Toward Practical Fluid Antenna Systems: Co-Optimizing Hardware and Software for Port Selection and Beamforming

Baiyang Liu; Chan-Byoung Chae; Hanjiang Hong; Kai-Kit Wong; Kin-Fai Tong; Sai Xu; Yanan Du

REVIEW 4 major objections 5 minor 35 references

Toward Practical Fluid Antenna Systems: Co-Optimizing Hardware and Software for Port Selection and Beamforming

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A graph neural network with random port selection, accelerated on an FPGA, makes fluid-antenna beamforming and port selection practical.

desk verdict Solid but incremental FAS engineering: the GNN-RPS + FPGA co-design is plausible and the hardware scheduling is genuinely useful, but the paper overclaims inter-cell interference management when its GNN inputs are strictly local CSI. read the letter →

arxiv 2507.14035 v1 pith:F53EHTV2 submitted 2025-07-18 eess.SP

Sai Xu , Kai-Kit Wong , Yanan Du , Hanjiang Hong , Chan-Byoung Chae , Baiyang Liu , Kin-Fai Tong This is my paper · ORCID

classification eess.SP

keywords fluidantennasystemsportselectionbeamforminggraphneuralnetworksrandomFPGAaccelerationweightedsumratemaximizationhardware-softwareco-design

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 establish that fluid antenna systems can be made practical by co-designing the optimization algorithm with the hardware that runs it. The algorithmic claim is that a multi-cell graph neural network (GNN) for beamforming, paired with random port selection, reaches near-exhaustive weighted-sum-rate performance after only tens of random port choices and outperforms minimum mean square error (MMSE), zero-forcing (ZF), and maximum ratio transmission (MRT) baselines. The hardware claim is that an instruction-driven field-programmable gate array (FPGA) accelerator can run several of these port-selection beamforming inferences concurrently with little added latency. If both claims hold, the computationally prohibitive mixed-integer optimization of port selection and beamforming can be replaced by a deployable real-time pipeline.

What carries the argument

The load-bearing mechanism is a multi-GNN architecture with centralized training and distributed inference, in which each base station runs a homogeneous GNN module that maps local channel state information, the real and imaginary parts of its channels to the served users, into beamforming vectors. Each GNN consists of an input multi-layer perceptron (MLP), two GNN layers whose aggregation is an MLP followed by max-pooling over the other users and whose combination is concatenation followed by an MLP, and a final fully connected layer with power-normalizing LayerNorm. Port selection is handled by random port sampling, keeping the best of several trials. On the FPGA, the key mechanism is an instruction-driven overlay accelerator with a custom instruction set architecture, systolic-array matrix units, ping-pong double buffering, and a scheduling algorithm that concatenates inputs from multiple port selections, reuses shared weights and intermediate results, and reorders computation so that memory-bound GNN tasks overlap instead of stalling.

What would settle it

Run the trained GNN on the FPGA in 8-bit fixed point and in a higher-precision reference using the same channel samples as the simulations, and compare the output beamforming vectors or the resulting weighted sum rate; a non-negligible gap would break the link between the measured latency and the claimed communication performance.

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Extended reading notes

Core claim

The paper claims that the mixed-integer problem of jointly choosing fluid-antenna ports and computing downlink beamforming vectors can be split into a GNN for beamforming and random port selection for port choice. In the simulated two-cell, four-user-per-cell setting, 20 random port selections reach about 70% of the weighted sum rate obtained with 2,000 selections, and the GNN-based scheme beats MMSE, ZF, and MRT at every transmit power tested. On the hardware side, an instruction-driven FPGA accelerator with a custom instruction set and a scheduling algorithm that shares model parameters and reuses intermediate results executes up to four concurrent port-selection inferences in 3.994 to 6.222 ms, nearly the same as the 3.926 to 6.104 ms needed for a single inference. The paper presents the combination as a complete hardware-software path toward real-time intelligent beamforming in fluid antenna systems.

Load-bearing premise

The load-bearing premise is that the FPGA's 8-bit fixed-point arithmetic loses negligible beamforming accuracy; if quantization materially degrades the beamforming vectors, the measured low latency would not reproduce the communication performance shown in simulation.

Editorial extensions

If this is right

Random port selection with tens of trials can approximate the performance of a far larger port search, so the combinatorial port-selection bottleneck in fluid antenna systems is much smaller than exhaustive enumeration suggests.
GNN-based beamforming can outperform MMSE, ZF, and MRT in multi-cell fluid-antenna downlinks because the multi-GNN learns inter-cell and inter-user interference patterns from channel features.
Because the accelerator reuses loaded model weights and intermediate results, the latency of processing several port selections is close to that of one, up to about four concurrent tasks.
Measured inference latencies of about 3.9 to 6.2 ms provide a prototype baseline for real-time beamforming, with model compression and ASIC implementations expected to push latency lower.

Reading between the lines

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

If the 8-bit fixed-point quantization truly costs negligible accuracy, the same scheduling strategy should scale beyond four concurrent port selections once the workload shifts from memory-bound to compute-bound, so adding on-chip compute or sparsity could extend the parallelism further.
The RPS result suggests port selection can be treated as a cheap stochastic search; a learned selection policy trained alongside the GNN could capture additional gains over random trials at modest extra inference cost.
Because the accelerator is instruction-driven and overlay-based, the same hardware design could be retargeted to other GNN-based wireless optimization problems, such as RIS-assisted or cell-free beamforming, by recompiling instructions rather than redesigning the chip.
A direct precision comparison on the FPGA would be the natural next experiment; until it is reported, the communication-performance claims and the latency claims rest on separate evidence.

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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 paper is a legitimate, well-executed incremental contribution: it applies GNN-based beamforming to fluid antenna port selection and builds an FPGA accelerator with a scheduling algorithm that lets four port-selection inferences run almost at single-inference latency. The RPS analysis (70% of the 2000-trial WSR with only 20 trials) is useful engineering knowledge, and the hardware measurements are real experiments, honestly caveated as still exceeding typical coherence times. The authors are clearly fluent in both the FAS literature and the GNN-beamforming literature; the writing is straightforward and the approach is reproducible in simulation from the described details.

The biggest soft spot is the mismatch the stress-test note flags: the GNN inputs (Eq. 6) contain only the desired channels from each BS to its own UEs, no inter-cell channels. The multi-cell WSR objective depends on cross links, so the trained GNN cannot adapt to instantaneous inter-cell interference. Claims in Sec. IV-A4 that the model "effectively learns to characterize both inter- and intra-cell interference patterns" and enables "network-wide performance optimization through distributed cooperation" are not supported by the architecture. At best, centralized training over a global WSR loss learns a policy that is robust to interference in expectation, but the inference is per-cell and local. This is an overstatement rather than a fatal flaw: the baselines (MMSE, ZF, MRT) also use local CSI, so the comparisons are fair, but the paper should not claim coordinated multi-cell beamforming gains.

Second, the absence of a WMMSE or other optimization-based baseline weakens the "competitive performance" claim. GNN beating ZF/MMSE/MRT is not a high bar; a WMMSE comparison would calibrate how much is lost by the learned local policy. Third, the 8-bit fixed-point FPGA results are presented with latency only, no resource/power, and no quantified accuracy loss in beamforming output or WSR, so the link between hardware speed and communication performance is unverified. Fourth, no code or data are released; given the heavy self-citation and the incremental nature, community access to code would materially strengthen the paper.

The citation pattern is heavy on the authors' own FAS work, but that is common in a young subfield where they are central; it is not a disqualifier. The central contribution is new, clearly described, and supported by real experiments. This deserves a serious referee, but the authors should be asked to either add inter-cell CSI to the GNN input and rerun the simulations, or substantially tone down the inter-cell interference claims. The hardware section is fine and could be a separate contribution on its own. For a reader in FAS or GNN-based beamforming, this is worth reading and citing once the claims are aligned with the architecture.

Referee Report

4 major / 5 minor

Summary. The paper proposes a hardware-software co-design framework for fluid antenna systems (FASs). It formulates a weighted-sum-rate (WSR) maximization problem for an FA-enabled downlink multi-cell MIMO network with port selection and beamforming, proposes a multi-GNN architecture with random port selection (GNN-RPS) to solve it, and implements the GNN inference on an FPGA with a custom instruction set, systolic-array micro-architecture, and a scheduling algorithm for concurrent inference. Simulations compare GNN-RPS against MMSE, ZF, and MRT baselines under random port selection, and FPGA experiments report inference latency for single and multiple concurrent port-selection tasks.

Significance. If fully supported, the paper would be a useful step toward practical FAS by showing that a learned beamformer combined with random port selection can approach the performance of much larger search budgets, and by demonstrating that multiple GNN inference tasks can share an FPGA accelerator with nearly unchanged latency. The scheduling result in Section VI-C, where four concurrent inferences run almost as fast as one, is an interesting and clearly reported hardware contribution. The central communication claim, however, is weakened by the mismatch between the inter-cell objective and the local-only GNN input features, and by the absence of an optimization-based baseline such as WMMSE. The hardware claim also lacks quantization-fidelity evidence for the 8-bit fixed-point implementation. With those points addressed, the paper could make a solid contribution to system-level FAS design.

major comments (4)

[Sec. IV-A, Eq. (6), Sec. IV-A4] The node feature matrix X_in_i in Eq. (6) contains only Re/Im of the desired channels h_{ik,i} for UEs in cell i; no cross-cell channels h_{ik,j}, j≠i, are provided to any GNN. Because the SINR in Eq. (5) and hence the WSR objective (P1) depend on inter-cell interference terms |h_{ik,j}w_{jr}|^2, a beamformer computed from X_in_i is invariant to the instantaneous realizations of those interference links. The claim in Sec. IV-A4 that the multi-GNN 'effectively learns to characterize both inter- and intra-cell interference patterns' and enables 'network-wide performance optimization through distributed cooperation' is therefore not supported by the architecture. Training on a global WSR loss cannot introduce information that is absent from the input; at best the model learns a policy optimized in expectation over the channel distribution. Please either incorporate cross-cell channels into the input features or revise the claims and interpret Figs. 7-10 as gains of a per-cell policy rather than coordinated inter-cell beamforming.
[Sec. VI-B, Figs. 7-10] The conclusion that GNN-RPS achieves 'competitive communication performance' is drawn only against MMSE, ZF, and MRT baselines. Since P1 is a standard WSR maximization problem, a WMMSE-type optimization baseline using the same random port selections and the same CSI is the natural reference. Without such a baseline, the reader cannot judge how close the learned beamformers are to the optimum, or whether the reported gains reflect the GNN or merely the relative weakness of the baselines. Please add a WMMSE or other state-of-the-art optimization-based baseline.
[Sec. VI-C] The FPGA experiments use 8-bit fixed-point arithmetic and state that this gives 'only negligible loss in accuracy,' but no comparison is provided between 8-bit and floating-point beamforming outputs or WSR values. Since all latency numbers in Sec. VI-C are obtained with this representation, the hardware-software co-design claim requires evidence that quantization does not materially change the communication performance reported in Sec. VI-B. Please report quantization-aware simulation results or a hardware-in-the-loop comparison.
[Sec. IV-A5, Algorithm 1 line 19] The output normalization Xout_i ← √P LayerNorm(X_i^(8)) is not shown to enforce the per-BS power constraint C1. Standard LayerNorm normalizes each row (or the full matrix) to zero mean and unit variance, so the resulting total transmit power is not necessarily equal to P and may violate C1 when K_i>1. Please specify the exact normalization operation, state how the power constraint is enforced, and confirm that the WSR values in Figs. 6-10 are computed with feasible beamformers.

minor comments (5)

[Sec. VI-B] The scheme labeled 'GNN-Exhaustive' uses 500 independent random trials, which is not an exhaustive search over all L^N port combinations; the label and the associated 'upper bound' claim should be revised to avoid overstating the reference.
[Sec. IV-A5] The complexity notation L1,...,L8 is not mapped to the dimensions given in Table II; please define these quantities or align them with the table so that the complexity expressions can be verified.
[Eq. (1)] Equation (1) appears to have a typesetting error in the Bessel-function argument, with a missing closing parenthesis; please correct the formula.
[Algorithm 1] In Algorithm 1, lines 5-9 compute MLP1(x_i,k') repeatedly for every k, although the MLP output does not depend on k; the text should clarify whether this is intentional or a simplified description, since it affects the stated O(K_i^2) complexity.
[Sec. III] The manuscript should state explicitly how the channel vector for a selected port is obtained from the correlated model in Eqs. (1)-(3), since this is needed to reproduce the RPS simulations.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction found; self-citations are background, but the paper's inter-cell coordination claim is not supported by its local-only GNN inputs.

full rationale

No circular step was found. The GNN is trained with the WSR loss and evaluated on WSR in Figs. 6-10, which is standard learning-based optimization with independent test samples, not a fitted parameter renamed as a prediction. Comparisons to MMSE, ZF, and MRT are external benchmarks, so the central performance claim is self-contained. The paper's self-citations are not load-bearing: [6,7] establish FAS as background, and [32] supplies a standard Jake's-model correlation form with stated assumptions that do not include the target result. No uniqueness theorem is imported from the authors' prior work. Two non-circular weaknesses should be noted. First, Eq. (6) supplies each GNN only with local desired-channel features Re/Im{h_{ik,i}}, yet Section IV-A4 claims the multi-GNN effectively learns to characterize both inter- and intra-cell interference and enables network-wide performance optimization through distributed cooperation; because inter-cell channel information is absent from the input, instantaneous inter-cell coordination is not realizable as described. Second, Section VI-C asserts 8-bit fixed-point arithmetic gives negligible loss in accuracy without comparing beamforming or WSR against higher precision, so the reported latency does not by itself establish communication performance. These are evidence gaps, not circular derivation.

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

No new physical entities are introduced; the FA concept, GNN, and FPGA overlay are all drawn from prior literature. The load-bearing postulates are the channel model, full-CSI assumption, quantization accuracy, and local-vs-global CSI consistency.

free parameters (3)

Number of RPS trials (RandomMax) = 20
Chosen from Fig. 6 where gains saturate; no principled selection criterion is given.
GNN hidden layer sizes = 1024, 512, 512, ...
Listed in Table II without tuning or ablation; these sizes determine the compute and memory load of the accelerator.
Fixed-point bit-width = 8-bit
Design choice; the paper asserts negligible accuracy loss but provides no measurement linking 8-bit inference to WSR.

assumptions (4)

domain assumption FA correlation follows Jake's model and FAs are spaced >= lambda/2 so mutual coupling is negligible
Section III-A, Eqs. (1)-(3): the entire channel simulation depends on this model; real FAS hardware may deviate.
domain assumption Full and perfect CSI is available at the BSs
Section III-B: the problem formulation assumes full CSI; CSI acquisition for many ports is a known practical bottleneck not addressed.
ad hoc to paper 8-bit fixed-point quantization has negligible accuracy loss
Section VI-C: asserted, never verified against floating-point WSR or beamforming error.
domain assumption Distributed GNN inference with local CSI matches centrally trained performance
Section IV-A4: the multi-GNN is trained with global CSI but deployed with only local CSI; no experiment isolates the effect of this mismatch.

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Pith. "Pith review of Toward Practical Fluid Antenna Systems: Co-Optimizing Hardware and Software for Port Selection and Beamforming." pith.science (2026). https://pith.science/paper/F53EHTV2

@misc{pith2026250714035,
  author       = {Pith},
  title        = {Pith review of: Toward Practical Fluid Antenna Systems: Co-Optimizing Hardware and Software for Port Selection and Beamforming},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F53EHTV2}},
  note         = {Machine review of arXiv:2507.14035}
}

read the original abstract

This paper proposes a hardware-software co-design approach to efficiently optimize beamforming and port selection in fluid antenna systems (FASs). To begin with, a fluid-antenna (FA)-enabled downlink multi-cell multiple-input multiple-output (MIMO) network is modeled, and a weighted sum-rate (WSR) maximization problem is formulated. Second, a method that integrates graph neural networks (GNNs) with random port selection (RPS) is proposed to jointly optimize beamforming and port selection, while also assessing the benefits and limitations of random selection. Third, an instruction-driven deep learning accelerator based on a field-programmable gate array (FPGA) is developed to minimize inference latency. To further enhance efficiency, a scheduling algorithm is introduced to reduce redundant computations and minimize the idle time of computing cores. Simulation results demonstrate that the proposed GNN-RPS approach achieves competitive communication performance. Furthermore, experimental evaluations indicate that the FPGA-based accelerator maintains low latency while simultaneously executing beamforming inference for multiple port selections.

Figures

Figures reproduced from arXiv: 2507.14035 by the authors.

**Figure 2.** An illustration of graph representation and neural n [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** An illustration of customized ISA. evaluated to ultimately identify the highest-performing port selection. In the simulation section (see Section VI for details), it can be observed that the WSR distribution with varying numbers of selections demonstrates that RPS, when independent trials are conducted tens of times, can achieve a suboptimal performance very close to the optimal solution. V. INSTRUCTION-DRIVEN FPGA… view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: An illustration of hardware micro-architecture. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Training and inference performance of the multi-GNN [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: WSR distribution with varying numbers of RPSs. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 9.** Figure 9: The relationship between the WSR and the number of UEs [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 8.** Figure 8: The relationship between the WSR and the number of BSs [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

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