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REVIEW 3 major objections 7 minor 20 references

Fair Rate Maximization for Fluid Antenna Relay (FAR)-assisted Multi-user MISO Communications

T0 review · 3 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read An alternating SCA algorithm that jointly optimizes user, relay, and base-station fluid-antenna positions can maximize the minimum achievable rate in a FAR-assisted multi-user MISO uplink.

desk verdict The FA-position max-min algorithm is built on a false equivalence: maximizing minimum signal power is not maximizing minimum SINR, so the central claim does not hold. read the letter →

arxiv 2507.00529 v1 pith:VCH4HYTM submitted 2025-07-01 eess.SP

Ruopeng Xu , Zhaohui Yang , Ting Zhang , Mingzhe Chen , Chen Zhu , Zhaoyang Zhang This is my paper · ORCID
classification eess.SP
keywords fluidantennasystemrelaymax-minfairnesssuccessiveconvexapproximationMISOuplinkpositionoptimizationrate
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 asks whether giving every antenna in a relay-assisted uplink the freedom to move—user antennas, both faces of the relay, and the base station—can protect the weakest user's rate instead of maximizing total throughput. It claims yes: an alternating successive-convex-approximation algorithm updates one antenna position at a time under minimum-separation and power constraints and maximizes the smallest user's effective channel gain. If correct, fairness-critical uplinks behind obstacles would no longer have to sacrifice the weak user's rate to sum-rate designs. Simulation results across SNR and normalized antenna-region size are presented as evidence.

What carries the argument

The load-bearing object is the field-response channel model: each antenna's channel is a phase-weighted sum over multipath directions, $\mathbf{h}(t_k,\mathbf{R}_U)=[\mathbf{F}_{k,U}(\mathbf{R}_U)]^H\boldsymbol{\Sigma}_k\mathbf{u}_k(t_k)$, with the relay represented by a diagonal amplify-and-forward gain matrix $\mathbf{F}$. On top of that, the argument runs on SCA surrogate lower bounds: every non-concave objective in $t_k$, $\mathbf{r}_{U_m}$, $\mathbf{t}_{B_m}$, and $\mathbf{r}_n$ is replaced by a quadratic surrogate from first/second-order Taylor expansion, and the non-convex minimum-distance constraints are replaced by first-order approximations, so each alternating subproblem is convex and solvable by standard tools.

What would settle it

In a two-user setup, run Algorithm 2 and compare the returned positions against a feasible alternative that lowers user 1's signal power but also lowers user 2's interference to user 1; if the alternative yields a higher true minimal rate $\min_k\log_2(1+\gamma_k)$, then the equivalence in (16) does not hold as an optimization statement.

Watch

Extended reading notes

Core claim

The paper's central claim is that max-min rate fairness in the FAR-assisted uplink can be pursued by reformulating the problem as maximizing the minimum received signal power $\|p_k\tilde{\mathbf{H}}\tilde{\mathbf{h}}_k\|_2^2$ over all users, introducing an auxiliary variable $\alpha$, and then solving the resulting problem (17) and its worst-user variant (18) with an alternating SCA routine (Algorithms 1 and 2). Each antenna-position subproblem is turned into a convex program by lower-bounding the non-concave objective with Taylor-expansion surrogates and by linearizing the minimum-distance constraints. The paper reports that this procedure consistently beats fixed-antenna and relay-only-movement baselines in the simulated SNR and region-size ranges, indicating that antenna positioning is what improves the weakest user's outcome.

Load-bearing premise

The paper's transformation from max-min rate to max-min signal power relies on all users' SINR denominators staying in the same order, but those denominators contain every other user's signal power and change as antennas move, so maximizing the weakest signal power is not shown to coincide with maximizing the weakest SINR.

Editorial extensions

If this is right

  • In blocked-line-of-sight scenarios, moving all fluid antennas—users, relay, and base station—raises the weakest user's achievable rate compared with keeping them fixed.
  • The advantage over the relay-only and fixed baselines persists across the tested SNR range, not just at one operating point.
  • Larger normalized antenna regions improve the maximized minimum rate for all schemes, and the gap between the proposed scheme and the baselines widens with region size.
  • The alternating SCA structure keeps each subproblem convex, so the approach offers a tractable route to fairness-oriented fluid-antenna deployment rather than a combinatorial search over ports.

Reading between the lines

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

  • A natural extension is to multi-relay or multi-cell FAR deployments, since each subproblem only needs the local field-response model and a minimum-distance constraint.
  • The paper leaves implicit that it optimizes the minimum effective channel gain as a proxy for the minimum rate; in regimes with strong cross-user interference, a direct max-min-SINR objective would be the more exact formulation to compare against.
  • The widening gain with region size suggests a testable scaling law: the minimal-rate improvement should track the position diversity available to the weakest user, which fixed-aperture systems cannot exploit.
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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 / 7 minor

Summary. The manuscript considers an uplink FAR-assisted multi-user MISO system with fluid antennas at the users, the relay (FAR), and the base station, where the direct LoS paths are blocked. It formulates a max-min rate (fairness) problem over the antenna positions, subject to minimum-distance, region, and power constraints, and proposes an alternating successive convex approximation (SCA) algorithm. The authors claim that maximizing the minimum rate is equivalent to maximizing the minimum signal power, and they provide simulation results showing that the proposed method outperforms fixed-antenna and relay-only-movement baselines.

Significance. The fairness objective is practically relevant: sum-rate maximization in fluid-antenna systems can starve weak users, and the FAR relay model addresses realistic blockage scenarios. The channel model using field-response vectors is more general than many existing FAS papers. If the proposed transformation and algorithm were correct, the work would constitute a useful contribution to fairness-oriented fluid-antenna design. However, the central mathematical equivalence in Eq. (16) is invalid, so the algorithm does not directly address the stated max-min rate problem. The paper also provides no convergence or optimality analysis, and the SINR simplification in Eqs. (12)-(13) is not consistent with the stated EGC assumption. As a result, the main claim of the abstract is not supported.

major comments (3)
  1. [III, Eq. (16)] The equivalence claimed in Eq. (16) is incorrect. Eq. (15) shows that, for a fixed set of channel gains S_k = ||p_k \tilde{H}\tilde{h}_k||^2, the user with the smallest S_k also has the smallest SINR γ_k. It does not imply that maximizing min_k S_k over antenna positions maximizes min_k γ_k, because γ_k = S_k / (σ^2 + Σ_{i≠k} S_i) and the denominators change as the antenna positions move. For K=2 and σ^2=1, gains (S_1,S_2) = (100,1) give min_k γ_k ≈ 0.0099, whereas gains (5,0.5) give min_k γ_k ≈ 0.0833; the latter has a lower minimum signal power but a higher minimum SINR. Thus problems (17) and (18), and therefore Algorithms 1 and 2, optimize min_k S_k rather than the min-rate objective in (14). The simulation curves labeled 'maximized minimal achievable rate' do not establish maximization of the minimal rate; at best they represent a heuristic that maximizes the minimum signal power.
  2. [II-B, Eqs. (12)-(13)] The simplification from (12) to (13) is not consistent with the stated equal-gain-combining (EGC) assumption. If ω_k is an N-dimensional all-ones vector, the numerator in (12) is |p_k|^2 |1^T \tilde{H}\tilde{h}_k|^2, the noise term is σ_U^2 ||1^T \tilde{H}||^2 + σ_B^2 N, and the interference terms are |p_i|^2 |1^T \tilde{H}\tilde{h}_i|^2; none of these reduces to ||p_k \tilde{H}\tilde{h}_k||^2 or σ^2 = F σ_U^2 + σ_B^2 without additional assumptions, such as orthogonality of the rows of \tilde{H}, that are not stated. Because S_k in Eq. (16) is defined from this simplified SINR, the objective function used throughout the algorithm does not follow from the system model. The authors should either derive the correct SINR for the employed combiner or explicitly state the simplified model as an assumption.
  3. [III, Algorithms 1-2] The paper provides no convergence or stationarity analysis for Algorithm 1. The pseudo-code is also ambiguous: the role of the two 'while j ≤ K' loops is unclear, and the stopping criterion α(i) - α(i-1) < ε is not shown to be well-defined. Even if the objective in (17) were correct, the claim that the algorithm 'maximizes' the minimal rate would require at least a monotonicity/convergence argument; without it, the method is a heuristic, and the simulation comparisons do not quantify the gap to the optimum.
minor comments (7)
  1. [Abstract] The phrase 'with meeting the minimum distance requirements' should be 'while meeting the minimum distance requirements'.
  2. [Notation] In the notation paragraph, 'scaler' should be 'scalar'.
  3. [III, Eq. (16)] The symbol '⇐ ⇒' appears to be a typographical artifact; it should be '⇔', and the equivalence should be stated as being between optimization problems, not between the numeric objective values.
  4. [II-C, Eq. (14)] The power constraints (14i) are included in the problem, but Section III states that power control is not considered; please either remove (14i) or explicitly state that p_k is fixed to P_k for all k.
  5. [III, Algorithm 1] The input to Algorithm 1 includes maximal transmitting powers P_1,...,P_K, but these are never used in the algorithm body; please remove them or clarify their role.
  6. [III-D, Complexity Analysis] The complexity expression 'O(N M2I + ...)' should read 'O(N M^2 I + ...)', and the meaning of each factor should be defined in the text.
  7. [IV, Figs. 2 and 3] The figures contain typos 'acheivable' and 'vers.'; please correct them.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the SCA derivation chain is self-contained; the questionable max-min-to-channel-gain equivalence in Eq. (16) is a mathematical validity concern, not a self-referential reduction.

full rationale

The claimed derivation chain is an alternating SCA procedure whose subproblems are lower-bounded by first- and second-order Taylor expansions. There is no fitted parameter later relabeled as a prediction: Algorithm 2 directly maximizes the effective-channel-gain objective, and the simulation curves compare against fixed-position and FAR-only baselines defined in the paper, which is a benchmarking choice rather than a self-referential derivation. The only potentially load-bearing transformation is Eq. (16), which asserts equivalence between min_k R_k, min_k gamma_k, and min_k ||p_k H̃h̃_k||^2. Even if that equivalence is mathematically questionable because SINR denominators change as antenna positions move, this would be a correctness or false-equivalence issue, not circularity: the equivalence is not created by defining one quantity in terms of the other; it is an independent and contestable mathematical claim. References to prior work, including the authors' ICC workshop paper [14], are contextual and are not used to supply the SCA bounds; the δ_k closed form is cited from [15] as an external technical lemma, not as the target result. Hence no step reduces to its own input, and no circularity score above zero is warranted.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper inherits the movable-antenna channel model (field response vectors and matrices) from [15], [16], the fluid antenna relay architecture from the authors' own [14], the SCA lower-bound toolkit (quadratic surrogate with delta_k bound) from [15] and [19], and the channel statistics for simulation from [20]. Nothing is fitted to data. The central non-inherited step, the equivalence between min-rate and min-signal-power in Eqs. (15)-(17), is introduced by the authors and is not justified, since the SINR denominator couples all users through common antenna positions.

assumptions (6)
  • domain assumption The movable-antenna field-response channel model (Eqs. 1-10) from [15], [16] accurately describes FA-to-FA and FA-to-BS propagation with L_k = L_U = L_B = L_b paths.
    Used throughout Section II; the entire optimization is built on this channel model, including the field response vectors and path response matrices.
  • domain assumption Setting the receiving beamformer omega_k = 1 (all-ones vector) is treated as equal-gain combining and defines the SINR in Eq. (13).
    Section II-C: 'we employ the equal-gain combining (EGC) method and set a typical omega_k = 1'. This ignores channel phase alignment and is not the standard EGC choice, yet optimality of FA positions is claimed under it.
  • ad hoc to paper Maximizing the minimum signal power min_k S_k is equivalent to maximizing the minimum rate min_k R_k (used to build problem (17) from (14)).
    Section III, Eqs. (15)-(17). The equivalence in (15)-(16) only identifies which user has the worst SINR. The SINR denominator sigma^2 + sum_{i != k} S_i depends on all users' positions, so (17) is not equivalent to (14). This is the load-bearing flaw.
  • domain assumption Power variables p_k are not optimized; they are effectively fixed at their maximum (power control deferred to a 'conventional method').
    Section III, paragraph after (16): 'the power control problem can be solved via the conventional method, it is not considered in this paper'. Despite p_k appearing in (14i) and (17c), the algorithm never updates p_k.
  • domain assumption Simulation channels: angles i.i.d. uniform in [0, pi], diagonal path response matrices with LoS factor beta = 1 and L = 4 paths.
    Section IV; the numerical claims depend on these statistics, and no sensitivity analysis is given for other beta or L values.
  • domain assumption The relay gain is assumed identical across all M antennas: f_i = F for all i, with F never assigned a value.
    Section II-B: 'Without loss of generality, we assume fi = F, for all i'. The SINR and all rate curves depend on F indirectly through the noise term sigma^2 = F sigma_U^2 + sigma_B^2, yet no value is specified, which also hurts reproducibility.

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Cite this review

Pith. "Pith review of Fair Rate Maximization for Fluid Antenna Relay (FAR)-assisted Multi-user MISO Communications." pith.science (2026). https://pith.science/paper/VCH4HYTM

@misc{pith2026250700529,
  author       = {Pith},
  title        = {Pith review of: Fair Rate Maximization for Fluid Antenna Relay (FAR)-assisted Multi-user MISO Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VCH4HYTM}},
  note         = {Machine review of arXiv:2507.00529}
}
read the original abstract

In this paper, we investigate the problem of max-min rate maximization in fluid antenna relay (FAR)-assisted multi-user uplink multiple-input single-output (MISO) wireless systems, where each user is equipped with a single fluid antenna (FA) and the base station (BS) is equipped with multiple FAs. Unlike most existing relevant work focusing on maximizing sum rate of the fluid antenna system (FAS), which may cause unbearable rate loss to weak users, we propose to maximize the minimal rate of the system to ensure fairness. The max-min optimization problem is formulated by jointly optimizing the positions of FAs with meeting the minimum distance requirements of FAs, maximum transmitting power limit, and feasible antenna region constraints. To solve this problem, we propose an alternating algorithm with utilizing the successive convex approximation (SCA) method. Simulation results demonstrate that the proposed method significantly outperforms conventional methods in terms of maximizing the minimal achievable rate across different signal-to-noise ratios (SNRs) and normalized region sizes.

Figures

Figures reproduced from arXiv: 2507.00529 by the authors.

Figure 1
Figure 1. FAR-assisted wireless communication system [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Maximized minimal rate vers. SNR 2.5 3 3.5 4 4.5 normalized region size A/ 0 0.2 0.4 0.6 0.8 1 1.2 Maximized minimal acheivable rate (bps/Hz) Fixed U-FAR Proposed [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Maximized minimal rate vers. normalized region [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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