{"id":"3268aef2-4b1f-46e7-ac18-2d76948ea71a","arxiv_id":"2411.17056","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A robust max-min fair beamforming scheme for RSMA-aided VLC networks, built on a new entropy-power-based rate lower bound, beats SDMA and NOMA under imperfect CSIT in simulations.","lead":"The paper derives a rate lower bound for rate-splitting multiple access in visible-light communication networks and designs a robust beamforming algorithm that maximizes the worst-case user rate under imperfect channel knowledge. The proposed RSMA design is shown by simulation to outperform SDMA and NOMA in both underloaded and overloaded VLC networks.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Private-stream rate lower bound (21) rests on an invalid entropy power inequality step at (20d), so the claimed MMF gains over SDMA and NOMA are not supported.","rationale":"The reader's weakest_assumption identifies exactly the same step: the derivation of the private-stream rate lower bound (21) through the intermediate expression (20d), which does not follow from the preceding entropy power inequality. My stress-test confirms this is the most load-bearing gap. The paper's other components, including the S-lemma transformation and the CCCP/penalty algorithm, are plausible and could in principle be repaired, but the rate bound is the foundation of both the optimization objective and the numerical comparison against SDMA and NOMA. If (20d) is invalid, the computed MMF rates are not guaranteed achievable, and the reported gains may be artifacts. Because the issue is a specific derivation gap rather than an obviously unfixable flaw, a conditional acceptance requiring a corrected derivation is the appropriate response; this matches the reader's verdict, so no adjustment is needed. The concrete test proposed here, a direct re-derivation plus a numerical check on a simple Gaussian instance, would settle whether the concern actually lands.","tokens_in":23166,"tokens_out":7499,"duration_ms":64107,"concrete_test":"Independently re-derive (20d) from (20c) using the entropy power inequality on the independent summands Δh_k^T p0 s0, {h_k^T p_i s_i}_{i=1}^K, and n_k, and compare with the claimed expression. Then instantiate a two-user case (K=2) with independent Gaussian s_i and n_k and feasible values of Δh_1^T p0 and h_1^T p_i; compute both sides of the claimed inequality numerically. If the RHS of the step (20c) to (20d) exceeds the true entropy difference for any feasible parameter set, (21) is not a valid lower bound. If the bound is invalid, re-run the experiments in Figs. 7 and 8 with the corrected EPI bound to determine whether the reported RSMA gains over SDMA and NOMA persist.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central performance claim depends on the closed-form private-stream rate bound (21), which is obtained from (20d). The step (20c) to (20d) is not a consequence of the entropy power inequality as stated. In (20c), the first entropy is H(Δh_k^T p0 s0 + Σ_{i=1}^K h_k^T p_i s_i + n_k). Applying EPI to the independent summands Δh_k^T p0 s0, {h_k^T p_i s_i}_{i=1}^K, and n_k yields 2^{2H(·)} ≥ 2^{2H(Δh_k^T p0 s0)} + Σ_{i=1}^K 2^{2H(h_k^T p_i s_i)} + 2πeσ_k^2, not the claimed sum over i of 2^{2H(Δh_k^T p0 s0 + h_k^T p_i s_i + n_k)}. The quantities Δh_k^T p0 s0 + h_k^T p_i s_i + n_k are not independent across i because they share the same residual common signal s0 and the same noise n_k, so no entropy power inequality can sum their entropies. The subsequent subtraction of 1/2 log2(2πeσ_k^2) also does not cancel the variance of the second entropy term in (20c), which includes the residual common interference |Δh_k^T p0|^2 ε0. Consequently, (21) is not established as a valid lower bound and may exceed the true achievable rate. Since the MMF problem P0 and all numerical comparisons are built on this bound, the paper's headline superiority of RSMA over SDMA and NOMA is not supported without a corrected derivation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies robust max-min fair (MMF) beamforming for rate-splitting multiple access (RSMA) in visible light communication (VLC) networks with imperfect channel state information at the transmitter (CSIT). It derives closed-form lower bounds on the achievable rates for the common and private streams using entropy power and entropy inequalities under a bounded-uncertainty CSIT model. These bounds are then used to formulate an MMF rate maximization problem subject to optical and electrical power constraints, which is solved by a combination of semidefinite relaxation, S-lemma, CCCP, and a penalty method for the rank-one constraint. Numerical results compare the proposed RSMA design with SDMA and NOMA in both underloaded and overloaded regimes and report MMF rate gains for RSMA.","tokens_in":23556,"tokens_out":11575,"duration_ms":100921,"significance":"If the derivation and optimization are correct, the paper would be the first to provide VLC-specific rate lower bounds for RSMA with imperfect CSIT and a robust beamforming algorithm under practical power constraints. The problem formulation and the algorithmic pipeline (SDR, S-lemma, CCCP, penalty) are relevant to the VLC and RSMA communities. The numerical evidence of RSMA's superiority over SDMA and NOMA, if supported, would strengthen the case for RSMA in VLC. However, the central private-stream rate bound in (21) rests on an entropy power inequality step that is not valid as written, and the optical power constraint is not faithfully preserved in the problem reformulation. These issues are load-bearing for the main claims, so the current version is not yet acceptable.","major_comments":[{"comment":"The inequality from (20c) to (20d) is not a consequence of the entropy power inequality. For the first entropy in (20c), applying the EPI to the independent summands Δh_k^T p_0 s_0, {h_k^T p_i s_i}_{i=1}^K, and n_k yields 2^{2H(·)} ≥ 2^{2H(Δh_k^T p_0 s_0)} + Σ_{i=1}^K 2^{2H(h_k^T p_i s_i)} + 2πeσ_k^2, not Σ_{i=1}^K 2^{2H(Δh_k^T p_0 s_0 + h_k^T p_i s_i + n_k)}. The variables Δh_k^T p_0 s_0 + h_k^T p_i s_i + n_k are not independent across i because they share the same residual common signal s_0 and the same noise n_k. Moreover, the second entropy in (20c) is upper bounded by (1/2) log2(2πe( |Δh_k^T p_0|^2 ε_0 + Σ_{j≠k} |h_k^T p_j|^2 ε_j + σ_k^2 )), so the two subtracted logarithms in (20d) do not follow from the displayed entropy inequality. Consequently, (21) is not established as a lower bound. Since the MMF problem P0 and the numerical comparisons in Section IV are built on (21) via (26c), the claimed superiority of RSMA over SDMA and NOMA is not supported without a corrected derivation.","section":"II-C, Eq. (20d)"},{"comment":"Constraint (23d) is not equivalent to the optical power constraint (3). The original constraint (3) imposes both a lower bound, IL ≤ Σ_i A_i p_i^T e_n + b, and an upper bound, Σ_i A_i p_i^T e_n + b ≤ IH. Constraint (23d) only imposes an upper bound on Σ_i A_i p_i^T e_n using min{b−IL, IH−b} and drops the lower bound. The subsequent squared form in (26d) replaces the interval [IL−b, IH−b] by a symmetric interval of radius min{b−IL, IH−b}, which further changes the feasible set. As a result, the beamformers returned by Algorithm 1 may violate the original optical constraint (3). Please correct the constraint or justify the restriction as a conservative approximation with explicit conditions, e.g., IL ≤ b ≤ IH and b−IL = IH−b.","section":"II-D, Eq. (23d) and (26d)"},{"comment":"The convergence claim in Section III-E is not fully justified. The argument states that the solution at iteration n is also feasible at iteration n+1, but the feasible set of problem (44) changes between iterations because the linearized constraints (38) are tied to the previous iterate and the penalty surrogate (43) is a first-order approximation of ||P_i||_2. While the first-order expansion of the convex function e^y is a global lower bound, making the linearized constraints a valid inner approximation, the penalty term F_penalty in (43) is an upper bound on the true penalty when ρ is negative. Thus the monotonic increase of t + F_penalty is not guaranteed by the stated argument. A standard SCA convergence proof with a proper surrogate function, or an explicit treatment of the varying feasible set, is needed.","section":"III-E, Convergence Analysis"}],"minor_comments":[{"comment":"The text says 'close-form expressions' but should read 'closed-form expressions'.","section":"Section V"},{"comment":"In the sentence 'we present a penalty-based method... to address the rand-one constraint,' 'rand-one' should be 'rank-one'.","section":"Section III-D"},{"comment":"In the discussion after Fig. 8, 'severe multi-user interfernece' should be 'severe multi-user interference'.","section":"Section IV"},{"comment":"The caption reads 'Numer of iterations' and should be 'Number of iterations'.","section":"Fig. 5 caption"},{"comment":"The symbol ŷ_{k,i} is introduced after the equation in which it appears; please define it before its first use for readability.","section":"Eq. (20d)"}],"recommendation":"major_revision","confidential_remarks":"The primary issue is the unjustified entropy power inequality step in (20d), which invalidates the private-stream rate lower bound and hence the main performance comparison. The optical power constraint mismatch in (23d) is also concerning. These are load-bearing but potentially fixable with a corrected derivation and a revised optimization formulation. I recommend a major revision rather than rejection, provided the authors can re-derive the private-stream rate bound and re-run the numerical experiments accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper deserves a careful look, but the central rate bound for the private stream has a real gap, and the numerical RSMA-vs-SDMA/NOMA story rests on it.\n\nWhat it does well: it is the first RSMA-VLC treatment I know that uses the maximum-entropy input distribution from [47] together with the entropy power inequality to get closed-form rate expressions under peak optical, average optical, and electrical power limits. The robust MMF formulation with bounded CSIT and the S-lemma conversion of the semi-infinite constraints are competently done. The CCCP/SDR/penalty machinery is standard, but the authors apply it carefully and report convergence. The self-citations to [47] and [57] are not a problem: those are published, independently derived results.\n\nWhere it falls: equations (20c) to (20d). The first entropy in (20c) is H(Δh_k^T p0 s0 + Σ_i h_k^T p_i s_i + n_k). The independent summands are Δh_k^T p0 s0, each h_k^T p_i s_i, and n_k. EPI gives a sum of their individual entropy powers. Instead the paper writes a sum over i of 2^{2H(Δh_k^T p0 s0 + h_k^T p_i s_i + n_k)}. Those three-way sums are not independent across i because they share s0 and n_k, so no EPI can sum them. The second line's subtraction also does not follow from the entropy bound: splitting the conditioning variance into σ^2 and interference terms and subtracting both logarithms is stronger than the Gaussian upper bound on H(y|s_k), and it is not valid in general. So (21) is not established as a lower bound. Since P0 and all the comparisons minimize over this lower bound, the headline gains over SDMA and NOMA are not supported without a corrected derivation.\n\nSmaller issues: the penalty method's convergence to a rank-one point is asserted rather than proved; the choice of ρ is heuristic, and the numerical results appear to lack averaging over user drops (at least it is not stated). These are fixable and secondary.\n\nWho this is for: RSMA-VLC researchers and anyone doing robust beamforming for optical channels. If the bound can be repaired, the paper has a useful contribution. As it stands, I would not cite it for the rate bound. I would send it to review rather than desk reject, with a clear instruction that the authors must fix (20d) or remove the unsupported comparisons.","headline":"The private-stream rate bound that drives the RSMA gains is not proved—(20d) misapplies the entropy power inequality—so the paper's headline MMF comparisons are unsupported as written.","tokens_in":24067,"tokens_out":4809,"would_cite":false,"duration_ms":41778,"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":"This paper establishes closed-form rate lower bounds for RSMA-aided VLC under imperfect CSIT and gives a robust max-min fair beamforming algorithm that outperforms SDMA and NOMA.","keywords":["rate splitting multiple access","visible light communication","robust beamforming","max-min fairness","imperfect channel state information","semidefinite relaxation","CCCP","entropy power inequality"],"falsifier":"Take a one-user or two-user instance, choose any feasible channel-error vector from the uncertainty set, and check numerically whether expression (21) is really bounded above by the true mutual information in (20c); a single instance where the claimed inequality reverses, or where the entropy power step (20d) fails, would invalidate the bound and with it the MMF comparison.","tokens_in":22994,"feed_emoji":"💡","tokens_out":6126,"duration_ms":56789,"temperature":0.7,"pith_summary":"This paper asks whether rate-splitting multiple access (RSMA), which has proven robust in radio-frequency networks, can deliver its usual gains in visible-light communication (VLC) when the transmitter's channel knowledge is imperfect. It derives closed-form lower bounds on the achievable rates of the common and private streams, using a capacity lower-bound distribution suited to intensity modulation and direct detection with peak optical, average optical, and electrical power constraints. On top of those bounds, it formulates a max-min fairness beamforming problem that maximizes the worst-case user rate, and solves it with an algorithm that combines semidefinite relaxation, CCCP, the S-lemma, and a penalty method for rank-one recovery. Numerical results report that the proposed RSMA design outperforms SDMA and NOMA in both underloaded and overloaded VLC networks, with the largest margins in overloaded and uncertain-channel regimes.","feed_headline":"RSMA beamforming beats SDMA and NOMA in VLC with imperfect CSI","feed_subtitle":"Max-min fair design under imperfect channel knowledge raises worst-case user rate above NOMA and SDMA baselines.","key_machinery":"The load-bearing objects are the two rate lower bounds (18) and (21). The common-stream bound (18) is obtained from the entropy power inequality on the received signal entropy and the entropy inequality on the noise-plus-interference term, followed by a closed-form capacity lower bound for the optical intensity channel with input distribution (15). The private-stream bound (21) is the analogous expression after imperfect SIC, in which the residual common-stream term proportional to the channel estimation error $\\Delta h_k$ appears in the numerator and denominator. These closed forms convert an intractable mutual-information maximization into difference-of-convex constraints that the paper then handles with semidefinite relaxation, the S-lemma for the semi-infinite uncertainty constraints, CCCP linearization, and a penalty term $\\rho\\sum_i(\\operatorname{Tr}(P_i)-\\|P_i\\|_2)$ to drive the relaxed matrices to rank one.","core_discovery":"The paper's central claim is that RSMA-aided VLC is not only feasible under imperfect CSIT but superior to existing SDMA and NOMA benchmarks. The supporting discovery is a pair of closed-form rate lower bounds: expression (18) for the common stream and expression (21) for the private stream after successive interference cancellation, both derived from entropy power and entropy inequalities under a truncated exponential-quadratic input distribution and three practical optical and electrical power constraints. Combining these bounds with a robustness model in which each user's channel lies in a bounded uncertainty region, the paper formulates the MMF rate maximization and provides an iterative algorithm that returns rank-one beamformers and yields a monotonically rising objective. If the bounds and algorithm are correct, the consequence is that RSMA can robustly manage multiuser interference in VLC, outperforming NOMA and SDMA in worst-case rate.","pith_inferences":["If the private-stream lower bound (21) is accepted, the same bounding technique could be transferred to other optical multiple-access settings with bounded channel uncertainty, such as multi-cell VLC, hybrid RF/VLC, and integrated sensing and communications, where robust MMF would likely inherit the RSMA advantage.","A fairer benchmark comparison might re-derive the NOMA and SDMA baselines under the same imperfect-SIC assumption, since the residual common-stream interference term appears only in the RSMA model; this could make the reported gains more conservative or more pronounced depending on how the baselines are formulated.","A testable extension is to replace the outer entropy-power step with the exact entropy calculation for discrete VLC inputs; if the resulting bound is tighter, the MMF rates reported here are conservative and the relative gains would increase."],"forward_implications":["In both underloaded and overloaded VLC networks, the proposed robust RSMA beamforming achieves the largest worst-case rate among the three schemes; in the numerical settings the gain reaches roughly 150% over SDMA and 185% over NOMA in the underloaded regime, and 274% over SDMA and 180% over NOMA in the overloaded regime.","As the user uncertainty radius grows, the MMF rate of all schemes decreases, but RSMA retains a larger advantage, indicating that the rate-splitting structure preserves robustness when CSIT is less accurate.","The proposed algorithm converges within a few iterations to a rank-one solution, so beamformers can be recovered by eigenvalue decomposition without Gaussian randomization.","The derived rate lower bound yields higher MMF rates than the commonly used $\\frac{1}{2}\\log_2(1+\\varrho\\,\\mathrm{SINR})$ bounds with $\\varrho=2/(\\pi e)$ or $e/(2\\pi)$ at the simulated SNRs."],"supporting_citations":[{"why":"Supplies the input distribution (15) and the closed-form achievable-rate result for VLC channels that the paper adapts to the RSMA common and private streams.","marker":"[47]"},{"why":"Provides the bounded imperfect-CSIT model expressed as an uncertainty region $\\mathcal{H}_k$, which defines the robust problem's channel-error set.","marker":"[57]"},{"why":"Gives the CCCP-based iterative convex approximation framework that the paper adapts for the nonconvex rate constraints.","marker":"[59]"},{"why":"States the S-lemma used to convert the semi-infinite CSI-uncertainty constraints into finite linear matrix inequality constraints.","marker":"[60]"},{"why":"Defines one-layer RSMA and the common/private stream structure on which the system model and the total rate composition (22) rely.","marker":"[16]"}],"fun_headline_variants":["RSMA robust beamforming tops NOMA and SDMA in VLC","Max-min fair RSMA beats NOMA and SDMA in VLC","Imperfect CSI? RSMA still wins in VLC fairness","RSMA outdoes NOMA and SDMA for VLC max-min rate","Robust RSMA design lifts worst-case VLC user rates"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole MMF optimization and the reported superiority over SDMA and NOMA rest on the validity of the private-stream rate lower bound (21); if that inequality does not actually follow from the entropy power step or is too loose, the robust design has no proven objective to maximize.","fun_headline_variants_meta":{"raw":{"variants":["RSMA robust beamforming tops NOMA and SDMA in VLC","Max-min fair RSMA beats NOMA and SDMA in VLC","Imperfect CSI? RSMA still wins in VLC fairness","RSMA outdoes NOMA and SDMA for VLC max-min rate","Robust RSMA design lifts worst-case VLC user rates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000553,"raw_usage":{"total_tokens":2619,"prompt_tokens":909,"completion_tokens":1710,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":525,"completion_tokens_details":{"reasoning_tokens":1627}},"tokens_in":525,"tokens_out":1710,"duration_ms":10751,"temperature":1.0,"reasoning_tokens":1627,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:36:02.317576+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a one-user or two-user instance, choose any feasible channel-error vector from the uncertainty set, and check numerically whether expression (21) is really bounded above by the true mutual information in (20c); a single instance where the claimed inequality reverses, or where the entropy power step (20d) fails, would invalidate the bound and with it the MMF comparison.","supporting_citations":[{"cited_title":"Achiev able rate with closed-form for SISO channel and broadcast channel in v isible light communication networks,","cited_arxiv_id":null,"evidence_quote":"Supplies the input distribution (15) and the closed-form achievable-rate result for VLC channels that the paper adapts to the RSMA common and private streams."},{"cited_title":"Optimal and rob ust secure beamformer for indoor MISO visible light communication,","cited_arxiv_id":null,"evidence_quote":"Provides the bounded imperfect-CSIT model expressed as an uncertainty region $\\mathcal{H}_k$, which defines the robust problem's channel-error set."},{"cited_title":"A fr amework of robust transmission design for IRS-aided miso communica tions with imperfect cascaded channels,","cited_arxiv_id":null,"evidence_quote":"Gives the CCCP-based iterative convex approximation framework that the paper adapts for the nonconvex rate constraints."},{"cited_title":"Boyd and L","cited_arxiv_id":null,"evidence_quote":"States the S-lemma used to convert the semi-infinite CSI-uncertainty constraints into finite linear matrix inequality constraints."},{"cited_title":"Rate-splitting multiple access: Fundamentals, sur vey, and future research trends,","cited_arxiv_id":null,"evidence_quote":"Defines one-layer RSMA and the common/private stream structure on which the system model and the total rate composition (22) rely."}],"review_version":1}