{"id":"37918e1e-ae57-4054-a6ac-420ef91f3801","arxiv_id":"2504.16386","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A robust alternating-optimization scheme for RIS-enabled symbiotic radio with movable antennas is derived, and simulations show primary-rate gains of 1.62 and 2.37 bps/Hz over fixed antennas.","lead":"This paper designs a radio system that uses movable antennas and a smart reflecting surface to improve data rates while a secondary device piggybacks on the primary signal. It is a candidate 6G spectrum-sharing technique, but the reported gains come from simulations with a questionable worst-case formula and no defined comparison antenna position.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (18) splits a coupled worst-case minimization into separate minima; the reported CSR rates are lower bounds, so the headline CSR-vs-PSR and MA-vs-FPA margins compare incompatible quantities.","rationale":"The reader's weakest-assumption analysis identifies the same step that I regard as the most load-bearing concern: Eq. (18) incorrectly interchanges a minimum over shared uncertainty with separate minima. My stress-test refines the consequence: because the inequality goes in the conservative direction, the reported CSR rates are valid lower bounds rather than fabricated rates, so the qualitative CSR-versus-PSR ordering may survive. What does not survive is the quantitative claim of a 2.37 bps/Hz gain over FPA and the claim that the algorithm solves the stated worst-case CSR problem; the simulated margins compare a lower-bound objective against other curves computed on different bases. A corrected paper could re-run the CSR simulations with the true worst-case rate, or explicitly rephrase the contribution as a robust lower-bound design and compare lower bounds only. Without that correction, the central quantitative claims in the abstract are not established. I therefore keep the reader's rejection verdict, while noting that the flaw is a reformulation error rather than a fabricated result. Secondary issues, such as the 2x2 LMI reduction in the PSR passive-beamforming subproblem and the SA-PSO acceptance of worse global-best solutions, reinforce the correctness concern but are not needed to decide the verdict.","tokens_in":24159,"tokens_out":12840,"duration_ms":135616,"concrete_test":"Take one optimized CSR design (w*, psi*, p*) from P6.2/P7.1, with the Section V parameters, and compute the true worst-case rate by solving min over ||Delta_Hbs||_F <= xi_bs and ||Delta_hu||_2 <= xi_u of R_csr(w*, psi*, p*) using a dense grid or a multi-start nonlinear optimizer on the real and imaginary entries of the uncertainty matrices. Compare this value with the P6.2 objective at the same design. Repeat for the FPA baseline using its optimized w and psi. If the true worst-case FPA rate reaches or exceeds the proposed MA design's reported lower bound, or if the difference between the two true worst-case rates differs from the claimed 2.37 bps/Hz by more than the simulation tolerance, the headline CSR gain is not supported as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing mathematical step is Eq. (18) in Section IV-A. The paper rewrites the worst-case CSR rate, min over the shared uncertainties (Delta_Hbs, Delta_hu) of a sum of two log terms, as the sum of two individual minima, one for |(hu^H + psi^H Hbs)w|^2 and one for |(hu^H - psi^H Hbs)w|^2. Because the same Delta_Hbs and Delta_hu appear in both terms, the true minimum of the sum is generally larger than the sum of the separate minima; the claimed equality is false. The direction of the mistake makes the right-hand side a conservative lower bound on the true worst-case CSR rate, so the algorithm can be interpreted as maximizing a guaranteed lower bound rather than solving the stated max-min problem. This still matters for the central claims: the CSR curves in Figs. 4, 6, 8, and 9, for both the proposed MA design and the FPA baseline, are lower-bound quantities, while the PSR curves use the exact worst-case transformation. Consequently, the reported 2.37 bps/Hz CSR gain over FPA and the claimed optimality of the robust CSR design are not established on a common footing. The qualitative statement that CSR can outperform PSR is not automatically destroyed, because the reported CSR value is a lower bound, but the quantitative comparison in the abstract and Section V is not a comparison of true worst-case primary rates.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":24386,"tokens_out":9018,"duration_ms":79169,"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":[{"comment":"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.","section":"Section IV-A, Eq. (18)"}],"minor_comments":[{"comment":"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.","section":"Section III-D, convergence"},{"comment":"The return statement 'Return w⋆ = ψ^(⋆,ς), ψ⋆ = ψ^(⋆,ς)' contains a typo; it should read 'Return w⋆ = w^(⋆,ς), ψ⋆ = ψ^(⋆,ς)'.","section":"Algorithm 2, line 18"},{"comment":"Reference [26] is typed as 'IEEE EEE Wireless Commun. Lett.'; the 'EEE' should be removed.","section":"Reference [26]"},{"comment":"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":"Section V-B, Eqs. (21)-(22)"},{"comment":"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)).","section":"Section III-C, Eq. (13)"}],"recommendation":"major_revision","confidential_remarks":"The paper is incremental but potentially useful. The main technical concern is the incorrect equality in Eq. (18); this is fixable by reframing the CSR results as guaranteed lower bounds and qualifying the quantitative claims. I would not reject outright, because the qualitative findings may still hold, but the abstract and Section V comparisons must be revised. The convergence claim in Section III-D also needs correction."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nNet: 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.","headline":"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.","tokens_in":25027,"tokens_out":2698,"would_cite":false,"duration_ms":30484,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["symbiotic radio","movable antenna","reconfigurable intelligent surface","robust beamforming","channel uncertainty","primary rate maximization","parasitic and commensal SR","SA-PSO"],"falsifier":"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.","tokens_in":23853,"feed_emoji":"📡","tokens_out":6688,"duration_ms":64832,"temperature":0.7,"pith_summary":"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.","feed_headline":"Movable antennas add up to 2.37 bps/Hz in symbiotic radio","feed_subtitle":"Jointly moving antennas, tuning beamforming, and setting RIS phases lifts worst-case primary rates in both parasitic and commensal modes.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the parasitic and commensal symbiotic-radio scenarios whose rate models organize Sections III and IV.","marker":"[4]"},{"why":"Supplies the bounded cascaded CSI error model and the robust beamforming machinery that the paper adapts to movable antennas.","marker":"[20]"},{"why":"Introduces the field-response model for movable-antenna channels, the paper's core channel model.","marker":"[22]"},{"why":"Extends the movable-antenna field-response modeling and performance analysis that justifies the phase-position dependence.","marker":"[24]"},{"why":"Provides the simulated-annealing improved particle-swarm algorithm used for antenna-position optimization.","marker":"[37]"},{"why":"Is the source of the General S-Procedure that turns uncertain quadratic constraints into linear matrix inequalities.","marker":"[38]"},{"why":"Is the source of the General Sign-Definiteness Principle used to bound uncertainty in the beam constraints.","marker":"[39]"},{"why":"Earlier robust beamforming for the CSR case with direct and cascaded uncertainties, the closest baseline the paper extends.","marker":"[16]"}],"fun_headline_variants":["Symbiotic radio: movable antennas add up to 2.37 bps/Hz","Movable antennas add 2.37 bps/Hz to primary rate in symbiotic radio","Robust design with movable antennas lifts symbiotic radio rate by 2.37 bps/Hz","MA and RIS co-design yields 2.37 bps/Hz gain in symbiotic radio"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Symbiotic radio: movable antennas add up to 2.37 bps/Hz","Movable antennas add 2.37 bps/Hz to primary rate in symbiotic radio","Robust design with movable antennas lifts symbiotic radio rate by 2.37 bps/Hz","MA and RIS co-design yields 2.37 bps/Hz gain in symbiotic radio"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000935,"raw_usage":{"total_tokens":4018,"prompt_tokens":982,"completion_tokens":3036,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":598,"completion_tokens_details":{"reasoning_tokens":2940}},"tokens_in":598,"tokens_out":3036,"duration_ms":20378,"temperature":1.0,"reasoning_tokens":2940,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:05:21.098078+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Symbi otic radio: A new communication paradigm for passive Internet of Things,","cited_arxiv_id":null,"evidence_quote":"Defines the parasitic and commensal symbiotic-radio scenarios whose rate models organize Sections III and IV."},{"cited_title":"A framework of robust transmission desi gn for IRS- aided MISO communications with imperfect cascaded channel s,","cited_arxiv_id":null,"evidence_quote":"Supplies the bounded cascaded CSI error model and the robust beamforming machinery that the paper adapts to movable antennas."},{"cited_title":"A novel hybrid pa rticle swarm optimization algorithm for path planning of UA Vs,","cited_arxiv_id":null,"evidence_quote":"Provides the simulated-annealing improved particle-swarm algorithm used for antenna-position optimization."},{"cited_title":"Boyd et al., Linear Matrix Inequalities in System and Control Theory","cited_arxiv_id":null,"evidence_quote":"Is the source of the General S-Procedure that turns uncertain quadratic constraints into linear matrix inequalities."},{"cited_title":"The sign-definiteness lemma and i ts applications to robust transceiver optimization for multiuser MIMO syst ems,","cited_arxiv_id":null,"evidence_quote":"Is the source of the General Sign-Definiteness Principle used to bound uncertainty in the beam constraints."}],"review_version":1}