Robust Transmission Design for Reconfigurable Intelligent Surface and Movable Antenna Enabled Symbiotic Radio Communications

Abbas Jamalipour; Bin Lyu; Feng Tian; Hao Liu; Meng Hua; Shimin Gong; Wenqing Hong

REVIEW 1 major objections 5 minor 42 references

Robust Transmission Design for Reconfigurable Intelligent Surface and Movable Antenna Enabled Symbiotic Radio Communications

T0 review · 1 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper claims that jointly positioning movable antennas, transmit beamforming, and RIS phase shifts maximizes the worst-case primary rate in symbiotic radio, with simulated gains of 1.62–2.37 bps/Hz over fixed antennas.

desk verdict A workmanlike robust beamforming paper for a genuinely new MA+RIS symbiotic-radio combination, but a false worst-case equivalence in the CSR derivation puts the headline rate comparisons on shaky ground. read the letter →

arxiv 2504.16386 v1 pith:FZM34NFV submitted 2025-04-23 eess.SP

Bin Lyu , Hao Liu , Meng Hua , Wenqing Hong , Shimin Gong , Feng Tian , Abbas Jamalipour This is my paper · ORCID

classification eess.SP

keywords symbioticradiomovableantennareconfigurableintelligentsurfacerobustbeamformingchanneluncertaintyprimaryratemaximizationparasiticandcommensalSRSA-PSO

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

Symbiotic radio lets a secondary device ride its own data on a primary transmitter's signal, and a reconfigurable intelligent surface can do both jobs. This paper asks whether letting the primary transmitter's antennas physically move, rather than fixing them, makes the arrangement more robust when the channels are only imperfectly known. It formulates, for both parasitic (same symbol period, secondary signal is interference) and commensal (long secondary symbol, secondary signal acts as useful multipath) modes, the problem of maximizing the primary user's worst-case rate subject to a secondary quality-of-service constraint. The proposed alternating algorithm optimizes transmit beamforming, discrete RIS phase shifts, and antenna positions, and simulations report gains of 1.62 bps/Hz (PSR) and 2.37 bps/Hz (CSR) over fixed-position antennas, with the commensal mode doing better overall. A sympathetic reader would take the contribution to be a concrete, if incremental, robust-design method for combining two hardware ideas.

What carries the argument

The load-bearing object is the field-response channel model for movable antennas: each channel vector is a sum of propagation paths whose amplitudes and angles stay fixed while the phase of each path rotates with the antenna position, so $G_\kappa = [g_\kappa(p_1),\dots,g_\kappa(p_K)]$ with $g_\kappa(p_k)$ containing phase factors $e^{j(2\pi/\lambda)\rho^t_{\kappa,\iota}(p_k)}$. This makes antenna positions optimization variables inside the channel matrices. The robust part is carried by the General S-Procedure and the General Sign-Definiteness Principle, which convert norm-bounded CSI uncertainties into linear matrix inequalities, and by successive convex approximation for the beamformer and the discrete phase-shift constraints. Antenna positions are then updated by a simulated-annealing particle-swarm search whose fitness is the optimized primary rate minus a penalty for violating minimum antenna spacing.

What would settle it

For a fixed optimized $(w,\psi,p)$, evaluate the true worst-case CSR rate $\min_{\Delta H_{bs},\Delta h_u} \frac12\log_2\left(1+\left|(h_u^H+\psi^H H_{bs})w\right|^2/\sigma^2\right)+\frac12\log_2\left(1+\left|(h_u^H-\psi^H H_{bs})w\right|^2/\sigma^2\right)$ over the same uncertainty balls, for example by fine sampling or local search from the worst-case points the S-Procedure produces. If this value lies clearly above the value produced by Eq. (18)'s sum of separate minima, then the optimization solved a strictly looser problem and the reported robust CSR rates are not the stated worst-case rates.

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Extended reading notes

Core claim

The paper's central claim is that jointly optimizing movable-antenna positions, transmit beamforming, and RIS phase shifts under bounded channel-estimation error yields a robust symbiotic-radio design: the worst-case primary rate is maximized while the secondary link's SNR requirement is always met. The channel model makes the MA-to-RIS and MA-to-PU responses functions of the antenna position vectors through a far-field response matrix, so moving antennas changes both the direct and cascaded links. Under parasitic SR the reflected secondary signal is treated as interference when decoding the primary signal; under commensal SR the secondary symbol is long and the reflected path is treated as part of the primary multipath, giving a rate expression that is the average of two log terms. The paper reports that the commensal scenario substantially outperforms the parasitic one and that, at the tested parameters, the MA design beats the fixed-position design by 1.62 bps/Hz and 2.37 bps/Hz in the PSR and CSR cases, respectively.

Load-bearing premise

The load-bearing premise is that the worst case of the two-term commensal rate can be minimized term-by-term even though both terms are governed by the same channel errors; if the shared uncertainty forces the errors to hurt both terms together, the optimization is solving a strictly easier lower-bound problem than the stated one.

Editorial extensions

If this is right

With the tested parameters, movable antennas raise the guaranteed primary rate by 1.62 bps/Hz in the PSR case and 2.37 bps/Hz in the CSR case relative to fixed-position antennas.
The commensal mode is the better operating point because its reflected secondary signal strengthens the primary path instead of interfering with it.
Larger uncertainty radii for either the direct or the cascaded channel reduce the guaranteed primary rate, so channel estimation quality still sets a ceiling on robustness.
Adding more movable antennas increases the guaranteed rate through extra spatial diversity in the simulated scenarios.

Reading between the lines

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

Because Eq. (18) replaces the minimum of a sum by the sum of separate minima over the same uncertainty region, the CSR numbers are computed against a lower-bound objective; the exact worst-case optimum for the stated problem remains an open gap, and the reported gains may understate the true worst-case advantage.
The same S-Procedure plus Bernstein-type inequality machinery could be repurposed for a statistical CSI error model with outage-probability constraints, a direction the paper itself flags as future work.
In a multi-PU broadcast setting, the bottleneck moves to the farthest user; movable antennas could be steered toward that user, but the paper does not optimize positions per user, so a fairness-aware extension would be needed for that deployment.

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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

Colleague, the thing to know about this paper is that it has a real, novel system combination—multiple movable antennas at the primary transmitter plus an RIS-as-secondary under bounded CSI uncertainty for both PSR and CSR modes—and one genuine mathematical mistake in the CSR part that infects the headline numbers. The novelty is not huge, but it is real: I checked the cited [11]–[16] and [33], [34], and none of them combine MA position optimization with RIS-enabled symbiotic radio under robust constraints. The authors also get credit for a fairly complete treatment: the PSR lower-bound reformulation, the S-Procedure/Sign-Definiteness transformations, and the SA-PSO baseline are all standard but competently assembled, and the multi-PU extension is a reasonable bonus. There is no circularity; self-citations are legitimate and not load-bearing.

The soft spot is exactly where the stress-test put it. Equation (18) splits the minimum over the shared uncertainties (ΔHbs, Δhu) of a sum of two log terms into the sum of two separate minima. That is not an equality—the true worst-case value of the sum is generally larger than the sum of the individual worst cases. So the CSR objective being maximized is a guaranteed lower bound, not the exact worst-case primary rate. That means the claimed 2.37 bps/Hz CSR gain over FPA and the CSR-versus-PSR comparison in Figs. 4, 6, 8, and 9 are not established on a common footing. This is fixable: reframe the solution as maximizing a conservative lower bound, re-run the baselines under the same bound, and soften the abstract's quantitative claims. But as submitted, the central CSR claims do not follow from the math. A secondary issue: the passive beamforming subproblem P3.1 retains the nonconvex constraint C3b (the complex-exponential equality) even after the binary relaxation, and the paper does not clearly show how that constraint becomes convex. Also, the convergence proof says the objective is non-decreasing, but the SA step explicitly accepts worse solutions with probability ǫ, so the monotonicity claim is not true as written. Minor points: the FPA baseline positions are never specified, there are no error bars or code, and Algorithm 2 has an obvious w↔ψ typo in its return line.

Net: I would not cite this as it stands, and I would not trust the CSR numbers until the lower-bound issue is fixed. But this is not a desk-reject paper. The combination is new, the PSR side is largely sound, and the CSR error is local and repairable. With a revision that corrects Eq. (18), redoes the simulations as lower-bound comparisons, and clarifies the convexity of P3.1, it becomes a decent incremental contribution. I would send it to serious peer review, not because it is important, but because the referee time is warranted and the authors have something salvageable.

Referee Report

1 major / 5 minor

Summary. The paper studies an RIS-enabled symbiotic radio system in which the primary transmitter is equipped with movable antennas. It considers both parasitic SR (PSR) and commensal SR (CSR) scenarios under bounded ellipsoidal uncertainties in the direct and cascaded channels, and formulates max-min problems that maximize the worst-case primary rate subject to secondary QoS constraints. An alternating optimization framework is proposed that sequentially optimizes transmit beamforming via SCA with the General S-Procedure and Sign-Definiteness Principle, passive beamforming with binary phase-shift variables, and antenna positions with an SA-PSO algorithm. Numerical results are presented for single- and multi-PU settings, reporting gains over fixed-position antenna and PSO baselines and claiming that CSR significantly outperforms PSR.

Significance. If the technical claims are correct, the paper makes an incremental but useful contribution at the intersection of movable antennas, RIS, and symbiotic radio: it is the first to combine MA with RIS-enabled SR under imperfect CSI, and it provides a complete optimization recipe with numerical validation. The paper is careful in modeling the MA channel and in applying standard robust-optimization tools, and the simulation study covers several relevant parameter variations. However, the significance of the quantitative findings is contingent on the correctness of the worst-case rate reformulation in the CSR scenario, and that reformulation contains a load-bearing error.

major comments (1)

[Section IV-A, Eq. (18)] Equation (18) states that min_{ΔH_bs,Δh_u} R_csr equals 1/2 log2(1 + min_{ΔH_bs,Δh_u}|(h_u^H + ψ^H H_bs)w|^2/σ^2) + 1/2 log2(1 + min_{ΔH_bs,Δh_u}|(h_u^H - ψ^H H_bs)w|^2/σ^2). This equality is false because the same uncertainties ΔH_bs and Δh_u appear in both the '+' and '−' terms; the minimum of a sum is generally greater than the sum of the individual minima. The correct relation is '≥', so the right-hand side is a lower bound on the true worst-case rate. Since P6.1, P6.2, P7.1, the CSR fitness function in (20), and the multi-PU objective in (22) are all built on this step, the CSR primary rates reported in Figs. 4, 6, 8, and 9 are lower bounds rather than exact worst-case values. Consequently, the 2.37 bps/Hz gain over the FPA scheme and the claim that CSR significantly outperforms PSR compare quantities that are not on a common footing: the PSR design is an explicitly stated lower-bound maximization, while the CSR design is presented as exact though it is also a lower bound, and the difference of two lower bounds is not a guaranteed bound on the true performance difference. The authors should either prove the equality (which appears impossible under the stated coupling) or reframe the CSR problem as maximizing a guaranteed lower bound and adjust the quantitative claims in the abstract, Section IV, and Section V accordingly.

minor comments (5)

[Section III-D, convergence] The convergence analysis states that the objective of P1 is non-decreasing because the surrogate problems P2.2 and P3.1 are solved via SCA. However, these surrogates are lower bounds on the true objective, so monotonicity of the surrogate does not imply monotonicity of the true worst-case rate. The theoretical convergence claim is therefore not established; Fig. 2 provides useful empirical evidence, but the claim should be softened or proved with respect to the true objective.
[Algorithm 2, line 18] The return statement 'Return w⋆ = ψ^(⋆,ς), ψ⋆ = ψ^(⋆,ς)' contains a typo; it should read 'Return w⋆ = w^(⋆,ς), ψ⋆ = ψ^(⋆,ς)'.
[Reference [26]] Reference [26] is typed as 'IEEE EEE Wireless Commun. Lett.'; the 'EEE' should be removed.
[Section V-B, Eqs. (21)-(22)] The notation with Π in the objective functions is ambiguous: the minimization over the Π primary users should be written explicitly, e.g., min_{1≤̟≤Π} min_{ΔH_bs,̟, Δh_u,̟} ..., to avoid confusion between the number of users and the product symbol.
[Section III-C, Eq. (13)] In the fitness function (13), the notation R̂_psr(w*, ψ*) does not show the explicit dependence on the particle position p_s^(q); since the channel matrices H_bs and h_u are functions of the antenna positions, the fitness should be written as R̂_psr(w*, ψ*, p_s^(q)).

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the robust MA/RIS design is derived from external channel models and convex-transformation tools; the main weakness (Eq. 18) is a soundness/conservativeness gap, not a circular reduction.

full rationale

After walking the derivation chain, I find no step in which a predicted quantity is defined in terms of the target result, no fitted parameter renamed as a prediction, and no load-bearing self-citation chain. The MA channel model is adopted from externally published field-response models [22], [24]; the robust reformulations use the General S-Procedure [38], General Sign-Definiteness Principle [39], and the SCA method, which are external mathematical tools with stated assumptions that do not include the paper's conclusions. The authors' own prior works ([1], [15], [33]) appear only in the introduction/footnote as related work and gap statements, not as the justification for the optimization claims. The numerical evaluation is against fixed-position-antenna, PSO, and random-passive-beamforming benchmarks; no parameter is fitted to force the reported gains. The one genuinely load-bearing mathematical step, Eq. (18), asserts min over shared (Delta_Hbs, Delta_hu) of a sum of two log terms equals the sum of the two individual minima; this is generally false because the same uncertainty couples both terms, so the CSR rate maximized in Section IV is a conservative lower bound. That is a correctness/soundness issue that undermines the quantitative CSR-vs-PSR and MA-vs-FPA comparisons, but it is not circularity: the right-hand side is not equal to the input by construction, and the analysis does not assume the conclusion it is trying to prove. Under the stated rules, this warrants a low score, not a circularity flag.

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

The central results rest on standard far-field channel and bounded-uncertainty models, plus one unjustified minimization interchange in Eq. (18) and an unproven convergence argument. The simulation gains depend on many hand-picked parameters, none of which are fitted against external data.

free parameters (5)

CSI uncertainty radius proportions gbs and gu = gbs=0.05, gu=0.1
Set xi_bs = gbs * ||Hhat_bs||_F and xi_u = gu * ||hhat_u||_2 in Section V. These values define the robust region and are chosen by hand without measurement support.
Secondary QoS thresholds gamma_pmin and gamma_cmin = not specified
These thresholds appear in constraints C2 and C11 but no numeric values are given in the simulation setup, so any reproduction must choose them arbitrarily.
Multipath and path-loss parameters = L=9, v=-10 dB, nu=1.3
The numbers of transmit and receive paths, path-loss exponent, and path-loss coefficient determine the simulated channel realizations and therefore the reported rates.
SA-PSO hyperparameters = S=150, Q=150, c1=c2=1.4, omega=1.2, r1=r4=50, empirical T(0)
Algorithm 1 parameters are chosen by hand. The penalty factors and the empirical initial temperature affect the search trajectory and the final reported gains.
MA region size and minimum antenna spacing = A=3*lambda, dmin=0.5*lambda
The movable region size and spacing constraint shape the spatial diversity the MAs can exploit and are chosen by the authors.

assumptions (5)

domain assumption Far-field field-response model: MA movement changes only phases, not amplitudes, AoAs, or AoDs
Adopted from [22], [24] in Section II-A. If near-field effects are significant within the 3-lambda region, the channel model is invalid.
domain assumption Bounded norm CSI uncertainty with known radii xi_bs and xi_u
Eqs. (1)-(2) assume the estimation errors lie in known norm balls, which is the basis for all robust transformations.
domain assumption The reflected product s(l)c(l) is circularly symmetric complex Gaussian in the PSR scenario
Used in Section II-C1 to treat the secondary reflection as worst-case Gaussian interference when deriving R_psr.
ad hoc to paper The minimum over a shared uncertainty can be interchanged with the sum of two log terms in Eq. (18)
Section IV-A assumes min[f1(Delta)+f2(Delta)] = min f1(Delta)+min f2(Delta), which is false in general because the same Delta couples both terms. This underpins the CSR objective.
domain assumption AO and SA-PSO produce a non-decreasing objective and converge
Section III-D asserts monotone convergence, but the SA step in Algorithm 1 can accept worse positions, so the objective is not monotonically non-decreasing and convergence is not rigorously established.

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Cite this review

Pith. "Pith review of Robust Transmission Design for Reconfigurable Intelligent Surface and Movable Antenna Enabled Symbiotic Radio Communications." pith.science (2026). https://pith.science/paper/FZM34NFV

@misc{pith2026250416386,
  author       = {Pith},
  title        = {Pith review of: Robust Transmission Design for Reconfigurable Intelligent Surface and Movable Antenna Enabled Symbiotic Radio Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FZM34NFV}},
  note         = {Machine review of arXiv:2504.16386}
}

read the original abstract

This paper explores the application of movable antenna (MA), a cutting-edge technology with the capability of altering antenna positions, in a symbiotic radio (SR) system enabled by reconfigurable intelligent surface (RIS). The goal is to fully exploit the capabilities of both MA and RIS, constructing a better transmission environment for the co-existing primary and secondary transmission systems. For both parasitic SR (PSR) and commensal SR (CSR) scenarios with the channel uncertainties experienced by all transmission links, we design a robust transmission scheme with the goal of maximizing the primary rate while ensuring the secondary transmission quality. To address the maximization problem with thorny non-convex characteristics, we propose an alternating optimization framework that utilizes the General S-Procedure, General Sign-Definiteness Principle, successive convex approximation (SCA), and simulated annealing (SA) improved particle swarm optimization (SA-PSO) algorithms. Numerical results validate that the CSR scenario significantly outperforms the PSR scenario in terms of primary rate, and also show that compared to the fixed-position antenna scheme, the proposed MA scheme can increase the primary rate by 1.62 bps/Hz and 2.37 bps/Hz for the PSR and CSR scenarios, respectively.

Figures

Figures reproduced from arXiv: 2504.16386 by the authors.

**Figure 2.** Convergence performance of the proposed AO framewor [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Primary rate versus the maximum transmit power for the PSR. 36 38 40 42 44 34 36 38 40 42 44 Primary rate (bps/Hz) Proposed scheme with SA-PSO Proposed scheme with PSO FPA scheme Random passive beamforming scheme [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: Primary rate versus the CSI uncertainty level for the PSR. 0.05 0.1 0.15 0.2 0.25 28 30 32 34 36 38 Primary rate (bps/Hz) [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 7.** Figure 7: Primary rate versus the number of MAs for the PSR. 2 3 4 5 6 Number of MAs 34 35 36 37 38 39 Primary rate (bps/Hz) Proposed scheme with SA-PSO Proposed scheme with PSO FPA scheme Random passive beamforming scheme [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

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Reference graph

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