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arxiv: 2604.10897 · v1 · submitted 2026-04-13 · 📡 eess.SP

FAS-aided Robust Anti-Jamming Communications: Continuous and Discrete Positioning Designs

Yifan Guo , Junshan Luo , Shilian Wang , Zhenhai Xu This is my paper

Pith reviewed 2026-05-10 16:28 UTC · model grok-4.3

classification 📡 eess.SP
keywords fluid antenna systemanti-jammingantenna positioningsparse recoverysum-rate optimizationrobust beamformingdiscrete design
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The pith

In FAS-aided anti-jamming MIMO, discrete antenna positioning via sparse recovery outperforms continuous alternating optimization in worst-case sum-rate.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that jointly designing beamforming and discrete fluid antenna positions, by recasting the problem as sparse recovery under minimum mean squared error, produces higher worst-case sum-rates than an alternating optimization scheme applied to continuous positions. This holds in multi-user downlink scenarios with multiple jammers and imperfect jammer channel knowledge, subject to quality-of-service and power limits. A sympathetic reader cares because the result questions the default assumption that continuous optimization always extracts more value from the spatial degrees of freedom offered by fluid antennas.

Core claim

The discrete joint design yields superior sum-rate performance compared to the AO-based continuous counterpart under identical conditions. This superiority stems from the sparse recovery formulation which effectively circumvents the severe local optima.

What carries the argument

The sparse recovery reformulation of the discrete positioning subproblem, obtained via minimum mean squared error and majorization minimization, solved jointly by block coordinate descent combined with simultaneous orthogonal matching pursuit.

If this is right

  • The discrete method enables true joint optimization of beamforming and positions without alternating between the two blocks.
  • Discretization plus sparse recovery supplies a practical route to higher sum-rate when the underlying problem is highly non-convex.
  • The conventional preference for continuous position variables can be overturned when local-optima traps dominate.
  • Sparse-recovery techniques become a viable alternative to successive convex approximation for exploiting fluid-antenna spatial freedom.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • In other positioning or array-configuration problems that suffer from severe non-convexity, imposing a discrete grid may improve global-search behavior more than refining a continuous solver.
  • Hardware implementations of fluid antennas could adopt fixed discrete position sets to gain both performance and reduced control complexity.
  • The same sparse-recovery lens might be applied to related robust beamforming tasks that currently rely on alternating optimization.

Load-bearing premise

The minimum mean squared error criterion together with the sparse recovery reformulation faithfully models the discrete positioning problem without modeling errors large enough to erase the claimed performance edge over continuous alternating optimization.

What would settle it

A simulation or hardware experiment, using the same channel realizations, power budgets, and jammer statistics, in which the alternating-optimization continuous design produces equal or higher worst-case sum-rate than the discrete sparse-recovery design.

Figures

Figures reproduced from arXiv: 2604.10897 by Junshan Luo, Shilian Wang, Yifan Guo, Zhenhai Xu.

Figure 1
Figure 1. Figure 1: Downlink anti-jamming transmission of FAS-assiste [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Achievable sum rate versus number of iterations, giv [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Beampattern of different architectures in differen [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Achievable sum rate versus SJNR, given ∆ = 4◦. position and beamforming, while the discrete design achieves joint optimization of both by reconstructing the original problem into a sparse recovery task. The resluts reveal two important phenomena and one key insight. First, by trading spatial resolution for mathematical tractability, the proposed discrete joint optimization paradigm significantly overcomes … view at source ↗
read the original abstract

This paper investigates the joint optimization of beamforming and antenna positions in fluid antenna system (FAS)-aided anti-jamming communications. We consider a multi-user multiple-input multiple-output downlink scenario where multiple malicious jammers exist and the jammer channel state information is imperfect. The goal is to maximize the worst-case sum-rate under quality-of-service and transmit power constraints. To achieve this, we develop two distinct optimization frameworks for continuous and discrete antenna position designs, respectively. For continuous design, we propose an alternating optimization (AO) framework that integrates successive convex approximation and majorization minimization (MM) to handle the highly non-convex problem. For discrete design, based on the minimum mean squared error criterion and MM, we reformulate the problem as a sparse recovery task and propose a low-complexity block coordinate descent and simultaneous orthogonal matching pursuit, which enables joint design rather than AO. Through systematic comparison, we uncover a practical phenomenon: the discrete joint design yields superior sum-rate performance compared to the AO-based continuous counterpart under identical conditions. This superiority stems from the sparse recovery formulation which effectively circumvents the severe local optima. Our findings challenge the conventional view that continuous optimization is inherently superior, and reveal that discretization combined with sparse recovery can offer a more effective paradigm for exploiting spatial degrees-of-freedom in FAS-aided anti-jamming communications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops two frameworks for joint beamforming and fluid antenna system (FAS) positioning to maximize worst-case sum-rate in a multi-user MIMO downlink with multiple jammers and imperfect jammer CSI. The continuous-position framework employs alternating optimization (AO) integrating successive convex approximation (SCA) and majorization-minimization (MM). The discrete-position framework reformulates the problem via a minimum mean squared error (MMSE) criterion and MM into a sparse-recovery task solved by block coordinate descent (BCD) combined with simultaneous orthogonal matching pursuit (SOMP). Systematic simulations are reported to show that the discrete joint design achieves higher sum-rate than the continuous AO counterpart under identical conditions, with the gain attributed to the sparse-recovery formulation circumventing severe local optima.

Significance. If the performance comparison can be shown to isolate the effect of the sparse-recovery formulation rather than differences in the optimized objective, the result would usefully challenge the assumption that continuous optimization is always preferable for exploiting spatial degrees of freedom in FAS anti-jamming systems. The explicit comparison of continuous AO versus joint discrete design is a constructive contribution; the use of standard tools (AO, SCA, MM, BCD, SOMP) is technically sound.

major comments (2)
  1. [Abstract and discrete-design section] Abstract and the discrete-design section: the central claim attributes the reported sum-rate superiority of the discrete joint design to the sparse-recovery formulation 'circumventing severe local optima.' However, the continuous AO framework applies SCA+MM directly to the non-convex worst-case rate expression, while the discrete framework switches to an MMSE surrogate (plus MM) to obtain the sparse-recovery problem. Because the objectives are not identical, the observed gain may arise from the surrogate's different sensitivity to jammer-CSI errors or its amenability to global search, rather than from avoidance of local optima per se. A side-by-side comparison under a common objective is required to support the attribution.
  2. [Simulation-results section] Simulation-results section: the paper states that the discrete design yields superior sum-rate 'under identical conditions,' yet provides no quantitative assessment of the modeling error introduced by the MMSE reformulation relative to the original rate objective, nor of the tightness of the SCA/MM approximations used in the continuous case. Without such verification (e.g., via duality gaps, approximation-error bounds, or additional Monte-Carlo trials with the original objective), the claim that the superiority stems specifically from the sparse-recovery paradigm remains insecure.
minor comments (2)
  1. Notation for the worst-case sum-rate and the MMSE surrogate should be aligned more explicitly across the two frameworks to facilitate direct comparison.
  2. Figure captions for the sum-rate versus SNR or jammer-power curves should state the exact number of Monte-Carlo trials and the precise channel-error model used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the insightful comments. We address each major comment below and propose revisions to improve the clarity and rigor of our comparisons between the continuous AO and discrete sparse-recovery designs.

read point-by-point responses

  1. Referee: Abstract and the discrete-design section: the central claim attributes the reported sum-rate superiority of the discrete joint design to the sparse-recovery formulation 'circumventing severe local optima.' However, the continuous AO framework applies SCA+MM directly to the non-convex worst-case rate expression, while the discrete framework switches to an MMSE surrogate (plus MM) to obtain the sparse-recovery problem. Because the objectives are not identical, the observed gain may arise from the surrogate's different sensitivity to jammer-CSI errors or its amenability to global search, rather than from avoidance of local optima per se. A side-by-side comparison under a common objective is required to support the attribution.

    Authors: We appreciate this observation regarding the differing objectives. The MMSE reformulation is chosen specifically to cast the problem as a sparse recovery task, enabling the use of BCD with SOMP for joint beamforming and position design, which is not feasible in the direct rate formulation. This joint approach helps avoid the local optima that plague the alternating optimization in the continuous case. Both methods are assessed on the identical worst-case sum-rate performance metric. To strengthen the manuscript, we will add a detailed explanation of the MMSE-rate relationship and its validity in this anti-jamming context, along with additional numerical results comparing the achieved rates under a unified evaluation. We will also tone down the attribution to focus on the benefits of the joint discrete optimization paradigm. revision: partial

  2. Referee: Simulation-results section: the paper states that the discrete design yields superior sum-rate 'under identical conditions,' yet provides no quantitative assessment of the modeling error introduced by the MMSE reformulation relative to the original rate objective, nor of the tightness of the SCA/MM approximations used in the continuous case. Without such verification (e.g., via duality gaps, approximation-error bounds, or additional Monte-Carlo trials with the original objective), the claim that the superiority stems specifically from the sparse-recovery paradigm remains insecure.

    Authors: We agree that providing quantitative measures of approximation quality would enhance the credibility of our claims. In the revision, we will incorporate additional simulation results that quantify the modeling error of the MMSE surrogate (e.g., by comparing the optimized MMSE value to the actual rate) and assess the convergence and tightness of the SCA/MM approximations in the continuous framework through metrics such as duality gaps and residual errors over multiple trials. This will help isolate the contribution of the sparse-recovery approach. revision: yes

Circularity Check

0 steps flagged

No circularity: two independent optimization frameworks with empirical performance comparison

full rationale

The paper defines two distinct frameworks without reduction to self-defined quantities. Continuous design applies AO+SCA+MM directly to the worst-case sum-rate objective under imperfect CSI. Discrete design explicitly switches to an MMSE surrogate plus MM to enable sparse recovery via BCD+SOMP. The superiority claim is presented as an observed simulation outcome under identical conditions, not a mathematical identity or fitted prediction. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling appears in the derivation chain; established techniques (AO, SCA, MM, BCD, SOMP) are applied to the stated problem without equating outputs to inputs by construction. The modeling switch is acknowledged and does not create circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from convex optimization and sparse signal processing applied to the FAS anti-jamming scenario; no new physical entities are postulated and no explicit free parameters beyond typical algorithm hyperparameters are described.

axioms (2)
  • domain assumption The non-convex joint optimization can be made tractable via successive convex approximation and majorization minimization.
    Invoked to enable the alternating optimization framework for continuous positioning.
  • domain assumption The discrete positioning problem can be reformulated as a sparse recovery task under the minimum mean squared error criterion.
    Basis for the block coordinate descent and simultaneous orthogonal matching pursuit approach.

pith-pipeline@v0.9.0 · 5541 in / 1339 out tokens · 76271 ms · 2026-05-10T16:28:41.786967+00:00 · methodology

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