{"id":"097b0198-92bb-4011-9178-36dd84242eac","arxiv_id":"2412.05623","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"An alternating optimization algorithm combining consensus ADMM, accelerated projected gradient, and conjugate gradient maximizes weighted sum-rate in wideband IRS-assisted cell-free networks under a Lorentzian reflection model.","lead":"This paper builds a joint beamforming algorithm for cell-free wireless networks whose intelligent reflecting surfaces respond differently at different frequencies. The method, called CADMM-APG-FRCG, reports higher weighted sum-rate than a published baseline while claiming lower computational cost.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lorentzian realizability is never enforced: P(7) penalizes φ=b only softly and projects only φ, so reported WSR values may use reflection coefficients outside the passive feasible set (9c)-(9d).","rationale":"The reader's weakest assumption is exactly the Lorentzian feasibility issue, and I agree that it is the most load-bearing concern. The central claim is that CADMM-APG-FRCG outperforms PDS with lower complexity; that claim is only meaningful if both solutions are feasible for the stated problem. The paper's own initialization violates the passive constraint, and the algorithm's penalty formulation never guarantees that the final φ lies in the Lorentzian feasible set. The reported performance advantage could therefore be an artifact of optimizing over a larger, physically unrealizable set of reflection coefficients. This is an internal inconsistency, not a matter of differing modeling conventions, so it directly undermines the correctness of the simulation-based claim. Secondary issues—the unfair baseline where PDS uses an ideal frequency-flat reflection model while the proposed method has per-tone Lorentzian degrees of freedom, and the unsupported assertion of global optimality for a nonconvex problem—reinforce the rejection but are not needed for it. The concrete test above would settle the feasibility concern: if the final solution passes both the residual and magnitude checks, the concern is resolved; if it fails, the headline claim is not supported as presented. The verdict should remain REJECT, so I recommend UNCHANGED.","tokens_in":22483,"tokens_out":9143,"duration_ms":88695,"concrete_test":"Independently re-implement Algorithm 3 with the Section IV-A settings. After convergence, record (φ,ϕ,ψ,κ), compute b_{i,r,m} from (4), and check (i) ||φ−b||²/||φ||² ≤ ε and (ii) max_{i,r,m}|b_{i,r,m}| ≤ 1. If either fails, the solution violates (9c)-(9d). To rule out a parameterization artifact, additionally solve the constrained least-squares problem min_{ϕ,ψ,κ} ||φ−b(ϕ,ψ,κ)||² subject to max_{i,r,m}|b_{i,r,m}| ≤ 1 for the optimized φ; if the minimal residual is not near zero, the optimized φ is not physically realizable and the WSR values in Figs. 2-6 are not achievable under the paper's own model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The simulation initializes ψ=3×10^9, κ=6×10^7, ϕ=1 (Section IV-A). At resonance f_m=ψ, equation (4) gives |φ|=ϕψ/κ=50, already violating (9d) before any iteration. After that, nothing in P(7)-(8) forces feasibility: the objective is f6(φ)+(1/2µ)||φ−b(ϕ,ψ,κ)||² with the unit-modulus constraint (48b) applied only to φ, while the b-update (53) is an unconstrained FRCG minimization of ||φ−b||². The APG step (49)-(52) projects ς onto the unit disc, but it does not project b or enforce b∈Ω. Thus a converged point can have |φ|≤1 yet remain arbitrarily far from any Lorentzian b, or have a b whose own magnitude exceeds 1. Since the WSR in Figs. 2-6 is computed with the optimized φ, the reported gains may correspond to physically unrealizable IRS reflection coefficients. The claim that CADMM-APG-FRCG 'optimally solves W and Φ in P(0)' therefore lacks a feasibility certificate, and the comparison with PDS is not a comparison between two feasible designs. This is an internal inconsistency with the paper's own constraint (9c)-(9d), not merely a disagreement with community conventions.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies joint active and passive precoding for weighted sum-rate (WSR) maximization in a wideband IRS-assisted cell-free MIMO-OFDM network, where each IRS element is modeled by a Lorentzian frequency response. The proposed CADMM-APG-FRCG algorithm uses Lagrangian dual transform and multidimensional complex quadratic transform to decouple the problem, CADMM with linearized updates for the active beamforming subproblem, and APG with FRCG for the passive Lorentzian parameter subproblem. Simulations compare the proposed algorithm with a primal-dual subgradient (PDS) baseline and report consistent WSR gains plus about 31% of the baseline computational complexity. The paper claims that the algorithm optimally solves the active and passive variables in P(0).","tokens_in":22722,"tokens_out":9815,"duration_ms":95806,"significance":"If the claims were valid, the paper would make a useful contribution: it addresses a realistic frequency-selective IRS model, provides a low-complexity algorithmic pipeline, and gives a concrete complexity comparison. The paper is clearly organized and includes pseudocode for all three algorithms, a full complexity table, and extensive numerical experiments, which are commendable. However, the central numerical claims are not established: the optimized Lorentzian reflection coefficients are not certified to satisfy the passive constraint, and the PDS baseline is not solving the same wideband problem. These issues affect the main conclusion that the proposed algorithm outperforms existing methods, so the contribution cannot be accepted in its current form.","major_comments":[{"comment":"The passive beamforming update does not enforce the physical feasibility constraint (9d) on the Lorentzian reflection coefficient. With the simulation initialization ϕ=1, ψ=3×10^9, κ=6×10^7 (Section IV-A), Eq. (4) gives |b|=ψ/κ=50 at the resonance frequency f_m=ψ, already violating (9d). P(7) replaces the equality constraint (48a) by a soft penalty, and the APG projection (52) is applied only to the auxiliary variable φ; the FRCG update (53) minimizes ||φ−b||² without any constraint on b. A converged point can therefore have |φ_{i,r,m}|≤1 while b(ϕ,ψ,κ) violates (9d), or can leave a nonzero penalty, in which case no feasible point of P(6) is recovered. Since the WSR values in Figs. 2–6 are computed from φ, the reported gains may correspond to reflection coefficients that a passive IRS cannot realize. The statement in Section IV-B that the algorithm \"optimally solves W and Φ in P(0)\" is therefore unsupported; a feasibility certificate for b (or an explicit projection onto the set {b: |b_{i,r,m}|≤1}) is required.","section":"§IV-A and P(7), Eqs. (48)–(53)"},{"comment":"The comparison with the PDS baseline is not apples-to-apples. The abstract and Section II state that PDS uses an ideal reflection matrix, and Remark 2 explicitly says that PDS cannot address passive precoding in wideband systems. Thus the PDS baseline is restricted to a narrowband/frequency-flat unit-modulus model, while the proposed method optimizes per-tone Lorentzian coefficients. Under these unequal feasible sets, the consistent WSR advantage claimed in Section IV-B may reflect the larger number of optimization variables or the relaxed soft-constraint formulation rather than the CADMM-APG-FRCG updates. A valid baseline should solve the same P(0) with constraints (9c)–(9d), for example an SCA or alternating optimization method over the Lorentzian parameters (ϕ,ψ,κ) with a feasibility guarantee. Without such a baseline, the paper's central claim of algorithmic superiority over PDS is not established.","section":"§IV-B, Figs. 2–6, Remark 2"},{"comment":"The optimality and convergence claims are not supported by the presented material. The passive subproblem P(7) is nonconvex, and APG with the extrapolation (50)–(51) and a constant step size ω=1/8 (Section IV-A) has no convergence proof for this problem; FRCG applied to the unconstrained, nonconvex P(8) also lacks a guarantee. Moreover, the W-subproblem P(3) is described as \"generally known to be NP-hard\" (Section III-C), yet the text later says CADMM \"optimally solves\" the QCQP; since the objective and constraints in P(3) are convex quadratic, the NP-hard statement is misleading, and in any case no convergence or optimality theorem for Algorithm 1 or 3 is stated. The authors should either provide formal convergence and stationarity results, or replace claims of solving P(0) optimally with statements about the heuristic performance of the proposed iterations.","section":"§III-D, Eqs. (49)–(53), §IV-B"}],"minor_comments":[{"comment":"The definition Φ = diag(Φ_1, · · ·, Φ_2, · · ·, Φ_M) contains an obvious typo; it should read diag(Φ_1, · · ·, Φ_M).","section":"§II-B, Eq. (10)"},{"comment":"The line \"Update η by (15)\" should refer to Eq. (14), where the closed-form optimal η is given.","section":"§III-B, Algorithm 3"},{"comment":"The name \"Flecher-Reeves\" should be spelled \"Fletcher-Reeves.\"","section":"Throughout"},{"comment":"The quality factor Qn is used without a definition in the parameter list; its relation to ψ and κ should be stated explicitly.","section":"§IV-A"},{"comment":"The displayed expression is not an equality (\"then WH DW = ...\"); it is a first-order approximation plus a proximal term and should be written with ≈.","section":"§III-C, Eq. (25)"},{"comment":"The table heading uses \"CADMM-APG\" while the algorithm is called \"CADMM-APG-FRCG\"; the notation should be made consistent.","section":"Table II"},{"comment":"Reference [38] is described in the Introduction as a narrowband work, but its title refers to a wideband framework; please clarify whether PDS is restricted to frequency-flat reflection or to narrowband signaling.","section":"§I and References"}],"recommendation":"reject","confidential_remarks":"The Lorentzian feasibility issue is not a cosmetic simulation error: P(7) optimizes an auxiliary φ while leaving the physical b unconstrained, so the reported WSR can be generated by reflection coefficients outside the passive set. Combined with the unequal PDS baseline, the central numerical claims are not trustworthy. I do not see a local fix short of reformulating the passive subproblem, adding feasibility constraints on the Lorentzian parameters, and redoing all comparisons, which is effectively a new validation of the method."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Punchline: the algorithmic core is plausible, but the main comparison is not apples-to-apples and the Lorentzian feasibility is never actually enforced. The reported gains over PDS are not established.\n\nWhat is actually new: combining CADMM with a linearized active precoding update and APG-FRCG for the Lorentzian passive parameters is new in this setting. Decomposing the QCQP into QCQP-1 subproblems with closed-form updates is a genuine complexity reduction, and the complexity table is transparent. The paper is readable and the simulation configuration is standard for the cell-free IRS literature.\n\nSoft spots: first, the baseline is unfair. PDS from [38] uses an ideal frequency-flat reflection matrix; this paper optimizes per-tone Lorentzian coefficients with |φ|≤1. That gives the proposed method extra degrees of freedom, so the observed WSR gap (e.g., 62.8% in Fig. 3) likely reflects model difference rather than algorithmic superiority. Second, feasibility is load-bearing and broken. Constraint (9d) requires |φ|≤1, but P(7) only penalizes the distance between φ and b(ϕ,ψ,κ) softly, and only φ is projected onto the unit disc. Nothing forces the converged b to be realizable with |b|≤1 across all subcarriers. The initialization ψ=3e9, κ=6e7 gives |b|=50 at resonance, so the physical realizability of the final design is never certified. Third, the claim that CADMM-APG-FRCG 'optimally solves W and Φ in P(0)' is unsupported: P(0) is nonconvex and no convergence proof is given. The QCQP-1 subproblems do have closed-form solutions, but that does not imply global optimality of the alternating algorithm. Minor issues: no error bars, no code, and the penalty parameters (α, β, µ, ̟) are chosen without sensitivity analysis.\n\nOverall: the algorithmic machinery is salvageable with a fair baseline, a corrected feasibility treatment, and tempered claims. As presented, the central result is not well supported. I would send it to review because the topic is timely and the flaws are the kind a referee can pin down, but I would expect major revision, and if the baseline and feasibility are not fixed, rejection. Reading group: maybe, as a case study in baseline selection and feasibility enforcement in IRS optimization.","headline":"Plausible algorithm, but the PDS comparison is not apples-to-apples and Lorentzian feasibility is never enforced; the reported gains are not established.","tokens_in":23318,"tokens_out":3844,"would_cite":false,"duration_ms":33478,"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 weighted sum-rate in wideband IRS-assisted cell-free networks can be maximized by a CADMM-APG-FRCG algorithm that outperforms the PDS baseline with about one-third the computational complexity.","keywords":["intelligent reflecting surface","cell-free network","wideband transmission","weighted sum-rate maximization","joint precoding","consensus ADMM","accelerated projected gradient","Lorentzian reflection model"],"falsifier":"Take the optimized $(\\phi,\\psi,\\kappa)$ returned by Algorithm 3 and evaluate $|\\varphi_{i,r,m}|$ via (4) across all subcarriers and elements; if any value exceeds 1, constraint (9d) is violated and the reported WSR is not achievable by a passive IRS. The paper's own initialization ($\\phi=1$, $\\psi=3\\times10^9$, $\\kappa=6\\times10^7$) gives $|\\varphi|=\\phi\\psi/\\kappa=50$ at resonance, so checking whether the final parameters keep $|\\varphi|\\le 1$ over the whole band is decisive.","tokens_in":22211,"feed_emoji":"📶","tokens_out":9892,"duration_ms":86989,"temperature":0.7,"pith_summary":"The paper aims to show that maximizing weighted sum-rate in wideband IRS-assisted cell-free networks, where each IRS element has a Lorentzian frequency-selective reflection, can be handled by an alternating algorithm that avoids the heavy iterative dual updates of existing methods. The authors decouple the non-convex problem with fractional programming, solve active base-station beamforming via consensus ADMM with closed-form per-base-station updates, and solve passive IRS reflection via accelerated projected gradient plus a conjugate-gradient fit of the Lorentzian parameters. Their simulations report that the resulting CADMM-APG-FRCG algorithm consistently outperforms the primal-dual subgradient (PDS) baseline, reaching about 62.8% higher weighted sum-rate at convergence while using roughly 31% of PDS's computational complexity. If it holds, this gives practical cell-free networks a way to get higher capacity from IRSs without paying PDS's computational cost.","feed_headline":"New precoding method lifts IRS cell-free sum-rate by 63%","feed_subtitle":"Joint active-passive beamforming via CADMM-APG-FRCG outperforms the PDS baseline at about one-third the complexity.","key_machinery":"The key machinery is a decoupling-and-closed-form-update chain. The Lagrangian dual transform introduces auxiliary variables η to pull the logarithm out of the SINR ratio, and the multidimensional complex quadratic transform introduces δ and ρ to convert the fractional objective into a quadratic form, separating W from Φ. The active subproblem is then a QCQP solved by consensus ADMM: a linearized update for W, per-base-station projections of the form $V = \\sqrt{P_{\\max}} e^{j\\angle(\\cdot)}$, and dual-variable updates, all in closed form. The passive subproblem is solved by APG with a projection of $\\varphi$ onto the unit disk, followed by FRCG, a conjugate-gradient method that fits the Lorentzian parameters $(\\phi,\\psi,\\kappa)$ to the current reflection vector.","core_discovery":"The paper's central claim is that the non-convex weighted sum-rate problem P(0), which jointly optimizes active beamforming W and passive reflection Φ under a Lorentzian frequency-selective response, can be solved by the CADMM-APG-FRCG algorithm, which the authors describe as optimally solving W and Φ in P(0). The decoupling is done by the Lagrangian dual transform and the multidimensional complex quadratic transform; the active subproblem becomes a QCQP that is decomposed into single-constraint QCQP-1 subproblems with closed-form solutions, and the passive subproblem is handled by projected gradient updates for the reflection coefficients and a conjugate-gradient fit for the Lorentzian parameters. The reported result is a weighted sum-rate about 62.8% higher than PDS at convergence, with about 31.44% of PDS's computational complexity.","pith_inferences":["A decisive physical check the paper leaves implicit: the Lorentzian fitting in P(7) does not constrain $b(\\phi,\\psi,\\kappa)$ to lie within the unit disk, so one should verify that the final parameters yield $|\\varphi|\\le 1$ over all subcarriers before accepting the WSR numbers; the initialization already violates the bound at resonance.","The 62.8%-over-PDS comparison may be partly explained by PDS converging to a suboptimal point rather than the new method reaching a global optimum; a stronger test would be to compare against a global-optimality bound or exhaustive search on a small instance.","The complexity ratio 31.44% is computed from one simulation setting's iteration counts; a useful extension would be to map the crossover problem sizes where the new method's advantage erodes.","As bandwidth shrinks toward narrowband, the Lorentzian model should reduce to a phase-shifter model; testing the algorithm in that limit would connect the wideband results to the existing narrowband literature."],"forward_implications":["If the central claim holds, the proposed CADMM-APG-FRCG algorithm gives a lower-complexity alternative to PDS for wideband IRS cell-free networks, with the reported complexity ratio of 31.44% making it attractive for dense deployments.","The closed-form per-base-station updates in the active subproblem can be computed in parallel, so the algorithm scales more gracefully with the number of base stations than PDS.","Because the passive subproblem explicitly fits a Lorentzian frequency response, the performance gains carry over to wideband OFDM systems where an ideal phase-shifter model would be inaccurate.","Under imperfect CSI, the algorithm's WSR degradation (about 14% at $\\omega=0.2$) is comparable to PDS while maintaining a roughly 66.6% higher WSR, so the advantage persists in non-ideal channel estimation.","Energy efficiency peaks at finite BS and IRS counts (the paper reports a maximum at $N_b=7$, $N_c=10$), meaning the method can inform deployment sizing rather than assuming more IRS elements always helps."],"supporting_citations":[{"why":"It supplies the PDS baseline algorithm and the cell-free network setup against which the proposed method is compared.","marker":"[38]"},{"why":"It provides the Lagrangian dual transform used to decouple the logarithm from the SINR ratio.","marker":"[64]"},{"why":"It provides the multidimensional complex quadratic transform used to reformulate the fractional objective.","marker":"[65]"},{"why":"It supplies the consensus-ADMM framework used to solve the active QCQP subproblem.","marker":"[66]"},{"why":"It supplies the Lorentzian polarizability model for the frequency-selective IRS reflection coefficients.","marker":"[53]"},{"why":"It provides the practical frequency-dependent IRS reflection model for wideband MIMO-OFDM that motivates the Lorentzian treatment.","marker":"[51]"},{"why":"It supplies the accelerated proximal gradient method underlying the APG update of the reflection coefficients.","marker":"[67]"},{"why":"It supplies the alternating direction method of multipliers foundation from which the consensus variant is derived.","marker":"[69]"}],"fun_headline_variants":["IRS cell-free sum-rate up 63% with joint precoding","Joint precoding lifts IRS cell-free sum-rate 63%","63% sum-rate gain in IRS cell-free via joint precoding","New joint precoding gives IRS cell-free 63% sum-rate boost","Joint beamforming: 63% sum-rate gain in IRS cell-free networks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the Lorentzian reflection formula (4) can be realized by passive IRS elements while keeping $|\\varphi|\\le 1$ on every subcarrier; the optimization only penalizes how far the chosen reflection vector is from that formula, so if no parameter set satisfies the bound across the band, the optimized solution is physically unrealizable.","fun_headline_variants_meta":{"raw":{"variants":["IRS cell-free sum-rate up 63% with joint precoding","Joint precoding lifts IRS cell-free sum-rate 63%","63% sum-rate gain in IRS cell-free via joint precoding","New joint precoding gives IRS cell-free 63% sum-rate boost","Joint beamforming: 63% sum-rate gain in IRS cell-free networks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000458,"raw_usage":{"total_tokens":2284,"prompt_tokens":920,"completion_tokens":1364,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":536,"completion_tokens_details":{"reasoning_tokens":1271}},"tokens_in":536,"tokens_out":1364,"duration_ms":9601,"temperature":1.0,"reasoning_tokens":1271,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:32:26.400707+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the optimized $(\\phi,\\psi,\\kappa)$ returned by Algorithm 3 and evaluate $|\\varphi_{i,r,m}|$ via (4) across all subcarriers and elements; if any value exceeds 1, constraint (9d) is violated and the reported WSR is not achievable by a passive IRS. The paper's own initialization ($\\phi=1$, $\\psi=3\\times10^9$, $\\kappa=6\\times10^7$) gives $|\\varphi|=\\phi\\psi/\\kappa=50$ at resonance, so checking whether the final parameters keep $|\\varphi|\\le 1$ over the whole band is decisive.","supporting_citations":[{"cited_title":"A joint precoding framework for wid eband reconfigurable intelligent surface-aided cell-free netwo rk,","cited_arxiv_id":null,"evidence_quote":"It supplies the PDS baseline algorithm and the cell-free network setup against which the proposed method is compared."},{"cited_title":"Fractional programming for communic ation systems Part I: Power control and beamforming,","cited_arxiv_id":null,"evidence_quote":"It provides the Lagrangian dual transform used to decouple the logarithm from the SINR ratio."},{"cited_title":"Fractional programming for communic ation systems¡ªPart II: Uplink scheduling via matching,","cited_arxiv_id":null,"evidence_quote":"It provides the multidimensional complex quadratic transform used to reformulate the fractional objective."},{"cited_title":"Consensus-ADMM for Ge neral Quadratically Constrained Quadratic Programming,","cited_arxiv_id":null,"evidence_quote":"It supplies the consensus-ADMM framework used to solve the active QCQP subproblem."},{"cited_title":"Polarizability extraction of complementary metamaterial elements in waveguides for aperture modeling ,","cited_arxiv_id":null,"evidence_quote":"It supplies the Lorentzian polarizability model for the frequency-selective IRS reflection coefficients."},{"cited_title":"Intelligent reflecting surface enhanced w ideband MIMO- OFDM communications: From practical model to reflection opt imiza- tion,","cited_arxiv_id":null,"evidence_quote":"It provides the practical frequency-dependent IRS reflection model for wideband MIMO-OFDM that motivates the Lorentzian treatment."},{"cited_title":"Accelerated proximal gradient method s for nonconvex programming,","cited_arxiv_id":null,"evidence_quote":"It supplies the accelerated proximal gradient method underlying the APG update of the reflection coefficients."},{"cited_title":"Distributed optimization and statistical learning via the alternative direction method of multipliers,","cited_arxiv_id":null,"evidence_quote":"It supplies the alternating direction method of multipliers foundation from which the consensus variant is derived."}],"review_version":1}