{"id":"11cb3592-fd1b-4e59-b0c5-7093f17ea940","arxiv_id":"2411.17725","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A Tucker2-BALS estimator plus a CNN-AR predictor achieves low-overhead, high-accuracy CSI acquisition and forecasting for fully- and group-connected BD-RIS MIMO systems.","lead":"This paper presents a joint channel estimation and prediction method for beyond-diagonal RIS-assisted MIMO systems, combining Tucker2 tensor decomposition with a CNN and autoregressive predictor. Simulations show the method can cut pilot overhead by up to 98% while maintaining high accuracy and downlink sum rate.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"CNN-AR prediction is validated only for Jakes ACF at Doppler values seen in training, so the prediction-phase pilot removal behind the 98% overhead claim is not established for unseen velocities or non-Rayleigh channels.","rationale":"The abstract's headline numbers depend on removing pilots during the prediction phase, and the only mechanism that makes this safe is the CNN-AR predictor. The paper's Section IV-B gives no train/test split by Doppler, no non-Jakes scenario, and no ablation showing the CNN is better than a direct AR predictor at unseen velocities; Section IV-B says the CNN can add more fn values in training, which suggests the training set already uses the same fn grid. In addition, Eq. (2) models E[l] with a static q_{e,k} times a single complex exponential, whose ACF is not J0(2π fn l) used in Eq. (25); this is either a notational error or a mismatch between the system model and the synthetic data used for CNN training. Since no code or data is provided, a reader cannot determine which model produced Figs. 9-10. These are not criticisms of the underlying tensor decomposition; the Tucker2-BALS estimator may well be sound and the 94-98% overhead arithmetic may be correct. But the central end-to-end claim of robustness to channel aging and low overhead is only as strong as the prediction-phase evidence. A held-out Doppler and model-consistency test would settle whether the concern lands, so the conditional verdict remains appropriate without additional experiments.","tokens_in":19698,"tokens_out":9892,"duration_ms":102271,"concrete_test":"Generate hold-out test sets with Doppler frequencies not used in CNN training (e.g., train on fn ∈ {0.001, 0.003, ..., 0.019}, test on fn ∈ {0.002, 0.006, 0.010, 0.014, 0.018}) under both the Jakes ACF used in Section IV-A and the ACF implied by Eq. (2); then recompute prediction NMSE at the P-th coherence interval and the average downlink sum rate. If NMSE at unseen fn or under the Eq. (2) ACF is more than an order of magnitude worse than the current Fig. 10 curves, the CNN-AR predictor is not robust to channel aging and the 98% overhead figure does not transfer. Also state in the text whether the Fig. 10 velocities were included in the training set.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The 98% pilot-overhead reduction is obtained by removing pilots for the P prediction intervals (Section V-C and Table III). This is valid only if the CNN-AR predictor in Section IV-B keeps prediction NMSE low over those intervals. The supporting evidence is Fig. 9 and Fig. 10, but the CNN is trained on 10 fn values and Fig. 10 reports five fn values without stating that the test fn values are held out from training; there is no evaluation at intermediate Dopplers or under non-Jakes/non-Rayleigh fading. Additionally, the system model in Eq. (2) writes E[l] as a static Rician vector times e^{j2π fd Ts l}, whose ACF is a pure tone, not the J0(2π fn l) ACF used to train the AR model in Eq. (25). As written, either the simulated channel is the trivial rank-1 rotation (making the CNN unnecessary) or the simulation uses Jakes fading and Eq. (2) is incorrect. The paper includes no code or data release, so the reader cannot tell which model generated Figs. 9-10. Since the prediction phase is the mechanism for the headline pilot-overhead reduction, this missing generalization and model-consistency evidence is load-bearing.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a joint channel estimation and channel prediction framework for beyond-diagonal RIS (BD-RIS) assisted MIMO systems under channel aging. Estimation is based on a Tucker2 tensor decomposition solved by bilinear alternating least squares (Tucker2-BALS), applied separately to fully-connected and group-connected architectures. Prediction uses a CNN combined with an AR model (CNN-AR) to extrapolate estimated channels during a pilot-free phase. The estimated/predicted CSI is then used to optimize the BD-RIS reflection matrix for downlink sum-rate maximization. The paper claims high estimation/prediction accuracy, a robust sum-rate performance close to perfect CSI, and a pilot overhead reduction of up to 98% relative to a DFT-LS baseline.","tokens_in":20048,"tokens_out":6894,"duration_ms":73034,"significance":"If the claims are fully supported, the contribution is valuable: it extends tensor-based channel estimation to non-diagonal RIS architectures, separates the RIS-BS and RIS-UE channels with reduced training overhead, and combines this with an ML-based predictor to mitigate channel aging. The Tucker2 formulation and the identifiability condition M <= min(NT,KT) are plausible and provide a useful starting point for BD-RIS channel estimation. The main weaknesses are that the prediction component is only validated in distribution, the channel model in Eq. (2) is inconsistent with the Jakes ACF used to train the predictor, and the scaling-ambiguity removal step appears infeasible for the BD-RIS architectures studied. These issues directly affect the credibility of the headline pilot-overhead and sum-rate claims.","major_comments":[{"comment":"The UE-RIS channel in Eq. (2) is written as a static Rician vector multiplied by a complex exponential e^{j2*pi*fd*Ts*l}. The ACF of this process is a pure tone, not the Jakes ACF R[l] = J0(2*pi*fn*|l|) used in Section IV-A to derive the AR coefficients for the CNN-AR predictor. The manuscript never states which channel model generated Figs. 9 and 10. If the simulator followed Eq. (2), the prediction problem is a trivial known rotation and the CNN-AR machinery is unnecessary; if the simulator used Jakes/Rayleigh fading, then Eq. (2) is incorrect. This ambiguity is load-bearing because the 98% pilot-overhead reduction in Section V-C depends on the prediction phase being accurate on the actual simulated channel.","section":"II, Eq. (2); IV-A, Eq. (25)"},{"comment":"The proposed scaling-ambiguity removal requires estimating [H]_{1,1} by 'switching on only the first element in RIS and the first antenna in BS.' For a fully-connected BD-RIS, a reflection matrix with only one nonzero entry violates the unitary constraint Theta*Theta^H = I_M stated in Section II-A; the same issue arises within each group for the group-connected architecture in Section II-B. The manuscript therefore does not provide a feasible calibration procedure for fixing the scalar ambiguity, and the sum-rate and NMSE evaluations implicitly assume that the ambiguity is resolved. This needs to be addressed with a feasible measurement or the performance claims must be revised.","section":"III-B2a, uniqueness and scaling ambiguity"},{"comment":"The CNN-AR predictor is under-specified and only evaluated in distribution. The architecture description is limited to activation functions, optimizer, and loss; no layer counts, kernel sizes, filter numbers, or input/output dimensions are given, and Eq. (33) does not fully specify the input tensor layout. Figure 10 shows five normalized Doppler values, but the paper never states that these test Doppler values are held out from the ten values used in training. There is no evaluation at intermediate Doppler values or under non-Jakes/non-Rayleigh fading. Since the prediction-phase pilot removal is the mechanism behind the headline pilot-overhead reduction, this missing generalization and reproducibility evidence is load-bearing.","section":"IV-B and Figs. 9-10"},{"comment":"The pilot-overhead reduction percentages in Table III are not reproducible without specifying the values of Q and P used in the calculation. The expression for the proposed average pilot overhead, (T+1)Q/(Q+P) for fully-connected and (T+G)Q/(Q+P) for group-connected, depends on the ratio Q/(Q+P), but no Q or P values are given in Table III or in the surrounding text. Additionally, the '+1' and '+G' terms are not derived; if they represent calibration pilots for the scaling-ambiguity removal introduced in Section III-B2a, that connection should be made explicit.","section":"V-C and Table III"}],"minor_comments":[{"comment":"In the optimization problem P1, the symbol T in the term (e_k Theta^H T)^H u_k is undefined; it should presumably be the RIS-BS channel matrix H or its transpose, depending on the reciprocity convention. Please clarify the notation.","section":"V-A, Eq. (36)"},{"comment":"The system model introduces a correlated Rician channel for E[l], while Section IV-A adopts a Rayleigh fading assumption for the ACF model. The relationship between the Rician components and the Jakes ACF should be stated explicitly.","section":"II, Eq. (2) and IV-A"},{"comment":"The sentence 'Even though we use 10 different fn values to train the CNN model, Our proposed CNN model is capable of adding more fn values in training' is unclear and contains a capitalization error; it should be rewritten to describe how the training set is constructed and how additional Doppler values would be incorporated.","section":"IV-B"},{"comment":"The paper does not report whether the simulation code or data will be released, which makes it difficult to verify the CNN training details and the exact pilot-overhead computation. A reproducibility statement would strengthen the manuscript.","section":"VI-C and Table III"},{"comment":"There are several typographical and grammatical issues, e.g., 'archives' for 'achieves' near Table I, 'the lower bound of MSE' usage, and inconsistent spacing in equations. A careful proofreading pass is recommended.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The central tensor-based estimation idea is a reasonable contribution, but the internal inconsistency between the channel model in Eq. (2) and the Jakes ACF used for prediction, together with the infeasible scaling-ambiguity calibration for BD-RIS, undermines the validity of the numerical results as currently presented. The paper would need a corrected channel model, a feasible calibration procedure, and a held-out evaluation of the CNN predictor before the claims can be trusted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the tensor decomposition half of this paper is the contribution worth refereeing. The CNN-AR prediction half is where the paper goes soft. Start there.\n\nWhat's new: They're the first to apply Tucker2-BALS to channel estimation for fully- and group-connected BD-RIS. The identifiability condition M ≤ min(NT, KT) (and the group analog) is new and plausible. The simulations show order-of-magnitude NMSE gains over DFT-LS, and the pilot-overhead math is transparent: you buy a 94–98% reduction by removing pilots in the prediction phase. The complexity analysis is also useful.\n\nWhere it goes soft: The system model in Eq. (2) has E[l] as a static vector times a pure phase rotation e^{j2πfdTs l}. That is not a fading channel with a Jakes ACF. The ACF of a pure tone is a complex exponential, not J0(2πfn|l|), yet the AR model in Eq. (25) and the CNN training assume J0. Either the simulation uses the phase-rotation model (then prediction is trivial and the CNN is unnecessary) or it uses Jakes fading (then Eq. (2) is wrong). The paper doesn't say which, and there's no code or data. That's load-bearing, because the headline overhead reduction relies on the CNN-AR keeping prediction NMSE low.\n\nSecond, the CNN-AR is under-specified—no layer sizes, no kernel sizes, no report of whether the five Doppler values in Fig. 10 were held out from the ten used in training. The paper says the CNN 'is capable of adding more fn values in training,' which suggests they never tested on unseen velocities or non-Jakes fading. At minimum, that generalization claim needs to be tested.\n\nThird, the scaling ambiguity removal by switching on the first RIS element and first BS antenna is questionable under the unitary constraint on the reflection matrix; for fully-connected BD-RIS you can't simply turn off other elements. This may be fixable with a known reference pilot, but it needs a concrete procedure.\n\nNone of these kill the Tucker2-BALS contribution. That part is plausible and the identifiability analysis is sound within its own assumptions. But the paper as written overclaims the prediction phase. A serious referee should ask the authors to fix Eq. (2) or the fading model, evaluate CNN-AR on held-out Doppler values and non-Jakes autocorrelations, and give a feasible scaling-ambiguity protocol. I'd send it to review with major revision; the tensor part deserves a fair hearing.","headline":"Tucker2-BALS for BD-RIS is a genuine contribution; the CNN-AR prediction is under-specified and the channel model contradicts its own fading statistics, so the headline 98% overhead claim is not established.","tokens_in":20508,"tokens_out":8017,"would_cite":false,"duration_ms":71285,"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 joint Tucker2-BALS estimator and CNN-AR predictor is proposed that reduces pilot overhead by up to 98% in beyond-diagonal RIS-assisted MIMO systems with channel aging, while preserving near-perfect-CSI downlink sum rates.","keywords":["beyond diagonal RIS","Tucker2 decomposition","bilinear alternating least squares","CNN-AR prediction","channel aging","pilot overhead","downlink sum rate","MIMO channel estimation"],"falsifier":"Hold out a normalized Doppler frequency between two training values (e.g., test at $f_n = 0.006$ when training used $0.005$ and $0.01$) and measure the prediction NMSE; if it jumps by an order of magnitude relative to neighboring trained frequencies, the CNN has memorized the training grid rather than learned a transferable aging pattern. A second decisive test is to run the full pipeline on measured channel traces from a moving terminal; if the CNN-AR predictions are no better than a conventional same-order AR predictor, the learned pattern does not transfer to real fading.","tokens_in":19549,"feed_emoji":"📶","tokens_out":10316,"duration_ms":89762,"temperature":0.7,"pith_summary":"The paper's target is the channel state information problem created by beyond-diagonal RISs (BD-RISs): surfaces whose reflecting elements are electrically coupled, so the reflection matrix is not diagonal and the cascade channel has many interdependent entries. The authors claim that in a BD-RIS-assisted MIMO system with fast-fading user channels, the received pilot tensor obeys a Tucker2 decomposition, which lets a bilinear alternating least squares (BALS) estimator recover the RIS-BS and user-RIS channels separately with far fewer pilots than a least-squares baseline. They then feed the estimated user channels to a CNN-augmented autoregressive predictor that forecasts future channels through coherence intervals in which no pilots are sent. If correct, the framework delivers downlink sum rates close to the perfect-CSI benchmark, a 10–50% sum-rate gain over DFT-LS estimation, and a pilot-overhead reduction of up to 98% for fully-connected and 88–97% for group-connected BD-RIS architectures.","feed_headline":"Tensor plus CNN prediction cuts RIS pilot overhead by 98%","feed_subtitle":"The Tucker2-BALS estimator plus CNN-AR predictor keeps sum rate near perfect-CSI levels without frequent pilot retraining.","key_machinery":"The load-bearing object is the Tucker2 decomposition of the received-signal tensor. Tucker2 factorizes a third-order tensor into a core tensor and two factor matrices while leaving the third mode unconstrained; here the core is $\\mathcal{W}$ (the sequence of known reflection matrices) and the factors are $\\mathbf{H}$ and $\\mathbf{E}[l]^T$. The identity $\\operatorname{vec}(\\mathbf{A}\\mathbf{B}\\mathbf{C}^T) = (\\mathbf{C}\\otimes\\mathbf{A})\\operatorname{vec}(\\mathbf{B})$ converts the cascade relation into linear systems, and the BALS algorithm alternates the two least-squares updates (19) and (20) until the normalized residual stops decreasing. The second mechanism is the CNN-AR predictor: a small convolutional network trained on the autocorrelation function of the aging channel maps a short window of estimated channels to AR coefficients, which are then used recursively to predict $P$ future coherence intervals without pilots.","core_discovery":"On the paper's own terms, the central discovery is that the BD-RIS channel estimation problem, which looks high-dimensional because a non-diagonal reflection matrix couples all elements, can be reshaped into a low-rank tensor model: stacking the received pilot signals across antennas, users, and training blocks gives a third-order tensor $\\tilde{\\mathcal{Y}}$ whose noiseless part is $\\mathcal{Y} = \\mathcal{W} \\times_1 \\mathbf{H} \\times_2 \\mathbf{E}[l]^T$, where $\\mathcal{W}$ holds the known BD-RIS reflection matrices. Fitting this Tucker2 model by BALS—alternating two least-squares updates for $\\mathbf{H}$ and $\\mathbf{E}[l]$—estimates the two channel factors separately, which the paper argues is both more accurate and lower-complexity than estimating the composite cascade, and it is unique up to a scalar that a one-element calibration step fixes. The user-side estimates feed a CNN that learns the autocorrelation (aging) pattern of the fading process and returns AR coefficients, so the AR recursion predicts $\\mathbf{E}[l]$ for the next $P$ coherence intervals without any pilot transmission. Using this CSI in a closed-form BD-RIS reflection optimization, the authors report near-perfect-CSI sum rates, order-of-magnitude NMSE gains, and up to 98% pilot-overhead reduction, with the same machinery adapted to group-connected RIS by processing each group independently.","pith_inferences":["If the CNN were retrained on measured fading traces rather than synthetic correlated-fading realizations, the predictor might extend to non-Rayleigh environments; the paper does not test this transfer, so it is an open question rather than a demonstrated property.","The 98% pilot saving assumes the RIS-BS channel is quasi-static; in deployments with a mobile RIS or moving scatterers, the training phase would need to repeat, shrinking the saving by an amount this paper does not quantify.","The complexity comparison counts online CNN inference only; the offline training cost (300 epochs over $7\\times10^4$ samples) would need to be amortized over long operation, or the CNN distilled to a lookup table, before the claimed low complexity holds at the edge.","A natural end-to-end test is to close the loop: feed the predicted CSI into the BD-RIS reflection optimizer and measure realized throughput on a testbed, since the sum-rate curves here assume the prediction errors only affect the bounds, not the actual beamforming."],"forward_implications":["The pilot length for fully-connected RIS becomes $(T+1)Q$ over $Q+P$ coherence intervals instead of $M^2(Q+P)$, which yields the reported 94–98% overhead reduction; the group-connected case scales as $(T+\\bar{G})Q$ and saves 88–97%.","Because $\\mathbf{H}$ and $\\mathbf{E}[l]$ are estimated separately, the per-iteration BALS complexity is $O(M^2T(K+N)+2NKTM)$, quadratic in $M$, whereas the DFT-LS baseline costs $O((Q+P)M^4(1+NK))$; the gap widens as the number of RIS elements grows.","The CNN-AR predictor lowers prediction NMSE by orders of magnitude relative to a same-order AR predictor, because it avoids computing AR coefficients from a short, noisy window and instead reads them from the learned autocorrelation pattern.","At low UE velocities the estimated/predicted CSI yields an average downlink sum rate close to the perfect-CSI bound, while at high velocities prediction accuracy degrades as the coherence time shortens (tested from 9 to 360 km/h at a 3 GHz carrier).","The same framework covers both major BD-RIS families: fully-connected RIS is one Tucker2 problem, and group-connected RIS is solved per group, so no new estimation machinery is needed for either architecture."],"supporting_citations":[{"why":"Defines Tucker2 decomposition and n-mode products, the tensor machinery the received signal is modeled with.","marker":"[8]"},{"why":"Supplies the DFT-LS channel estimator and minimum pilot-length formulas used as the baseline and overhead comparison.","marker":"[29]"},{"why":"Provides the channel-aging ACF model and the CNN-plus-AR prediction concept that the predictor builds on.","marker":"[7]"},{"why":"Gives the autoregressive fading model and the diagonal-inflation trick for stable high-order AR filters.","marker":"[28]"},{"why":"Introduces beyond-diagonal RIS and its fully- and group-connected architectures, the systems under study.","marker":"[3]"},{"why":"Offers the PARAFAC-based estimator for conventional diagonal RIS used as a comparison in the sum-rate and NMSE results.","marker":"[15]"},{"why":"Provides the closed-form BD-RIS reflection-matrix optimization that converts the estimated CSI into the reported sum rates.","marker":"[35]"},{"why":"Supplies the Tucker2 uniqueness/identifiability discussion and the bilinear alternating least-squares estimation approach being adapted.","marker":"[10]"},{"why":"Earlier CNN-AR channel predictor for conventional RIS that this paper generalizes to BD-RIS architectures.","marker":"[1]"}],"fun_headline_variants":["Tensor+CNN predicts BD-RIS with 98% fewer pilots","Tucker2 tensor + CNN-AR predicts BD-RIS channels, cuts pilots 98%","Near-perfect CSI sum rate from tensor-CNN predictor, 98% pilot cut","Low-rank tensor + CNN-AR: BD-RIS channels predicted without new pilots"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the CNN, trained only on synthetic correlated-fading channels and evaluated only at velocities seen during training, outputs prediction coefficients accurate enough for the actual channel; real measured channels or speeds outside the training set are never tested.","fun_headline_variants_meta":{"raw":{"variants":["Tensor+CNN predicts BD-RIS with 98% fewer pilots","Tucker2 tensor + CNN-AR predicts BD-RIS channels, cuts pilots 98%","Near-perfect CSI sum rate from tensor-CNN predictor, 98% pilot cut","Low-rank tensor + CNN-AR: BD-RIS channels predicted without new pilots"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000614,"raw_usage":{"total_tokens":2931,"prompt_tokens":1102,"completion_tokens":1829,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":718,"completion_tokens_details":{"reasoning_tokens":1750}},"tokens_in":718,"tokens_out":1829,"duration_ms":12514,"temperature":1.0,"reasoning_tokens":1750,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:42:21.039342+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Hold out a normalized Doppler frequency between two training values (e.g., test at $f_n = 0.006$ when training used $0.005$ and $0.01$) and measure the prediction NMSE; if it jumps by an order of magnitude relative to neighboring trained frequencies, the CNN has memorized the training grid rather than learned a transferable aging pattern. A second decisive test is to run the full pipeline on measured channel traces from a moving terminal; if the CNN-AR predictions are no better than a conventional same-order AR predictor, the learned pattern does not transfer to real fading.","supporting_citations":[{"cited_title":"Tensor Decompositions and Ap plications,","cited_arxiv_id":null,"evidence_quote":"Defines Tucker2 decomposition and n-mode products, the tensor machinery the received signal is modeled with."},{"cited_title":"Channel Estimation for Beyond Diagonal Reconfigurable Intelligent Surfaces with Group-C onnected Architectures,","cited_arxiv_id":null,"evidence_quote":"Supplies the DFT-LS channel estimator and minimum pilot-length formulas used as the baseline and overhead comparison."},{"cited_title":"Machine Learning-B ased Channel Prediction in Massive MIMO With Channel Aging,","cited_arxiv_id":null,"evidence_quote":"Provides the channel-aging ACF model and the CNN-plus-AR prediction concept that the predictor builds on."},{"cited_title":"Autoregressive modeling f or fading channel simulation,","cited_arxiv_id":null,"evidence_quote":"Gives the autoregressive fading model and the diagonal-inflation trick for stable high-order AR filters."},{"cited_title":"Reconfigurable Intelligent Surfaces 2.0: Beyond Diagonal Phase Shift Matrices,","cited_arxiv_id":null,"evidence_quote":"Introduces beyond-diagonal RIS and its fully- and group-connected architectures, the systems under study."},{"cited_title":"Channel Estimation for RIS-Empowered Multi-User MISO Wireless Communications,","cited_arxiv_id":null,"evidence_quote":"Offers the PARAFAC-based estimator for conventional diagonal RIS used as a comparison in the sum-rate and NMSE results."},{"cited_title":"Closed-Form Global Optimization of Beyond Diagonal Reconfigurable Intelligent Surfaces,","cited_arxiv_id":null,"evidence_quote":"Provides the closed-form BD-RIS reflection-matrix optimization that converts the estimated CSI into the reported sum rates."},{"cited_title":"Tensor-Based Joint Channel Estimation for Multi-Way Massive MIMO Hybrid Relay Systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the Tucker2 uniqueness/identifiability discussion and the bilinear alternating least-squares estimation approach being adapted."},{"cited_title":"Machine Learning-Based Channel Prediction for RIS-A ssisted MIMO Systems with Channel Aging,","cited_arxiv_id":null,"evidence_quote":"Earlier CNN-AR channel predictor for conventional RIS that this paper generalizes to BD-RIS architectures."}],"review_version":1}