{"id":"51059760-e665-4045-bbf2-ed60d46932c3","arxiv_id":"2505.04148","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A DRL-based energy efficiency optimization for an RSMA-based LEO satellite system with a UAV-mounted BD-active RIS is simulated, claiming TRPO achieves the highest energy efficiency.","lead":"A simulation study combines rate-splitting multiple access, a UAV-mounted beyond-diagonal active RIS, and deep reinforcement learning to maximize energy efficiency in LEO satellite links. The paper reports that TRPO outperforms TD3 and A3C, but the problem formulation contains several internal inconsistencies.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The objective (19a) double-counts the RSMA common rate, inflating every reported EE/sum-rate number, and constraint (19i) forbids the active amplification the architecture requires; the central claim therefore rests on an internally inconsistent model.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing defect: the optimization problem in (19) is not a valid model of the described RSMA-BD-ARIS system. I independently verified the double-counting of the common rate starting from equations (13)–(15), and the active-RIS constraint contradiction in (19i). Because the DRL reward is defined as the EE in (19a), the double-counted objective propagates into every simulation result, making the reported superiority of TRPO and the quantitative EE/sum-rate values unsupported. The active-RIS constraint issue independently undermines the physical model, but the objective double-counting alone is sufficient to invalidate the central empirical claim. No code, hyperparameters, or error bars are provided, so the numerical results cannot be rehabilitated post hoc. The rejection verdict is appropriate with moderate confidence; the internal inconsistencies are visible in the text, while the exact impact on reported numbers cannot be quantified without the missing implementation.","tokens_in":18532,"tokens_out":5113,"duration_ms":55335,"concrete_test":"Use the paper's own equations (13)–(15): since Σ_i δ_i = 1, the numerator in (19a) is Σ_i log2(1+γp,i) + 2R_c, not Σ_i log2(1+γp,i) + R_c. Then rerun the DRL training and evaluation with the corrected EE numerator Σ_i R_i (common rate counted once) while keeping all other parameters identical. If the corrected curves in Figs. 2–8 differ materially—as they must whenever R_c > 0—the reported TRPO advantage and EE values are artifacts of the double-counted objective, and the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assumption is that problem (19) correctly models the RSMA-BD-ARIS system. It does not. From (13)–(15), R_i = log2(1+γp,i) + δ_i R_c with Σ_i δ_i = 1, so Σ_i R_i = Σ_i log2(1+γp,i) + R_c. The objective (19a) then becomes [Σ_i log2(1+γp,i) + 2R_c] / Ptotal, counting the common rate twice. This double-counted EE is also used directly as the DRL reward in (22), so every reported EE and sum-rate curve in Figs. 2–8 reflects an inflated objective and does not establish the claimed RSMA advantage. A second internal inconsistency compounds this: constraint (19i), Φ_g Φ_g^H ⪯ I, restricts the singular values of Φ_g to at most 1, which prohibits |ϕ|>1 and therefore forbids signal amplification, contradicting the active-RIS power model (17) and the paper's central claim of a BD-Active RIS. These are not matters of disagreement with prior work; they are algebraic and physical contradictions within the formulated problem.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript proposes an RSMA-based LEO satellite downlink assisted by a UAV-mounted beyond-diagonal active RIS (BD-ARIS). It formulates an energy-efficiency maximization problem that jointly optimizes satellite beamforming, power allocation, rate-splitting ratios, the BD-ARIS reflection matrix, and the UAV horizontal position, and it solves this problem with three deep reinforcement learning algorithms: TRPO, TD3, and A3C. The simulation study claims that TRPO achieves the best energy efficiency and sum rate, that the proposed BD-ARIS framework outperforms conventional active/passive RIS designs and NOMA baselines, and that TRPO is robust to CSI errors. The paper contains detailed system, channel, and power-consumption models and a fairly complete account of the three DRL algorithms.","tokens_in":18802,"tokens_out":5861,"duration_ms":61106,"significance":"If the results were correct, the paper would offer a useful design study for a current topic at the intersection of non-terrestrial networks, active RIS, RSMA, and DRL. The authors are to be credited for assembling a complex system model, for deriving the Rician fading and power-consumption expressions, and for implementing and comparing three DRL algorithms in a common simulator. However, the central numerical claims rest on an internally inconsistent optimization problem: the objective double-counts the RSMA common rate, the reflection constraint forbids the active amplification the architecture requires, and the listed simulation parameters violate the power-allocation constraint. Because these issues affect the reward function and every reported number in the simulation study, the significance as demonstrated by the paper is presently not established.","major_comments":[{"comment":"The objective (19a) adds the common rate Rc to the sum of individual rates Σ_i R_i. However, from (15), R_i = log2(1+γp,i) + δ_i Rc with Σ_i δ_i = 1, so Σ_i R_i = Σ_i log2(1+γp,i) + Rc. Therefore (19a) equals [Σ_i log2(1+γp,i) + 2Rc]/Ptotal, counting the common rate twice. Since the same inflated EE is used as the reward in (22), all EE and sum-rate values in Figs. 2–8 measure this double-counted objective and cannot support the paper's claims about RSMA gains.","section":"Section III, Eq. (19a) and Eq. (15)"},{"comment":"Constraint (19i) imposes Φg Φg^H ⪯ I, which restricts the singular values of the reflection block to at most 1. For an active RIS with amplification factors βg,1, βg,2 > 1, this constraint is violated; the active-RIS power model in (17) and the term 'signal amplification' throughout the paper require reflection coefficients with magnitude greater than one. The paper never replaces (19i) with an active-RIS output-power constraint such as (19e). Thus the formulated problem is infeasible for exactly the active BD-ARIS configuration the paper claims to optimize.","section":"Section II-B and Section III, Eq. (19i)"},{"comment":"Table II lists ac = 0.3 and ai = 0.35 for I = 3. Then ac + Σ_i ai = 0.3 + 3×0.35 = 1.35 > 1, which violates constraint (19f) and the unit-power assumption in (16). This infeasible parameter set is used to generate all simulation results, so the reported rewards and EE numbers are not from a feasible instance of problem (19).","section":"Table II and Eq. (19f)"},{"comment":"The reward (22) is exactly the objective EE of (19a), so the training curves in Fig. 2 simply plot the same quantity that is later reported as the performance metric. With no external optimal or near-optimal benchmark and no comparison to an analytical bound, the conclusion that TRPO is the best algorithm and that the proposed framework outperforms passive/active RIS and NOMA is only a statement about the authors' simulator. Correcting the objective in (19a) and the constraint in (19i) will change these curves, so the algorithmic ranking and the baseline comparisons need to be re-evaluated.","section":"Section IV-A3 and Figs. 2–8"}],"minor_comments":[{"comment":"The power allocation coefficients are denoted ac, ai in Section III and Table II, but αc, αi in (16) and (21), and γi appears in (21) without definition; please unify the notation.","section":"Notation throughout"},{"comment":"Table II misassigns the symbols in (18): s is the rotor solidity, ρ is the air density, and δ is the blade profile drag coefficient, but the table lists 'Air density s', 'Profile drag coefficient ρ', and 'Rotor solidity δ'.","section":"Table II and Eq. (18)"},{"comment":"The y-axis label 'Sum Rate (Kbps/Hz)' is not a standard unit for rate; the text refers to sum rate in bits/s/Hz, so the units should be corrected and made consistent.","section":"Fig. 4"},{"comment":"The caption says 'spectral and energy efficiency' but the figure only plots energy efficiency; either add a spectral-efficiency panel or revise the caption.","section":"Fig. 6"}],"recommendation":"reject","confidential_remarks":"The manuscript is within the journal's scope, but the technical flaws are fundamental: the objective function is algebraically wrong, the active-RIS constraint is incompatible with the claimed hardware, and the simulation parameters are infeasible. These are not local presentation issues, and the entire numerical study would need to be rebuilt before the claims could be assessed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know two things about this paper. The optimization objective double-counts the RSMA common rate, and the RIS constraint in the problem formulation forbids the very signal amplification the architecture is supposed to provide. The reported EE and sum-rate numbers therefore do not correspond to the claimed system.\n\nWhat is new here is mostly the assembly: a LEO satellite, a UAV-mounted BD-active RIS, RSMA, and three DRL algorithms. The system model is detailed and the simulation study is broad. The authors do seem to have made an effort to model power consumption realistically, including UAV hovering power and RIS amplifier costs. That part is fine.\n\nBut the core formulation has algebraic and physical contradictions. From (13)-(15), each user's total rate already includes a fraction of the common rate, so summing over users plus the common rate gives the private sum plus twice the common rate. The objective (19a) maximizes that inflated sum over total power. Since the DRL reward in (22) is exactly this EE, every training curve and reported EE value is chasing a doubled common rate.\n\nWorse, constraint (19i) imposes Φg Φg^H ⪯ I, which restricts the singular values of each reflection block to at most one. That means no |φ| > 1, no signal amplification. Yet the power model (17) includes RIS output power and amplifier efficiency, and the whole point of a BD-ARIS is active gain. The constraint makes the active part impossible.\n\nThere are smaller inconsistencies too. Table II lists ac = 0.3 and ai = 0.35 per user with I = 3, which sums to 1.35, violating the constraint the text says should equal one. The connection between the altitude variation in Fig. 4 and the fixed altitude in Section II is not handled clearly. And the DRL implementation is underspecified: no hyperparameters, no network architecture, no code, no statistical significance. So the results are not independently checkable.\n\nWho is this paper for? Someone wanting a quick overview of DRL options for RSMA with RIS in non-terrestrial settings might skim it. But as a research contribution, the numbers are not meaningful, and the claims about RSMA's advantage and TRPO's stability rest on a flawed comparator. The authors could fix the double-counting and the constraint, rerun the simulations, and possibly come back with a defensible paper. As it stands, I would not accept this for peer review.\n\nRecommendation: desk reject with an invitation to resubmit after fixing the objective and the RIS active-power modeling.\n\nBest,\n[Your name]","headline":"The double-counted RSMA rate and a constraint that forbids the active amplification make the reported EE numbers untrustworthy.","tokens_in":19368,"tokens_out":2108,"would_cite":false,"duration_ms":22279,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A UAV-mounted beyond-diagonal active RIS combined with rate-splitting multiple access can push LEO satellite downlink energy efficiency to about 7-10 Kbits/Joule, and trust-region policy optimization (TRPO) is the best of the three DRL…","keywords":["LEO satellite communications","rate-splitting multiple access","beyond-diagonal active RIS","UAV-mounted RIS","energy efficiency","deep reinforcement learning","TRPO","non-terrestrial networks"],"falsifier":"Run a small exact instance of problem (19) — for example, three users and a two-element RIS group — and compute the maximum output power of the surface while enforcing $\\Phi_g \\Phi_g^H \\preceq I$. If no feasible reflection matrix delivers the output power assumed in the power model (17) and constraint (19e), then the simulated EE exceeds what the modeled hardware can achieve; equivalently, comparing the corrected sum rate with the reported one would show whether the common rate is double-counted.","tokens_in":18278,"feed_emoji":"🛰️","tokens_out":9760,"duration_ms":86233,"temperature":0.7,"pith_summary":"This paper argues that mounting a beyond-diagonal active reconfigurable intelligent surface (a reflecting surface whose elements both amplify signals and couple to their neighbors) on a UAV can raise the energy efficiency of LEO satellite downlinks when combined with rate-splitting multiple access (RSMA), which serves each user with a shared common message plus a private message. The authors jointly optimize UAV position, satellite beamforming, power allocation, and the surface's reflection matrix, and train three deep reinforcement learning (DRL) agents for the task; Trust Region Policy Optimization (TRPO) is reported to reach the highest energy efficiency, around 7-10 Kbits/Joule, and the highest sum rate, with Twin Delayed DDPG (TD3) converging faster and Asynchronous Advantage Actor-Critic (A3C) lagging. If these simulations are right, the practical message is that RSMA plus an actively amplifying group-connected RIS, controlled by a stable policy-gradient method, is a competitive design point for energy-efficient non-terrestrial 6G connectivity, beating NOMA and passive-RIS baselines as the antenna and surface sizes grow.","feed_headline":"UAV smart-surface relay lifts LEO link efficiency to 10 Kbits/Joule","feed_subtitle":"Rate-splitting over an active UAV relay beats NOMA and passive RIS when tuned by trust-region RL.","key_machinery":"The machinery is the joint energy-efficiency maximization problem (19) together with the group-connected BD-ARIS model. The BD-ARIS is a block-diagonal reflection matrix whose $2\\times 2$ blocks are symmetric coupling matrices, each element providing both a phase shift and amplification; the power it consumes includes an amplification term and per-element phase-shifter and DC costs, while the UAV's hovering power follows a rotary-wing model. RSMA splits each user's message into a common part decoded by all and a private part, and the objective maximizes the common plus private sum rate normalized by total power. Because this problem is non-convex and high-dimensional, it is recast as a Markov decision process and solved by TRPO, TD3, and A3C; TRPO's trust-region KL constraint is what the paper credits for the stable, high-reward policies.","core_discovery":"The paper's central claim is that a LEO satellite downlink serving multiple ground users through a UAV-mounted beyond-diagonal active RIS under RSMA, with all degrees of freedom learned by DRL, achieves its best energy efficiency when the policy is updated by TRPO. Across the simulations, TRPO converges to a reward near 1100 and energy efficiencies in the 7-10 Kbits/Joule range, exceeding TD3 and A3C, and it remains the most reliable scheme as satellite power, RIS transmit power, altitude, user count, and antenna count vary. The authors further claim that the group-connected BD-ARIS (group size two) outperforms both conventional active and passive RIS designs at equal element counts, and that RSMA with TRPO surpasses a NOMA baseline once the satellite uses more than about 64 antennas. These results are presented as evidence that adaptive physical-layer hardware plus learning-based control is a scalable, energy-efficient approach for 6G and massive IoT in non-terrestrial networks.","pith_inferences":["Not stated in the paper: the objective (19a) counts the common rate $R_c$ once directly and again inside each $R_i$ via $\\delta_i R_c$, so the reported sum rates are likely an overcount of the physically achievable throughput.","Not stated in the paper: the constraint $\\Phi_g \\Phi_g^H \\preceq I$ caps each group's singular values at one, which may rule out the very amplification the power model charges for; if so, the BD-ARIS advantage over passive RIS would come from coupling and phase degrees of freedom, not active gain.","Not stated in the paper: because UAV movement between positions is not charged in the power model, the reported EE is optimistic for missions that reposition frequently; including travel energy could lower the optimal altitude and alter the algorithm ranking.","Not stated in the paper: benchmarking the three agents against a classical alternating-optimization or small-scale exhaustive baseline would separate the contribution of the RSMA-BD-ARIS architecture from the contribution of the specific DRL optimizer."],"forward_implications":["Deploying TRPO rather than TD3 or A3C yields the highest energy efficiency and sum rate in the tested RSMA-BD-ARIS settings, particularly at high satellite transmit power and large UAV-to-user distances.","UAV altitude is a tuning knob with a floor: sum rates rise as the UAV descends toward 4 km, but above roughly 16 km all three algorithms converge to a throughput floor, so higher deployment buys little.","RSMA with TRPO surpasses a NOMA baseline optimized by TRPO once the satellite array exceeds about 64 elements, and the gap widens with further antenna growth.","Communication reliability degrades monotonically with channel-estimation error and drops below 75% near $\\sigma_X^2 \\approx 10^{-1}$, so accurate CSI matters more than the choice of DRL algorithm in that regime.","A group-connected BD-ARIS with TRPO yields higher energy efficiency than conventional active or passive RIS at equal element counts, and the advantage grows with the number of RIS elements."],"supporting_citations":[{"why":"Supplies the per-element phase-shifter power-consumption values used in the BD-ARIS power model.","marker":"[7]"},{"why":"Establishes the active-RIS amplification concept that the beyond-diagonal active surface extends.","marker":"[8]"},{"why":"Provides the RSMA-with-BD-RIS optimization approach this architecture adapts to an active, UAV-mounted surface.","marker":"[22]"},{"why":"Defines the LEO-satellite NOMA setting used as the baseline in the RSMA-versus-NOMA comparison.","marker":"[24]"},{"why":"Is the source of the group-connected block-diagonal symmetric reflection matrix model for the BD-ARIS.","marker":"[25]"},{"why":"Supplies the symmetry and unit-norm constraints $\\Phi_g=\\Phi_g^T$, $\\Phi_g\\Phi_g^H\\preceq I$ imposed on each RIS group.","marker":"[26]"},{"why":"Gives the RSMA SINR and common/private rate expressions that define the objective.","marker":"[28]"},{"why":"Provides the DC-biasing power cost per element in the BD-ARIS power consumption model.","marker":"[29]"},{"why":"Supplies the rotary-wing UAV hovering power formula used in the total power consumption.","marker":"[30]"}],"fun_headline_variants":["TRPO beats TD3 and A3C in LEO satellite-UAV active RIS energy efficiency","RSMA with TRPO maximizes LEO downlink energy via UAV active RIS","TRPO-tuned RSMA hits 10 Kbits/Joule in LEO satellite downlink","Energy-efficient LEO link via TRPO-tuned RSMA and UAV active RIS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that optimization problem (19) is a valid and feasible model of an amplifying RSMA-assisted active RIS; if the unit-norm constraint forbids the amplification the power model charges for, or the common rate is double-counted in the objective, the reported EE and sum-rate numbers would not describe the advertised hardware.","fun_headline_variants_meta":{"raw":{"variants":["TRPO beats TD3 and A3C in LEO satellite-UAV active RIS energy efficiency","RSMA with TRPO maximizes LEO downlink energy via UAV active RIS","TRPO-tuned RSMA hits 10 Kbits/Joule in LEO satellite downlink","Energy-efficient LEO link via TRPO-tuned RSMA and UAV active RIS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001656,"raw_usage":{"total_tokens":6632,"prompt_tokens":1057,"completion_tokens":5575,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":673,"completion_tokens_details":{"reasoning_tokens":5483}},"tokens_in":673,"tokens_out":5575,"duration_ms":38996,"temperature":1.0,"reasoning_tokens":5483,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:36:40.584376+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a small exact instance of problem (19) — for example, three users and a two-element RIS group — and compute the maximum output power of the surface while enforcing $\\Phi_g \\Phi_g^H \\preceq I$. If no feasible reflection matrix delivers the output power assumed in the power model (17) and constraint (19e), then the simulated EE exceeds what the modeled hardware can achieve; equivalently, comparing the corrected sum rate with the reported one would show whether the common rate is double-counted.","supporting_citations":[{"cited_title":"Opti- mization of rate-splitting multiple access in beyond diagonal ris-assisted urllc systems,","cited_arxiv_id":null,"evidence_quote":"Provides the RSMA-with-BD-RIS optimization approach this architecture adapts to an active, UAV-mounted surface."},{"cited_title":"Ris-assisted energy-efficient leo satellite communications with noma,","cited_arxiv_id":null,"evidence_quote":"Defines the LEO-satellite NOMA setting used as the baseline in the RSMA-versus-NOMA comparison."},{"cited_title":"Opti- mization of rate-splitting multiple access in beyond diagonal ris-assisted urllc systems,","cited_arxiv_id":null,"evidence_quote":"Is the source of the group-connected block-diagonal symmetric reflection matrix model for the BD-ARIS."},{"cited_title":"Beyond diagonal reconfigurable intelli- gent surfaces: A multi-sector mode enabling highly directional full-space wireless coverage,","cited_arxiv_id":null,"evidence_quote":"Supplies the symmetry and unit-norm constraints $\\Phi_g=\\Phi_g^T$, $\\Phi_g\\Phi_g^H\\preceq I$ imposed on each RIS group."},{"cited_title":"Energy minimization for wireless communication with rotary-wing uav,","cited_arxiv_id":null,"evidence_quote":"Supplies the rotary-wing UAV hovering power formula used in the total power consumption."}],"review_version":1}