{"id":"fad4aa28-952b-47fc-bde3-aa39b2e36b0d","arxiv_id":"2507.09458","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper's hybrid NOMA scheme with power adaptation and hybrid SIC is shown to outperform OMA in rate and energy with probability approaching 1 at high SNR, without special rate or power conditions.","lead":"This paper designs a hybrid NOMA scheme that combines hybrid successive interference cancellation with dynamic power adaptation, and derives the probability that it beats pure OMA in both data rate and energy use. In the high-SNR limit this probability approaches 1 without the restrictive rate or power conditions that earlier hybrid NOMA designs required.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lemma 1 misses the sign reversal in the rate inequality: in the typical regime τ_m>(1−β)/β, Eq. (17) counts non-failure events as failures, so the derived \\hat P_n and the no-error-floor conclusion are not established.","rationale":"The reader's weakest assumption was perfect CSI and exact γ selection, which is a practical limitation acknowledged in Section V but not an internal inconsistency. The central concern found here is more load-bearing: Lemma 1, used in both Theorems 1 and 2, makes a sign-dependent algebraic simplification without treating the sign. For τ_m > (1−β)/β, the simplified condition y>Θ with negative Θ is not equivalent to the original rate inequality; the correct flipped inequality y≤Ψ' is incompatible with y>Φ, so that branch should be empty. The over-counted region includes channel realizations where the proposed scheme actually beats OMA, so the derived \\hat P_n is not the true probability. This is not merely a missing proof: it is a concrete counterexample of the claimed equality, and it directly affects the high-SNR regime where τ_m grows. Because the central claim 'probability approaches 1' is established only through the erroneous \\hat P_n expression, the paper's main theoretical result is currently unverified. A revised derivation that correctly handles the two sign regimes might still show \\hat P_n → 0, but that conclusion cannot be drawn from the present text.","tokens_in":21038,"tokens_out":42862,"duration_ms":480640,"concrete_test":"Hand-check a single channel realization and a Monte Carlo comparison.  Take M=2, m=1, n=2, β=0.25, R_m=1, ρ_n=ρ_m=1000, |h_m|^2=0.01, |h_n|^2=0.1.  Then ε_m=1, α_m=0.001, τ_m=9, so Eq. (5)–(9) give R_n^II=log(1+25)=log26, R_n^{II,2}=log(1+9)=log10, total H-NOMA rate log260 > OMA rate log101, hence the true event is success.  Yet Eq. (17) counts this point in PT,1 because Φ=0.036, Ω=0.396, Θ=−0.006, and all conditions |h_n|^2>Θ, |h_n|^2<Ω, |h_n|^2>Φ, |h_m|^2>α_m hold.  Then run Monte Carlo of the definition in Eq. (13) and compare with Eq. (19) over the same parameters; any mismatch confirms the incorrect decomposition.","verdict_should_be":"REJECT","load_bearing_attack":"The reduction in Appendix A from Eq. (83) to Eq. (17) is algebraically incorrect for τ_m > (1−β)/β.  The inequality (1+τ_m)(1+βρ_n y) ≤ 1+ρ_n y with y=|h_n|^2 rearranges to y ≥ τ_m/[ρ_n((1−β)−βτ_m)] only when the denominator is positive.  When τ_m > (1−β)/β, the inequality direction flips to y ≤ τ_m/[ρ_n(βτ_m−(1−β))] = (x/α_m−1)/[ρ_n(βx/α_m−1)].  Because Type II also requires y > Φ = (x/α_m−1)/(βρ_n), and β<1/2 implies τ_m/[ρ_n(βτ_m−(1−β))] < Φ, this branch is empty.  Eq. (17) instead keeps y > Θ with Θ=(x/α_m−1)/[(1−βx/α_m)ρ_n], which is negative in this regime, thereby adding a positive-probability region that is not a failure event.  At high SNR, τ_m = ρ_m|h_m|^2/ε_m − 1 tends to infinity for typical nonzero |h_m|^2, so the erroneous regime is the dominant one rather than a corner case.  Consequently the exact expression for \\hat P_n in Theorems 1 and 2 is not the probability defined in Eq. (13), and the asymptotic claim \\hat P_n → 0 is not supported by the supplied derivation.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes an uplink hybrid NOMA (H-NOMA) scheme that combines hybrid successive interference cancellation (HSIC) with power adaptation (PA), and claims that the probability \\hat P_n of the total achievable rate over the NOMA and OMA slots being no larger than the pure-OMA rate tends to zero as the signal-to-noise ratios grow, for any \\beta<1/2, any target rate, and any power ratio. The theoretical part derives closed-form-looking expressions for \\hat P_n in the two user-ordering cases m<n and m>n, and asymptotic approximations showing \\hat P_n \\to 0. The paper builds its derivation on Lemma 1, which decomposes the Type II probability into two terms using thresholds \\Phi, \\Omega, \\Theta, and \\Psi. Numerical simulations are presented as verifying the analysis.","tokens_in":21341,"tokens_out":26380,"duration_ms":270245,"significance":"If the asymptotic claim were rigorously established, it would be a meaningful advance: it would show that the proposed HSIC-PA H-NOMA scheme achieves a higher rate than OMA with probability approaching one at high SNR while consuming less energy, without the restrictive conditions that cause error floors in earlier H-NOMA designs (e.g., [25]). The paper provides a substantial set of analytical expressions, piecewise tables, and simulation curves, and the system model is clearly described. However, the central derivation rests on a lemma that contains an algebraic sign error, so the claimed exact expression for \\hat P_n is not the probability defined in Eq. (13), and the asymptotic proof is not supported as written. The qualitative conclusion may still be correct, but the supplied analysis does not establish it.","major_comments":[{"comment":"The rearrangement of the rate inequality in the Type II, Case 2 branch is incorrect for \\tau_m > (1-\\beta)/\\beta. Starting from (1+\\tau_m)(1+\\beta\\rho_n y) \\le 1+\\rho_n y, where y=|h_n|^2, we obtain \\tau_m \\le \\rho_n y (1-\\beta-\\beta\\tau_m). If \\tau_m < (1-\\beta)/\\beta, this gives y \\ge \\tau_m/[\\rho_n(1-\\beta-\\beta\\tau_m)] = \\Theta. If \\tau_m > (1-\\beta)/\\beta, the right-hand side is negative, so the inequality has no solution for y>0; the correct condition is an empty set, not y \\ge \\Theta with a negative \\Theta. Equation (17) keeps the region |h_n|^2 > \\Theta, |h_n|^2 < \\Omega, |h_n|^2 > \\Phi, |h_m|^2 > \\alpha_m, which for \\tau_m > (1-\\beta)/\\beta includes a positive-probability set that does not satisfy the failure condition. Since at high SNR \\tau_m = \\rho_m |h_m|^2/\\varepsilon_m - 1 tends to infinity for typical nonzero |h_m|^2, the erroneous regime is the dominant one rather than a corner case. Consequently, the exact expression for \\hat P_n in Theorems 1 and 2 is not the probability defined in Eq. (13), and the asymptotic claim \\hat P_n \\to 0 is not established by the supplied derivation. This is a load-bearing error that requires a full re-derivation of Lemma 1 and all subsequent results that depend on it.","section":"Lemma 1, Eq. (17), and Appendix A"}],"minor_comments":[{"comment":"The definitions of c_p and \\hat c_p contain a typo: the binomial coefficient uses l where it should use p. For example, Eq. (22) writes c_p = \\binom{n-m-1}{l}(-1)^{n-m-1-p}, but the summation index is p, so it should be \\binom{n-m-1}{p}(-1)^{n-m-1-p}.","section":"Eq. (22) and Eq. (49)"},{"comment":"The paper repeatedly calls the derived expressions \"closed-form\", but several key terms (S2, S3, S5, V5, V7, etc.) rely on Gauss-Chebyshev quadrature with the parameter n_c, which is a numerical integration approximation, not a closed form. The language should be adjusted to \"semi-analytical\" or \"numerically evaluated\" where quadrature is used.","section":"Abstract and Section III"},{"comment":"The conclusion contains a sentence fragment: \"particularly in achieving \\hat P_n \\to 0 in the high SNR regime under all conditions. guaranteed performance superiority.\" The second phrase should be integrated into a complete sentence.","section":"Conclusion"},{"comment":"The paper relies heavily on results from [25] for P1 and P2,2 without re-deriving them; the manuscript would be easier to verify if those expressions were summarized or briefly re-derived in an appendix, or if the exact statements from [25] were stated explicitly.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The sign error in Lemma 1 is serious and sits at the root of the claimed exact and asymptotic results. I recommend asking the authors to correct the derivation and then re-check the subsequent theorems and corollaries. The simulations shown in the paper may not expose the error because the plotted SNR ranges can make the erroneously included region small; the authors should test at higher SNR and with parameters where \\tau_m > (1-\\beta)/\\beta clearly holds. If the corrected derivation still yields \\hat P_n \\to 0, the paper may be salvageable, but the current version does not support the main claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper combines hybrid SIC with power adaptation in hybrid NOMA and claims that the probability of H-NOMA underperforming OMA while using less energy goes to zero at high SNR with no restrictive conditions. That is a real extension of the prior HSIC-NPA result, and if true it removes a known error floor. The scheme itself is a natural fusion of [25] and [28]; the new asymptotic claim is specific and testable.\n\nThe good news: the problem is well posed, the decomposition of the failure probability is systematic, and the simulations appear to match the analysis in the plotted regimes. The energy accounting is clear, and the comparison with the NPA baseline is honest.\n\nThe soft spot is load-bearing. In Lemma 1, the inequality (1+τ_m)(1+βρ_n y) ≤ 1+ρ_n y is rearranged to y ≥ Θ without checking the sign of the denominator. When τ_m > (1−β)/β — which is the typical case at high SNR because τ_m grows with |h_m|^2 — the inequality has no positive solution, yet the expression in (17) counts the region Φ < y < Ω as failure. That adds a positive-probability region that is not actually a failure event. The true failure probability is smaller than the derived expression. So the exact expression for P_hat_n in Theorems 1 and 2 is not the probability defined in (13). The asymptotic claim that P_hat_n → 0 may survive because the spurious term decays, but the proof as written does not establish it. The authors need to correct Lemma 1 and redo the subsequent integrals, or provide a different argument.\n\nMinor points: the paper calls Gauss-Chebyshev quadrature expressions closed-form; that's a terminology stretch. Several components (P1, P2,2) are imported from [25] without re-derivation, so the independent check is harder. No code or data is released, but the simulation/analysis agreement in the figures suggests the numerics are reproducible in principle. The perfect-CSI assumption for the power adaptation equality is acknowledged and is standard for this line of work.\n\nWho is this for? Researchers in NOMA and H-NOMA energy efficiency will find the scheme interesting. It deserves a serious referee, but not in its current form. I'd recommend sending to review with a request for major revision: fix the sign error, provide full derivations (or at least the missing proofs), and either release code or show enough intermediate steps to allow independent verification.","headline":"Sign error in Lemma 1 undermines the exact derivation, but the core idea is sound and the conclusion may survive after a corrected proof.","tokens_in":21879,"tokens_out":13363,"would_cite":false,"duration_ms":136664,"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":"Power-adaptive hybrid NOMA beats OMA in rate and energy at high SNR","keywords":["hybrid NOMA","power adaptation","hybrid successive interference cancellation","energy efficiency","uplink NOMA","outage probability","asymptotic analysis","orthogonal multiple access"],"falsifier":"Simulate the uplink with a fixed channel-estimation error variance $\\sigma_e^2>0$ and sweep the SNR; if the measured $\\hat P_n$ stops decaying and flattens above zero instead of falling like $1/\\rho^n$, the exact-equality assumption is doing the work and the high-SNR dominance claim fails under imperfect CSI.","tokens_in":20826,"feed_emoji":"📶","tokens_out":8598,"duration_ms":83500,"temperature":0.7,"pith_summary":"Hybrid NOMA splits a user's transmission between a dedicated OMA slot and a shared NOMA slot, so the central question is whether the NOMA slot pays for itself. This paper proposes adding a power-adaptation coefficient, called HSIC-PA, to the hybrid scheme and analyzes the probability $\\hat P_n$ that the total rate over both slots falls short of what the user could get from pure OMA while using less energy. The paper proves that $\\hat P_n \\to 0$ as the signal-to-noise ratios of the legacy and opportunistic users grow with a fixed ratio, for every power-reduction coefficient $0<\\beta<1/2$ and every target rate $R_m$. That means the error floors seen in fixed-SIC and hybrid-SIC-without-power-adaptation H-NOMA disappear. If the result is right, the scheme gives a higher data rate than OMA with probability approaching one while consuming less energy in the high-SNR limit.","feed_headline":"Adaptive power lets hybrid NOMA beat OMA at high SNR","feed_subtitle":"Scaling one user to the interference threshold removes the error floor that limited earlier hybrid NOMA.","key_machinery":"The load-bearing mechanism is the power-adaptation coefficient $\\gamma$ used in Type II, Case 2 of the NOMA slot. When the opportunistic user's un-adapted received power exceeds the interference threshold $\\tau_m = \\max\\{0, \\rho_m |h_m|^2/(2^{R_m}-1)-1\\}$, the receiver chooses $\\gamma$ so that $\\gamma \\beta \\rho_n |h_n|^2 = \\tau_m$. This places the signal exactly at the maximum interference the legacy user can tolerate, allowing the opportunistic user to be decoded at the second SIC stage at rate $\\log(1+\\tau_m)$ rather than suffering the first-stage interference-limited rate $\\log\\bigl(1 + \\beta\\rho_n|h_n|^2/(\\rho_m|h_m|^2+1)\\bigr)$. The equality converts a bad channel draw into a deterministic rate that depends only on the legacy user's target rate, which is what removes the error floor of the earlier HSIC-NPA scheme.","core_discovery":"The central claim, stated as Theorems 1 and 2 of the paper, is that for the proposed HSIC-PA aided H-NOMA uplink, the probability $\\hat P_n$ that the achievable rate over the NOMA and OMA slots combined is no larger than the pure-OMA rate tends to $0$ as $\\rho_n,\\rho_m \\to \\infty$ with $\\rho_n/\\rho_m = \\eta$ fixed, for any $0<\\beta<1/2$, any target rate $R_m$, and any power ratio. Equivalently, at high SNR the scheme outperforms OMA in rate while using less energy with probability tending to one. The paper also derives exact closed-form expressions for $\\hat P_n$ in both pairing orders $m<n$ and $m>n$, and shows asymptotically that $\\hat P_n$ decays like $1/\\rho^n$, so the opportunistic user's channel-gain order $n$ dominates the decay. The restrictive conditions required by the earlier HSIC-NPA scheme disappear because the power-adaptation branch can force the opportunistic user's received power down to the legacy user's interference threshold.","pith_inferences":["Inference: A practical implementation would need to quantize $\\gamma$ and tolerate imperfect CSI; the analysis implies the loss appears as an error floor rather than just a slower decay, because the exact equality is what unlocks the clean second-stage rate.","Inference: The same scale-down-to-threshold trick should carry over to downlink H-NOMA or relay-aided NOMA wherever the receiver can compute $\\tau_m$ and feed it back; the proof structure needs only the exact equality to be reachable.","Inference: The scheme only reduces the opportunistic user's power; allowing $\\gamma>1$ when the legacy channel is weak could extend the gain to lower SNR, but that would require re-deriving the interference-threshold analysis."],"forward_implications":["At high SNR, any user paired under the scheme can be served at a higher rate than pure OMA with less energy, with probability tending to one, for every $0<\\beta<1/2$ and every target rate $R_m$.","The error floors that appear in fixed-SIC and HSIC-NPA H-NOMA under specific target-rate and power-ratio conditions are eliminated by the power-adaptation branch.","The failure probability $\\hat P_n$ decays exponentially at rate $n$, the channel-gain order of the opportunistic user, so system performance depends more on the opportunistic user than on its legacy partner.","Because the dominance holds for every power ratio $\\eta$ and every $R_m$, user pairing and power allocation become simpler at high SNR: no restrictive condition needs to be enforced."],"supporting_citations":[{"why":"Introduces the hybrid NOMA architecture that splits a user's transmission into OMA and NOMA slots; the paper's system model builds on this.","marker":"[11]"},{"why":"Supplies the HSIC-NPA H-NOMA baseline, the reused probability terms P1 and P2,2, and the error-floor conditions the proposed scheme removes.","marker":"[25]"},{"why":"Introduces hybrid SIC for uplink NOMA, the adaptive decoding-order idea that the proposed scheme inherits.","marker":"[26]"},{"why":"Provides the cognitive-radio-inspired robust uplink NOMA design that motivates coupling HSIC with power adaptation.","marker":"[27]"},{"why":"Establishes the single-slot HSIC-PA uplink NOMA result that the paper extends from one slot to the two-slot H-NOMA setting.","marker":"[28]"}],"fun_headline_variants":["Adaptive power removes hybrid NOMA error floor","Power-adaptive hybrid NOMA beats OMA asymptotically","No constraints needed: hybrid NOMA wins at high SNR","Energy-efficient hybrid NOMA with full probability gain"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result rests on perfect instantaneous channel knowledge at both transmitter and receiver and on the power adaptation coefficient $\\gamma$ being set so that $\\gamma \\beta \\rho_n |h_n|^2 = \\tau_m$ exactly; if channel estimation is imperfect or $\\gamma$ is quantized, the claimed rate $\\log(1+\\tau_m)$ and the asymptotic $\\hat P_n \\to 0$ are not established.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive power removes hybrid NOMA error floor","Power-adaptive hybrid NOMA beats OMA asymptotically","No constraints needed: hybrid NOMA wins at high SNR","Energy-efficient hybrid NOMA with full probability gain"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001034,"raw_usage":{"total_tokens":4403,"prompt_tokens":1045,"completion_tokens":3358,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":661,"completion_tokens_details":{"reasoning_tokens":3295}},"tokens_in":661,"tokens_out":3358,"duration_ms":27250,"temperature":1.0,"reasoning_tokens":3295,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:56:29.220172+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the uplink with a fixed channel-estimation error variance $\\sigma_e^2>0$ and sweep the SNR; if the measured $\\hat P_n$ stops decaying and flattens above zero instead of falling like $1/\\rho^n$, the exact-equality assumption is doing the work and the high-SNR dominance claim fails under imperfect CSI.","supporting_citations":[{"cited_title":"Impact of non-orthogona l multiple access on the offloading of mobile edge computing,","cited_arxiv_id":null,"evidence_quote":"Introduces the hybrid NOMA architecture that splits a user's transmission into OMA and NOMA slots; the paper's system model builds on this."},{"cited_title":"Hybrid sic- aided hybrid noma: A new approach for improving energy efficiency,","cited_arxiv_id":null,"evidence_quote":"Supplies the HSIC-NPA H-NOMA baseline, the reused probability terms P1 and P2,2, and the error-floor conditions the proposed scheme removes."},{"cited_title":"A new design of hybrid SIC for improving transmission robustness in uplink NOMA,","cited_arxiv_id":null,"evidence_quote":"Introduces hybrid SIC for uplink NOMA, the adaptive decoding-order idea that the proposed scheme inherits."},{"cited_title":"New designs of robus t uplink NOMA in cognitive radio inspired communications,","cited_arxiv_id":null,"evidence_quote":"Provides the cognitive-radio-inspired robust uplink NOMA design that motivates coupling HSIC with power adaptation."},{"cited_title":"Hybrid successive interference cancellation and power adapta- tion: a win-win strategy for robust uplink NOMA transmissio n,","cited_arxiv_id":null,"evidence_quote":"Establishes the single-slot HSIC-PA uplink NOMA result that the paper extends from one slot to the two-slot H-NOMA setting."}],"review_version":1}