{"id":"bcb6c171-2afe-43b7-9aaa-df0948df0ba4","arxiv_id":"2506.10662","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A semi-passive RIS with a few receive chains estimates two users' channels via ADMM-based matrix completion and then self-configures its reflection phases for MIMO capacity.","lead":"This chapter shows how a semi-passive reconfigurable intelligent surface (RIS) can receive pilot signals, estimate channels from two multi-antenna users, and then tune its reflection phases for a better MIMO link. The authors propose an ADMM-based estimator that uses random absorption sampling and channel sparsity, and they test it in simulations against least squares and other baselines.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Algorithm 2 does not implement the derived ADMM: the LASSO subproblem solution formula is incorrect and the H-update constants disagree with Eq. (28).","rationale":"The reader's verdict correctly identifies high correctness risk and missing recovery guarantees, but the most load-bearing defect is more specific and internal: the Z-subproblem is not solved by the stated soft-thresholding formula. This is not a missing proof but an algebraic error, since the soft-thresholded pseudoinverse is the exact minimizer only for orthonormal design matrices, and Φ̄ is not orthonormal. The H-update constants in Algorithm 2 also contradict Eq. (28). Hence the algorithm as presented is at best an undocumented approximation of ADMM, so the convergence discussion in Section 3.2 does not apply and the numerical NMSE and rate results cannot be interpreted as validating the derived method. The paper does have sensible motivation: beamspace sparsity and low-rank structure are natural for FR3-band extremely large MIMO, and the numerical study is reasonably extensive, though no code is provided. The central empirical claim might survive if the algorithm is corrected or reframed as a heuristic, but the current derivation is internally inconsistent, so the verdict should remain conditional pending a corrected derivation and re-run simulations.","tokens_in":22350,"tokens_out":11555,"duration_ms":125932,"concrete_test":"Run a small numerical check: set NRIS=8, N1=N2=2, NRF=1, T=16, P=Q=2, fixed random Ω, W, S̄, and DFT dictionaries; build Φ̄ and ξ̄ as in (31)–(34). Compute z_alg = S_{τ_Z}(Φ̄†ξ̄) and compare it with the exact LASSO solution of (33) obtained by a standard solver (e.g., FISTA or CVX) for the same τ_Z. If the relative error ||z_alg − z_lasso||/||z_lasso|| exceeds 1%, the closed-form update (35) is false. Separately, run Algorithm 2 with identical inputs and verify whether the iterates satisfy the analytical updates (28) and (35); a mismatch confirms the pseudocode does not implement the derived ADMM.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central claim is that the proposed ADMM estimator achieves superior NMSE and supports capacity-achieving RIS configuration. For that to hold, Algorithm 2 must solve the optimization in OP2 as derived. Section 3.2.2 claims that the LASSO subproblem (33), min_z τ_Z||z||_1 + 1/2||ξ̄ − Φ̄z||_2^2, is solved exactly by z = S_{τ_Z}(Φ̄†ξ̄) in (35). This is only exact when Φ̄ has orthonormal columns. Here Φ̄ = [Φ_1; √ρΦ_2], where Φ_1 contains the 0/1 mask diag(vec(Ω)) and (S̄^T D_UEs^*) ⊗ (W^H D_RIS), which is not unitary; Φ_2 is unitary but the stacked matrix is not. The soft-thresholded least-squares point is therefore not the minimizer of (33), so Step 4 of Algorithm 2 is an inexact heuristic, not an ADMM update, and the claimed convergence 'following SVT and LASSO' is unsupported. Additionally, Algorithm 2 Step 2 uses SVT_ρ with 4/ρ Γ, whereas the derived update (28) requires SVT_{τ_Y/ρ} with 2/ρ Γ; the pseudocode and derivation disagree. Since the channel estimates feed the RIS reflection design, this inconsistency directly undermines the central algorithmic contribution.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a semi-passive 'receiving RIS' architecture with RF chains that directly receive pilot signals from two multi-antenna UEs via tunable absorption profiles. It formulates the joint estimation of the two RIS-UE channels as a low-rank and beamspace-sparse optimization problem (OP2) and proposes an ADMM-based algorithm (Algorithm 2) that alternates between singular value thresholding and soft-thresholded LASSO steps. Using the channel estimates, the RIS controller then optimizes its reflection phase profile by a relaxed projected gradient ascent followed by quantization (Algorithm 1). The paper reports numerical NMSE and achievable-rate results showing that the proposed estimator outperforms least-squares benchmarks and that imperfect CSI at the RIS produces rates close to the perfect-CSI upper bound.","tokens_in":22661,"tokens_out":4504,"duration_ms":58232,"significance":"If the algorithmic claims are correct, the paper addresses a timely problem: equipping RISs with limited RF reception capability for on-board channel estimation and autonomous reflection optimization, with potential savings in pilot overhead and control signalling. The system model is explicit, the protocol is clearly described, and the numerical study covers several hardware configurations, including partially-connected reception. However, the value of the contribution rests on Algorithm 2 actually solving the derived ADMM problem and on the reported superiority not being an artifact of undisclosed tuning. At present, the derivations and the pseudocode disagree in load-bearing places, and the 'capacity-achieving' reflection design is a heuristic with no optimality guarantee. These issues need to be fixed before the central claims can be accepted.","major_comments":[{"comment":"The LASSO subproblem (33)-(34) is claimed to be solved exactly by z = S_{τ_Z}(Φ† ξ) in (35). This is exact only when Φ has orthonormal columns. Here Φ = [Φ1^T, sqrt(ρ)Φ2^T]^T, where Φ1 = diag(vec(Ω))((D_UEs^H S)^T ⊗ W^T P^H D_RIS) contains a 0/1 mask and Φ2 = D_UEs^* ⊗ D_RIS is unitary; the stacked matrix is in general not orthonormal. Therefore the update in Steps 3-4 of Algorithm 2 is not the exact minimizer of (33), and the statement in Section 3.2 that convergence follows from the convergence properties of SVT and LASSO is unsupported. Because the numerical results in Section 4 are obtained with Algorithm 2, this mismatch directly affects the central comparison claims.","section":"Section 3.2.2, Eq. (35)"},{"comment":"The derived H-update in Eq. (28) is SVT_{τ_Y/ρ}(D_RIS Z D_UEs^H - (2/ρ)Γ), but Algorithm 2 uses SVT_ρ(D_RIS Z D_UEs^H - (4/ρ)Γ). The threshold and the dual-variable scaling disagree with the derivation. Consequently, the implemented iteration is not the ADMM whose optimality and convergence properties are discussed in Section 3.2. The convergence curves in Figs. 3-4 therefore validate a different algorithm, and they cannot be cited as evidence for the proposed ADMM estimator.","section":"Section 3.2.1 and Algorithm 2, Step 2"},{"comment":"The paper calls the reflection design 'capacity-achieving', but Algorithm 1 is a projected gradient ascent on a continuous relaxation of OP1, followed by a quantization step in Eq. (9). No proof is given that this procedure reaches a global optimum of the nonconvex discrete problem OP1, nor is a bound on the quantization loss provided. The claim in the abstract and in Section 1.1 that the RIS controller designs the 'capacity-achieving reflection phase configuration' is therefore overstated; the scheme should be presented as a heuristic with empirical support.","section":"Section 2.1.2, OP1 and Algorithm 1"},{"comment":"The paper asserts that random spatial absorption sampling 'captures the entire signal space' and enables recovery of H1 and H2 with T training symbols, but it does not state any coherence, incoherence, or restricted-isometry conditions on the mask matrices Ω and W under which the low-rank/sparse recovery is guaranteed. In particular, the partially-connected architecture produces a structured sampling pattern rather than fully independent random measurements, so the matrix-completion premise is not automatic. A recovery guarantee, or at least a precise statement of the required conditions, is needed to support the claim that the estimator is doing more than fitting a heuristic optimization.","section":"Section 3.1, OP2"},{"comment":"The numerical evaluation never reports the values of the algorithm parameters τ_Y, τ_Z, and ρ used in Algorithm 2, nor the step size μ used in Algorithm 1, nor the initial phase vector for Algorithm 1. No sensitivity analysis with respect to these parameters is provided. Since the NMSE and rate comparisons in Section 4 depend on these choices, the reported superiority over the benchmarks is not reproducible without this information; the paper should disclose all tuning parameters and ideally show that performance is insensitive to reasonable variations.","section":"Section 4"}],"minor_comments":[{"comment":"The acronym NMSE is expanded as 'Mean Square Error' in the Introduction and as 'Normalized Mean Squared Error' in Section 4; the expansion should be consistent.","section":"Abstract and Section 4"},{"comment":"The page range of the SVT paper by Cai, Candès, and Shen is given as '1956-1952', which appears to be a typo; please correct the bibliographic details.","section":"Reference [52]"},{"comment":"The captions and the surrounding text refer to 'three different versions' of the fully-connected architecture, but the figures are not visible in the text and the text does not clearly state which curves correspond to NRF = 1, 4, and 360; the figures should include a legend and the caption should be explicit.","section":"Figures 3 and 4"},{"comment":"The sentence 'Let us introduce the weight parameters τ_Y and τ_Z that depend on the number of propagation paths' is confusing because these parameters were already introduced in OP2; the sentence should be removed or rephrased to describe a dependence that is used later.","section":"Section 3.2.1"}],"recommendation":"major_revision","confidential_remarks":"The most serious issue is the mismatch between the derived ADMM updates and the pseudocode in Algorithm 2; this is not a cosmetic problem because the numerical results validate the pseudocode, not the derivation. I would not reject the manuscript outright because the general framework is plausible and the mismatch could in principle be repaired by correcting the derivations or the pseudocode and rerunning the simulations. I recommend requiring the authors to reconcile the derivations with the implemented algorithm, disclose all tuning parameters, and moderate the 'capacity-achieving' wording before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nBottom line: the extension is real and the system-level story is coherent, but the paper's own algorithm doesn't match its derivation, and that is a load-bearing problem.\n\nWhat is new: the chapter takes the semi-passive receiving-RIS architecture from [29], adds a second multi-antenna UE, lets the two UEs send non-orthogonal pilots, and formulates joint low-rank/beamspace-sparse channel estimation as an ADMM problem for a partially-connected RF-chain front end. The protocol is clearly described, and the numerical evaluation is fairly broad: NMSE versus SNR, training length, number of RF chains, and a rate comparison with imperfect CSI. Moving both estimation and reflection optimization to the RIS controller is a sensible direction.\n\nThe soft spots are serious. The derived H-update in (28) is SVT with threshold τY/ρ and a 2/ρ Γ term; Algorithm 2 Step 2 uses SVT with threshold ρ and a 4/ρ Γ term. The Z-update is worse: (35) claims the LASSO subproblem is solved by soft-thresholding Φ̄†ξ̄, which is exact only when Φ̄ has orthonormal columns. Here Φ1 contains the binary mask diag(vec(Ω)) and a Kronecker product with W and D_RIS; it is not unitary. So the algorithm as written is not the ADMM that was derived, and the convergence claim 'following SVT and LASSO' is unsupported. Step 3 of Algorithm 2 also looks dimensionally inconsistent—it applies Φ† to a residual that mixes R and H rather than to the stacked ξ̄ from (31)-(32). This is not a cosmetic typo; it affects the core estimator and means the reported NMSE/rate results are not reproducible from the manuscript.\n\nThe 'capacity-achieving' reflection design is a relaxed gradient ascent with quantization; the text itself calls the quantized result suboptimal, so the abstract overstates the claim. No recovery guarantee is given for the random absorption sampling, and the weights τY, τZ and the step sizes are not selected by any stated rule, so the numerical superiority could depend on undisclosed tuning.\n\nThe citation pattern is fine; the self-citations are to the relevant prior work. Who is this for? Readers interested in a system-level treatment of receiving RISs and in CSI at the surface as a route to autonomous configuration. It deserves a serious referee, but only after a major revision that fixes the pseudocode/derivation mismatch, replaces the incorrect LASSO step with a provably convergent step (e.g., ISTA/FISTA) or proves the soft-thresholding claim under the actual Φ̄, and re-runs the simulations. I'd be cautious about citing it in its current form.","headline":"A plausible receiving-RIS extension with a coherent protocol, but Algorithm 2 disagrees with the ADMM derivation and the capacity-achieving label is too strong.","tokens_in":23147,"tokens_out":7058,"would_cite":false,"duration_ms":68152,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A semi-passive RIS can estimate the channels of two multi-antenna users and configure its own reflection phases to approach capacity, all with a few receive radio-frequency chains.","keywords":["reconfigurable intelligent surfaces","semi-passive RIS","channel estimation","ADMM","beamspace sparsity","low-rank matrix completion","random spatial absorption sampling","MIMO capacity optimization"],"falsifier":"Take a one-chain receiving RIS with a single propagation path and an absorption codebook whose profiles repeat with the same period as the beamspace grid; if the proposed estimator's NMSE stops improving as $T$ grows and stays far above the least-squares bound, the random-sampling premise fails.","tokens_in":22185,"feed_emoji":"📡","tokens_out":7093,"duration_ms":83946,"temperature":0.7,"pith_summary":"This paper is about making a reconfigurable intelligent surface (RIS) an active participant in its own operation. It claims that a 'receiving' RIS—one equipped with a small number of radio-frequency receive chains and a baseband processor—can estimate the MIMO channels between itself and two multi-antenna users, then use those estimates to set its own reflection phases so the end-to-end link approaches capacity. The method is a two-phase TDD protocol: users transmit non-orthogonal pilots, the RIS samples the incident field through random absorption profiles, and an ADMM algorithm recovers the channels by exploiting their beamspace sparsity and low-rank structure. The practical payoff is that the RIS no longer depends on an external node to learn channels or compute reflection coefficients, which matters for high-frequency systems where such overhead is expensive.","feed_headline":"Smart surfaces can learn their channels and set their own reflections","feed_subtitle":"A few radio-frequency chains let a metasurface estimate its channels and approach perfect-knowledge rates.","key_machinery":"Random spatial absorption sampling is the enabling measurement mechanism: at each of $T$ slots, the RIS selects $N_{\\mathrm{RF}}$ absorption profiles uniformly at random, so the observed data $\\mathbf{r}(t)=\\omega(t)\\circ(\\mathbf{W}^T\\mathbf{y}_{\\mathrm{RIS}}(t))+\\mathbf{n}(t)$ contains only a fraction $N_{\\mathrm{RF}}/N_{\\mathrm{RIS}}$ of entries of a linear transformation of the incident signal. The recovery model is the beamspace representation $\\bar{H}=D_{\\mathrm{RIS}}\\bar{Z}D_{\\mathrm{UEs}}^H$, where the $D$ matrices are DFT matrices; the optimization problem minimizes the nuclear norm of $\\bar{H}$ plus the $\\ell_1$ norm of $\\bar{Z}$ subject to a data-fit term. ADMM splits this into a singular value thresholding step for $\\bar{H}$ and a LASSO soft-thresholding step for $\\bar{Z}$, which is what lets the estimator work with very few RF chains and with $T$ much smaller than $N_{\\mathrm{RIS}}(N_1+N_2)$.","core_discovery":"The chapter's central claim is that a receiving RIS—a metasurface with a small number of receive radio-frequency chains and an attached baseband processor—can play the role of both channel sounder and beamformer for the MIMO link it serves. In the proposed TDD protocol, the two multi-antenna terminals synchronously send non-orthogonal pilot sequences; the RIS, configured in tunable absorption states, samples the incident signal through random spatial absorption profiles $\\boldsymbol{\\Omega}$ and $\\mathbf{W}$, producing a zero-padded received matrix $\\mathbf{R} = \\boldsymbol{\\Omega}\\circ(\\mathbf{W}^T \\mathbf{Y}_{\\mathrm{RIS}}) + \\mathbf{N}$. The baseband unit then solves a joint low-rank and sparse recovery problem in the beamspace, $\\bar{H}=D_{\\mathrm{RIS}}\\bar{Z}D_{\\mathrm{UEs}}^H$, using ADMM whose $\\bar{H}$ update is singular value thresholding and whose $\\bar{Z}$ update is a LASSO soft-thresholding step. With the recovered $\\hat{H}_1$ and $\\hat{H}_2$, the same controller runs a projected gradient ascent on the mutual-information objective to set the reflection phases, optionally quantized. The simulations show NMSE improving over least-squares and other benchmarks, and achievable rates close to the perfect-CSI upper bound at high SNR, even with one RF chain and two-bit phase quantization.","pith_inferences":["Inference: the same receive hardware and beamspace estimates could double as a localization or direction-finding front end, since the recovered $\\bar{Z}$ encodes the paths' angles of arrival; the paper cites direction estimation only as related work.","Inference: the training-length-to-RF-chain tradeoff seen in the simulations—partially connected with two chains tracks fully connected with one—suggests a designer can trade wiring complexity against chain count; a systematic exchange-rate analysis would be a natural follow-up.","Inference: extending the protocol to more than two users would likely require scheduling or contention among user pairs, and the ADMM structure would need to keep the concatenated beamspace matrix recoverable; the paper lists this as future work but does not analyze the overhead."],"forward_implications":["With the proposed protocol, the RIS controller becomes the node that performs channel estimation and reflection optimization, so no external feedback loop is needed to ship channel estimates or phase profiles back and forth.","Because the estimator uses beamspace sparsity and low rank, training can use $T$ much smaller than $N_{\\mathrm{RIS}}(N_1+N_2)$; in simulations $T=500$–$2000$ was enough for surfaces with $100$–$256$ elements.","At high SNR and with $T=2000$, the achievable rate with estimated channels nearly reaches the perfect-CSI upper bound even for a single receive RF chain.","Quantizing reflection phases to 2 bits costs negligible rate at high SNR, which makes low-resolution metasurface hardware viable."],"supporting_citations":[{"why":"Supplies the receiving-RIS hardware architecture with RX RF chains and a baseband processor that the whole system model builds on.","marker":"[29]"},{"why":"Provides the dynamic-metasurface-antenna architecture with groups of elements connected to RF chains, the basis for the partially-connected reception model.","marker":"[36]"},{"why":"Contributes the matrix-completion approach to massive MIMO channel estimation that the proposed ADMM method extends.","marker":"[34]"},{"why":"Contributes random spatial sampling for wideband hybrid-beamforming MIMO estimation, the direct precursor of the sampling and recovery formulation.","marker":"[35]"},{"why":"Defines the LASSO problem and soft-thresholding solution used in the $\\bar{Z}$ subproblem.","marker":"[37]"},{"why":"Supplies the singular value thresholding algorithm used to solve the $\\bar{H}$ subproblem.","marker":"[52]"},{"why":"Establishes the beamspace MIMO representation with DFT bases that gives the channels their sparse structure.","marker":"[51]"},{"why":"Provides the large-system capacity analysis and RIS-parametrized channel model that motivate the capacity-achieving reflection configuration objective.","marker":"[39]"}],"fun_headline_variants":["RIS with receiver chains estimates channels and tunes itself","Metasurface that listens sets its own reflection phases","Self-configuring RIS uses received pilots to optimize reflections","Receiving RIS: channel estimation and autonomous tuning in one"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that a few randomly chosen absorption profiles always see the whole signal space without blind spots, a property the paper asserts rather than proves.","fun_headline_variants_meta":{"raw":{"variants":["RIS with receiver chains estimates channels and tunes itself","Metasurface that listens sets its own reflection phases","Self-configuring RIS uses received pilots to optimize reflections","Receiving RIS: channel estimation and autonomous tuning in one"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000541,"raw_usage":{"total_tokens":2671,"prompt_tokens":1098,"completion_tokens":1573,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":714,"completion_tokens_details":{"reasoning_tokens":1510}},"tokens_in":714,"tokens_out":1573,"duration_ms":12631,"temperature":1.0,"reasoning_tokens":1510,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T04:20:44.214006+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a one-chain receiving RIS with a single propagation path and an absorption codebook whose profiles repeat with the same period as the beamspace grid; if the proposed estimator's NMSE stops improving as $T$ grows and stays far above the least-squares bound, the random-sampling premise fails.","supporting_citations":[{"cited_title":"In: Proc","cited_arxiv_id":null,"evidence_quote":"Supplies the receiving-RIS hardware architecture with RX RF chains and a baseband processor that the whole system model builds on."},{"cited_title":"IEEE Wireless Communications 28(2), 106–113 (2021)","cited_arxiv_id":null,"evidence_quote":"Provides the dynamic-metasurface-antenna architecture with groups of elements connected to RF chains, the basis for the partially-connected reception model."},{"cited_title":"IEEE Signal Process","cited_arxiv_id":null,"evidence_quote":"Contributes the matrix-completion approach to massive MIMO channel estimation that the proposed ADMM method extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Contributes random spatial sampling for wideband hybrid-beamforming MIMO estimation, the direct precursor of the sampling and recovery formulation."},{"cited_title":"Journal of the Royal Statistical Society","cited_arxiv_id":null,"evidence_quote":"Defines the LASSO problem and soft-thresholding solution used in the $\\bar{Z}$ subproblem."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the singular value thresholding algorithm used to solve the $\\bar{H}$ subproblem."},{"cited_title":"IEEE Transac- tions on Antennas and Propagation 61(7), 3814–3827 (2013)","cited_arxiv_id":null,"evidence_quote":"Establishes the beamspace MIMO representation with DFT bases that gives the channels their sparse structure."},{"cited_title":"IEEE Transactions on Wire- less Communications 22(12), 8736–8750 (2023)","cited_arxiv_id":null,"evidence_quote":"Provides the large-system capacity analysis and RIS-parametrized channel model that motivate the capacity-achieving reflection configuration objective."}],"review_version":1}