^H_{m,n,i} w_{m,k}|^2.
  2. [Algorithm 1 and Algorithm 2] The line 'W∗_m = f([H_m, G_m]; ω∗), ∀m ⊂ M' uses the subset symbol ⊂ instead of the membership symbol ∈; the correct form is ∀m ∈ M.
  3. [Section III-C, Eq. (18)] There is a notation inconsistency between ω and w: Eq. (18) writes ω_m^{(T+1)} = w_m^{(T)} − η∇ℓ, where the right-hand side uses w instead of ω. This should be ω_m^{(T)} for clarity.
  4. [Table II] In the provided text, Table II is not formatted correctly: the HFL row contains running text instead of a complexity expression, and the table appears incomplete. Please provide a clean table with the computational complexities for all three methods.
  5. [Section V-A and V-B] The benchmarks are not fully specified: for WMMSE, the authors cite [16] but do not describe how the communication-only WMMSE is extended to the ISAC objective (9) with the sensing rate; for the per-cell DL benchmark in Fig. 5(b), the network architecture and training details are not given. Adding these details would improve reproducibility.

Circularity Check

0 steps flagged · score 2.0 of 10

No circularity in the HFL/VFL derivation: performance is checked against external benchmarks; the heuristic surrogate loss and undisclosed α/β are robustness concerns, not circular reductions.

full rationale

The central derivation is not circular. The global objective (9) is defined from the true SINRs (3) and (7), which include inter-cell interference terms. The HFL method replaces these with a deliberately different local surrogate (21)-(22): interference-free local SINRs plus leakage penalties αΣ|h^H_{m,n,i}W_m|^2 and βΣ|g^H_{m,n}W_m|^2. The paper does not claim this surrogate is equivalent to (9); instead it states 'It can be verified through simulations that optimizing loss function (21) and (22) can achieve a good performance when the interference caused to the mth cell is eliminated by other BSs' (Section IV-A). That is an empirical validation against external benchmarks (WMMSE [16], per-cell DL [21], MRT [45], IMT [46], CBF [34]), so the performance claim is independently testable. The leakage-penalty construction follows [41], which shares an author with the present paper, but the paper cites it as a published 'workaround' and the leakage channels used in (19)-(20) are part of the local CSI model, not an output of this paper. The VFL branch similarly computes the true global loss (14)-(15) at the server and is therefore not self-definitional. The main weaknesses are not circularity: α and β are never disclosed in Section V, and the statement that minimizing local losses minimizes the global loss (Section IV-B) is asserted without a convergence or optimality bound. These are reproducibility and robustness concerns, not reductions of the predicted performance to the fitted inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The main hidden degrees of freedom are the two leakage-penalty hyperparameters α and β in the HFL loss, whose values are not reported. The paper also relies on several domain assumptions about the sensing model and about FL convergence that are stated but not proven.

free parameters (2)
  • α (CIL weighting factor) = not reported
    Controls the interference leakage penalty in HFL loss (21); the paper says simulations verify its effectiveness but does not give its value or selection procedure.
  • β (SIL weighting factor) = not reported
    Controls the sensing interference leakage penalty in HFL loss (22); also unreported.
assumptions (5)
  • domain assumption Radar information rate equals log2(1 + sensing SINR)
    Equation (8) uses this surrogate for sensing performance, citing [36].
  • domain assumption Self-interference at each BS can be perfectly canceled
    Section II-B assumes Gm,m is known from previous measurements and removed, following [12].
  • domain assumption Minimizing local HFL losses minimizes the global objective
    Section IV-B asserts this without proof for the leakage-penalized losses (21)-(22).
  • domain assumption Accurate CSI is available at BSs
    Section III-A says it is reasonable to assume accurate channel estimation for DNN training.
  • domain assumption Neural networks can represent the optimal beamforming mapping
    The paper relies on universal approximation and prior learning-based beamforming literature (e.g., [37], [20], [21]).

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Cite this review

Pith. "Pith review of Federated Learning Strategies for Coordinated Beamforming in Multicell ISAC." pith.science (2026). https://pith.science/paper/E744SZLX

@misc{pith2026250116951,
  author       = {Pith},
  title        = {Pith review of: Federated Learning Strategies for Coordinated Beamforming in Multicell ISAC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E744SZLX}},
  note         = {Machine review of arXiv:2501.16951}
}
read the original abstract

We propose two cooperative beamforming frameworks based on federated learning (FL) for multi-cell integrated sensing and communications (ISAC) systems. Our objective is to address the following dilemma in multicell ISAC: 1) Beamforming strategies that rely solely on local channel information risk generating significant inter-cell interference (ICI), which degrades network performance for both communication users and sensing receivers in neighboring cells; 2) conversely centralized beamforming strategies can mitigate ICI by leveraging global channel information, but they come with substantial transmission overhead and latency that can be prohibitive for latency-sensitive and source-constrained applications. To tackle these challenges, we first propose a partially decentralized training framework motivated by the vertical federated learning (VFL) paradigm. In this framework, the participating base stations (BSs) collaboratively design beamforming matrices under the guidance of a central server. The central server aggregates local information from the BSs and provides feedback, allowing BSs to implicitly manage ICI without accessing the global channel information. To make the solution scalable for densely deployed wireless networks, we take further steps to reduce communication overhead by presenting a fully decentralized design based on the horizontal federated learning (HFL). Specifically, we develop a novel loss function to control the interference leakage power, enabling a more efficient training process by entirely eliminating local channel information exchange. Numerical results show that the proposed solutions can achieve significant performance improvements comparable to the benchmarks in terms of both communication and radar information rates.

Figures

Figures reproduced from arXiv: 2501.16951 by the authors.

Figure 1
Figure 1. The considered multi-cell ISAC system. ceivers. Therefore, the loss function can be independently optimized at each BS, which eliminates the need for exchanging channel information during both training and online beamforming stages. This characteristic enhances data privacy and significantly reduces communication overhead, making the approach more adaptable and ef￾ficient for multi-cell systems. • Through numerical … view at source ↗
Figure 2
Figure 2. The proposed beamforming DNN structure. the output with a C2R block, which recovers the complex beamformer W∗ of size NT × K by combining the real and imaginary parts in the following way W∗ = Wˆ [:, :, 1] + jWˆ [:, :, 2]. (13) where the two terms on the right-hand side are the first and second elements along the third dimension of Wˆ . C. Learning-based Formulation and Training Due to the issue of local BSs lacking… view at source ↗
Figure 3
Figure 3. VFL training framework. 1) Forward propagation: In the global round T, the local BSs use the ith local channel sample to design the beamform￾ing matrices, the process can be given by Wm = f([H(i) m , G(i) m ]; ω (T) m ), (17) where ω (T) m is the model parameter set of the mth BS at the Tth global round. 2) Local uploading: Each BS uploads its independently designed beamforming matrices and the corresponding input c… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: HFL training framework. which results in a total communication cost of (M + 1)KNT for each local BS. As for the online deployment phase, the computational overhead is primarily attributed to forward propagation, which scales linearly with the number of cells M, communi…
Figure 5
Figure 5. Figure 5: Comparison of communication rate Rc and radar information rate Rs under different SNRs between the proposed methods and benchmarks. method [21], and the closed-form solutions maximum ratio transmission (MRT) [45] and the interference minimizing transmission (IMT) [46] …
Figure 6
Figure 6. Figure 6: Beampatterns for the scenario of point target at [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Comparison of communication rate Rc and radar information rate Rs with respect to the number of antennas NT between the proposed methods and benchmarks. (a) S&C tradeoff under different SNRs. (b) S&C tradeoff under different numbers of transmit antennas [PITH_FULL_IMA…
Figure 8
Figure 8. Figure 8: Tradeoff betweem communication rate Rc and radar information rate Rs when ρ ranges from 0.1 to 0.9. the unintended signal power leaking to surrounding BSs can disrupt their sensing. It is observed that the beampattern of per-cell DL method closely resembles that obtain…
Figure 9
Figure 9. Figure 9: Performance vs complexity trade-off: effect of model pruning to the beamforming DNNs trained with different frameworks. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.