{"id":"ec1c369b-61e3-436b-928e-598048e77677","arxiv_id":"2411.14088","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A multi-RIS MIMO channel estimation method uses fast-varying RIS reflections and positioning to create a sparse channel, cutting CSI acquisition complexity and downlink pilot overhead.","lead":"This paper proposes a way to estimate wireless channels in systems with several reconfigurable intelligent surfaces (RISs) by using the surfaces to simplify the channel during training. It shows how fast-varying surface reflections can separate signals from different paths, then reconstruct the channel with much lower complexity than full estimation, which matters for making multi-RIS systems practical.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The load-bearing gap is the leap from average-power dominance (Appendix A) to the instantaneous sparse model (27); the NLoS residual is unbounded in any fixed channel realization, which biases both the downlink single-path estimator and the (46) channel reconstruction.","rationale":"I read the paper in good faith. The scheme is coherent: fast-varying reflection phases separate the K link components (Section III-A), the positioning-based algorithm extracts the LoS parameters with reduced complexity (Section IV-B), and the customized sparse channel is then used for low-overhead downlink estimation (Section IV-C). The paper provides derivations for the reflection design (26), the expected path power ratios (Appendix A), and simulations with NOMP baselines. The strongest claim is correctly identified by the reader: (27) reduces the whole estimation task to K LoS paths. I agree with the reader's weakest-assumption identification. The concern is not that the algebra is internally inconsistent; it is a modeling/statistical step. Appendix A proves E{||Ξk||_F^2} ≈ E{|ξk,0,0|^2} for large Mk, but the algorithm and the downlink estimator are applied to a single channel realization with a fixed NLoS draw. There is no variance bound, no concentration inequality, and no per-realization residual control. The omitted NLoS power is non-zero and, for the parameters used in Section V, is about 4% in expectation, which is on the order of the NMSE plateaus in Fig. 11. This creates a bias floor for the downlink single-path estimator (43)-(45), because the residual acts as structured interference that is not accounted for in the ML formulation. The central claim is conditional on this gap being benign. I do not move the verdict to REJECT because the proposed scheme is otherwise well-posed and the simulations are consistent with the expected residual; the concern is precisely the need for a quantitative residual bound and a per-realization analysis, which is what a CONDITIONAL verdict should demand. One small correction I would add: the paper's (26) and Appendix A assume the RIS response follows the ideal array model; that is standard in the literature and not the main concern. The main test should be numerical and analytical as described in concrete_test.","tokens_in":23528,"tokens_out":4202,"duration_ms":30325,"concrete_test":"Take one random channel realization from the model (3)-(7) with K=4, Mk=25 (5×5), κur=10 dB, κrb=30 dB, Lrb_k=2, Lur_k=5, and compute the realized ratio ||H - Ab,eΞeA_u,e^H||_F^2 / ||H||_F^2 for γk as in (26), over, say, 10^4 realizations. If the median realized ratio is comparable to the expected value (≈ 0.04) and the 95th percentile is substantially larger, while the downlink NMSE in (46) from the (43)-(45) estimator plateaus near that same level, then the instantaneous sparse model (27) and the resulting downlink estimator are biased exactly as suspected. A further analytical check: derive an upper bound on ||H - Ab,eΞeA_u,e^H||_F^2 in terms of the NLoS path gains and Δh,k,l,c, Δv,k,l,c from (50), and compare it against the reported NMSE floor in Fig. 11; the bound should scale as (1/Mk)(1/κur + 1/κrb) times ||H||_F^2 plus array-gain leakage terms.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central argument of Section IV is that configuring each RIS with (26) makes the reflection channel approximately sparse, H ≈ Ab,eΞeA_u,e^H in (27), so that only LoS-path parameters are needed and downlink estimation reduces to K independent single-path detections. The only support for (27) is Appendix A, which computes E{|ξk,l,c|^2} for each cascaded path and shows that for large Mk, E{||Ξk||_F^2} ≈ E{|ξk,0,0|^2} in (63)-(64). That is an average-power statement. Equation (27) is used per-realization: the downlink received signal (40) is rewritten as the LoS-only term, the ML estimator (43)-(45) searches only over the single LoS angle, and the reconstructed channel (46) omits the non-LoS components. No variance, concentration, or per-realization bound is provided for the residual H - Ab,eΞeA_u,e^H. In a fixed channel drawn from the model in (3)-(7), the NLoS terms have non-zero power; their relative strength is controlled by Mk, κrb, κur, Lrb_k, Lur_k and the actual angular differences Δh,k,l,c, Δv,k,l,c in (50). For the simulation parameters (RIS 5×5, κur=10 dB, κrb=30 dB), the omitted NLoS power is roughly E{||Ξk||_F^2 - |ξk,0,0|^2}/E{|ξk,0,0|^2} ≈ (1/Mk)(1/κur + 1/κrb + 1/(κrbκur)) ≈ 0.041, i.e. about 4% in expectation. This is not negligible relative to the reported reconstruction NMSE and it is a floor: the estimator in (43)-(45) treats the NLoS residual plus noise as noise, producing a biased angle estimate and an NMSE that cannot decrease below the residual power, consistent with the plateaus visible in Figs. 7, 10, 11. No analysis quantifies this bias or this error floor, and Fig. 6 measures the power ratio E||He||^2/E||H||^2, another average quantity, not a per-realization norm bound. The paper's own Fig. 6(b) shows the ratio approaches 1 only gradually with Mk and κur, which confirms the residual is material in realistic regimes.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a joint CSI-acquisition and RIS-configuration scheme for multi-RIS-assisted MIMO systems. In the uplink, fast-varying RIS reflection phases across pilot symbols are used to separate channel components from different RISs and the direct link via the orthogonality of a DFT reflection matrix (Section III-A). The authors then propose a positioning-based algorithm that estimates only the LoS path parameters of each UE-RIS channel, uses those parameters to configure each RIS with the reflection vector in Eq. (26), and argues via Appendix A that the resulting cascaded reflection channel is approximately sparse, H ≈ A_{b,e} Ξ_e A_{u,e}^H in Eq. (27). This sparse model is then used to simplify downlink estimation to K independent single-path detection problems (Section IV-C). Numerical results in Section V evaluate parameter-extraction error, positioning error, channel-reconstruction NMSE, and spectral efficiency against a NOMP baseline.","tokens_in":23982,"tokens_out":2590,"duration_ms":27599,"significance":"If the sparse-channel approximation in Eq. (27) were reliable per channel realization, the proposed scheme would be a substantive contribution: it converts a high-dimensional multi-path channel estimation problem into a few single-path searches and reduces downlink pilot overhead, while preserving much of the achievable spectral efficiency. The channel separation step using F^T F^* = K_F I is clean and correctly derived, and Appendix A provides a careful average-power calculation for the cascaded path gains. The numerical study is reasonably extensive and the paper is generally well organized. However, the central theoretical claim—that average LoS power dominance licenses an instantaneous sparse approximation—is not established, and this gap is load-bearing for the downlink estimator and the channel reconstruction.","major_comments":[{"comment":"","section":"Section IV-A, Eq. (27); Appendix A, Eqs. (63)-(64)"},{"comment":"","section":"Section IV-C, Eqs. (40)-(46)"},{"comment":"","section":"Section IV-B, Algorithm 1 and Eq. (29)"},{"comment":"","section":"Section IV-C, Eq. (40)"}],"minor_comments":[{"comment":"","section":"Eq. (24)"},{"comment":"","section":"Notation, Section II"},{"comment":"","section":"Appendix A, Eq. (54)"},{"comment":"","section":"Section V-A, Fig. 6"},{"comment":"","section":"Section V-D, Fig. 12"}],"recommendation":"major_revision","confidential_remarks":"The paper has a solid algorithmic contribution and a clean channel-separation step, and the average-power calculation in Appendix A is internally consistent. The main concern is not circularity or fitted constants; it is that the central sparse-channel approximation is used per realization while only being justified in expectation. I recommend major revision rather than rejection because the gap is potentially fixable with an additional concentration argument or with a reformulated estimator that accounts for the NLoS residual, and because the numerical results otherwise support the practical claims of the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid engineering paper. It adapts the fast-varying DFT reflection trick from Keykhosravi–Wymeersch to separate multi-RIS cascaded channels, adds a positioning-based joint LoS identification scheme, and uses that partial CSI to configure RISs so the reflection channel is dominated by K LoS paths. That lets downlink estimation reduce to K independent single-path searches. The integration is new, the complexity reduction is concrete, and the Appendix A derivation is internally consistent. I checked the F^T F^* = KF I step and the expected-power calculation; both are clean. No code or data is shipped, so the simulations are not independently reproducible, but they are standard for this literature.\n\nThe real soft spot is exactly what the stress test flags. Equation (27) is introduced as an average-perspective approximation, and Appendix A proves average-power dominance for large M_k. But the downlink estimator in (40)–(45) and the reconstruction in (46) treat (27) as a per-realization statement: the NLoS residual is just absorbed into noise. There is no bound on that residual in any fixed channel. For their own simulation settings (5x5 RIS, κur = 10 dB, κrb = 30 dB), the expected omitted power is about 4%, which is not negligible next to the NMSE values they report, and it floors the estimator. The NMSE plateaus in Figs. 7, 10, and 11 are consistent with that. I do not think this sinks the paper; it is a fixable framing gap. They could add a per-realization residual bound or concentration argument, state honestly that the scheme targets regimes where the residual is small, or characterize the bias and error floor. Right now the central claim overreaches by a modest but real amount.\n\nMinor points: the scheme needs at least three LoS RISs for positioning, and it assumes perfect synchronization; both are stated, but robustness is not examined. Some simulation details (stopping threshold τ, number of positioning RISs K_L, grid oversampling factors) are not fully specified. The complexity comparison against NOMP is honest and clear.\n\nWho it is for: people working on RIS channel estimation and mmWave system design. It deserves a serious referee, and I would send it out. The average-to-instantaneous gap needs to be addressed in revision, but the core contribution is useful and the derivations are sound enough to build on.","headline":"A clean, useful engineering scheme for low-complexity multi-RIS CSI acquisition; the soft spot is real but fixable — the sparse-channel model (27) is justified only in expectation, while the estimators use it per realization.","tokens_in":24593,"tokens_out":1947,"would_cite":true,"duration_ms":20897,"reading_group":"yes","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 tuning each RIS to its cascaded LoS paths makes the multi-RIS MIMO channel approximately sparse, reducing CSI acquisition to a few path-parameter estimates.","keywords":["reconfigurable intelligent surface","MIMO channel estimation","channel customization","channel sparsification","positioning-based estimation","pilot overhead reduction","Newtonized orthogonal matching pursuit","millimeter-wave communications"],"falsifier":"Compute, over many channel realizations with a small RIS (for example 4 by 4 elements), Rician factor $\\kappa^{\\mathrm{ur}} = 0$ dB, and several strong NLoS paths, the ratio $\\|H - \\mathbf{A}_{b,e} \\boldsymbol{\\Xi}_e \\mathbf{A}_{u,e}^H\\|_F^2 / \\|H\\|_F^2$ after applying (26). If this ratio stays well above zero at high SNR and the downlink single-path estimator (45) shows a systematic bias that does not vanish with more pilots, the sparsification claim fails in that regime.","tokens_in":23287,"feed_emoji":"📡","tokens_out":10710,"duration_ms":94992,"temperature":0.7,"pith_summary":"The paper proposes jointly designing channel estimation and RIS configuration in a multi-RIS MIMO system, rather than first estimating the full channel and then setting the RIS phases. Its central claim is that if each RIS k is configured with $\\gamma_k = M_k \\mathbf{a}_r(\\Theta^{\\mathrm{D}}_{rb,k,0}) \\odot \\mathbf{a}_r^*(\\Theta^{\\mathrm{A}}_{ur,k,0})$, the cascaded reflection channel becomes approximately sparse, $H \\approx \\mathbf{A}_{b,e} \\boldsymbol{\\Xi}_e \\mathbf{A}_{u,e}^H$, with power concentrated in the K cascaded LoS paths. The sparsification is justified by an average-power calculation showing that for sufficiently large RISs the LoS term dominates the expected squared norm. With the channel made sparse, uplink estimation reduces to extracting LoS path parameters through a positioning-based algorithm that uses at least three RISs to locate the UE, and downlink estimation reduces to independent single-path detection per RIS with fewer pilots. The payoff would be CSI acquisition at a fraction of the exhaustive-search complexity of full Newtonized orthogonal matching pursuit (NOMP), a greedy path-parameter search algorithm, at the cost of a modest NMSE increase and roughly unchanged spectral efficiency.","feed_headline":"RIS tuning turns dense MIMO channels sparse, cutting CSI cost","feed_subtitle":"By aligning each surface with line-of-sight paths, multi-RIS channel estimation shrinks to a few single-path searches.","key_machinery":"The central mechanism is the channel-customization identity for the k-th RIS reflection vector, $\\gamma_k = M_k \\mathbf{a}_r(\\Theta^{\\mathrm{D}}_{rb,k,0}, \\Phi^{\\mathrm{D}}_{rb,k,0}) \\odot \\mathbf{a}_r^*(\\Theta^{\\mathrm{A}}_{ur,k,0}, \\Phi^{\\mathrm{A}}_{ur,k,0})$ in (26), where $\\mathbf{a}_r(\\cdot)$ is the RIS array response vector, together with the cascaded-gain expression $\\xi_{k,l,v}$ in (25). This choice makes the gain sum collapse to a Dirichlet-like kernel that is $M_k$, the number of elements on the surface, times larger for the LoS-LoS cascade than for any cascade involving an NLoS path, so in expectation the matrix $\\boldsymbol{\\Xi}$ becomes nearly diagonal and $H \\approx \\mathbf{A}_{b,e} \\boldsymbol{\\Xi}_e \\mathbf{A}_{u,e}^H$. The fast-varying reflection matrix $F = [\\mathbf{f}_0, \\ldots, \\mathbf{f}_K]$ acts as a channel-separation mechanism: multiplying the received training blocks by $F^*$ isolates the direct and RIS-cascaded components, converting the multi-RIS estimation problem into $K+1$ independent subproblems.","core_discovery":"The central claim is that the RIS itself can simplify the channel estimation problem instead of being treated as an unknown to be estimated. When each RIS's phases are chosen as in (26) to coherently combine the LoS paths from the UE side and the BS side, the per-path cascaded gains $\\xi_{k,l,v}$ become concentrated: in expectation, $E[|\\xi_{k,0,0}|^2]$ dominates the other cascaded terms by factors that grow with the RIS size $M_k$ and the Rician factors, so the full reflection channel is well approximated by the LoS-only matrix (27). The paper then exploits this customization: a positioning-based joint LoS-path estimation algorithm detects the LoS angles by triangulating the UE from at least three RISs and matching NOMP-extracted angles against the geometric prediction, and in the downlink the UE only needs to detect the departure angle of one LoS path per RIS, with the pilot count reduced from $K_S N_u$ to $N_b$. The simulations show the reconstructed channel has a higher NMSE floor than full NOMP estimation, but the spectral efficiency achieved with the estimated CSI is close to the perfect-CSI result.","pith_inferences":["The paper leaves implicit that the same customization idea could be closed-loop: after the first downlink estimate, the UE's detected angles could be fed back to refine the RIS phases, progressively hardening the channel over a few rounds and lowering the residual NLoS power.","The average-power justification suggests the scheme is strongest when each RIS has many elements and the UE-RIS links are strongly LoS-dominated; in the opposite regime, the LoS-only reconstruction has an irreducible per-realization residual, which the NMSE floor in the simulations already hints at.","Because the positioning step needs at least three RISs with LoS visibility to the UE, applying the scheme to multi-UE or cell-free deployments would require each UE to be visible to at least three surfaces, or the LoS-identification step would need another source of angular reference.","The complexity comparison depends on the NOMP baseline's grid oversampling factors; under a fixed accuracy target the downlink single-path search may need a finer grid, so the true savings are set by how many NOMP iterations the positioning-based match actually avoids."],"forward_implications":["If the approximation (27) holds, the uplink reflection channel can be reconstructed from the K LoS paths in the UE-RIS links, dropping the NOMP search complexity from roughly $K M \\eta^3 (L^{\\mathrm{ur}} N_u + L^{\\mathrm{rb}} N_b)$ to $K M \\eta^3 (N_u + N_b)$ in the best case.","Downlink training overhead falls from $K_S N_u$ pilots to $N_b$ pilots, and the UE's estimation task becomes one single-path angular search per RIS.","The RIS configuration (26) requires only the LoS departure angles in the UE-RIS channels, which are obtained from the positioning step, so no full instantaneous CSI is needed at the RIS.","The method's complexity advantage over full NOMP grows with the number of NLoS paths, because those paths are never searched for, while the channel reconstruction error stays nearly flat as the path count increases.","In the simulated mmWave scenario, the spectral efficiency obtained from the customized-channel estimate is close to that of perfect CSI despite the higher NMSE, because the dominant LoS paths carry most of the channel power."],"supporting_citations":[{"why":"Supplies the fast-varying reflection phase design used to separate direct and RIS-cascaded channel components during training.","marker":"[34]"},{"why":"Supplies the Newtonized orthogonal matching pursuit algorithm that serves as the full path-parameter extraction baseline and whose complexity the proposed method reduces.","marker":"[37]"},{"why":"Applies NOMP to cascaded RIS channel estimation in mmWave systems, the setting the paper's customization scheme extends and simplifies.","marker":"[35]"},{"why":"Provides the geometric multipath channel model used for the NLoS components of the UE-RIS and RIS-BS channels.","marker":"[32]"},{"why":"Earlier channel-customization concept for RIS-assisted FDD systems, extended here to joint estimation and configuration in multi-RIS TDD systems.","marker":"[40]"},{"why":"Motivates the positioning-based channel reconstruction direction by showing how localization can replace exhaustive channel parameter search in RIS-assisted massive MIMO.","marker":"[21]"}],"fun_headline_variants":["RIS customization sparsifies MIMO channels, slashing CSI cost","Sparse channels via RIS phases cut CSI acquisition complexity","Multi-RIS design simplifies channel estimation, boosts efficiency","Customized RIS phases turn dense MIMO channels sparse","RIS tuning reduces CSI overhead by making channels sparse"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the average-power dominance computed in Appendix A licenses replacing the instantaneous reflection channel by its LoS-only part; the paper does not bound the per-realization NLoS residual, so with small RISs or weak LoS the reconstructed channel carries an unquantified error floor.","fun_headline_variants_meta":{"raw":{"variants":["RIS customization sparsifies MIMO channels, slashing CSI cost","Sparse channels via RIS phases cut CSI acquisition complexity","Multi-RIS design simplifies channel estimation, boosts efficiency","Customized RIS phases turn dense MIMO channels sparse","RIS tuning reduces CSI overhead by making channels sparse"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000178,"raw_usage":{"total_tokens":1337,"prompt_tokens":1027,"completion_tokens":310,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":643,"completion_tokens_details":{"reasoning_tokens":232}},"tokens_in":643,"tokens_out":310,"duration_ms":3295,"temperature":1.0,"reasoning_tokens":232,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:34:58.971375+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute, over many channel realizations with a small RIS (for example 4 by 4 elements), Rician factor $\\kappa^{\\mathrm{ur}} = 0$ dB, and several strong NLoS paths, the ratio $\\|H - \\mathbf{A}_{b,e} \\boldsymbol{\\Xi}_e \\mathbf{A}_{u,e}^H\\|_F^2 / \\|H\\|_F^2$ after applying (26). If this ratio stays well above zero at high SNR and the downlink single-path estimator (45) shows a systematic bias that does not vanish with more pilots, the sparsification claim fails in that regime.","supporting_citations":[{"cited_title":"Multi-RIS Discrete-Phase Encoding for Interpath-Interference-Free Channel Estimation","cited_arxiv_id":"2106.07065","evidence_quote":"Supplies the fast-varying reflection phase design used to separate direct and RIS-cascaded channel components during training."},{"cited_title":"Newtonized or- thogonal matching pursuit: Frequency estimation over the continuum,","cited_arxiv_id":null,"evidence_quote":"Supplies the Newtonized orthogonal matching pursuit algorithm that serves as the full path-parameter extraction baseline and whose complexity the proposed method reduces."},{"cited_title":"Cascaded Channel Estimation for RIS Assisted mmWave MIMO Transmissions,","cited_arxiv_id":null,"evidence_quote":"Applies NOMP to cascaded RIS channel estimation in mmWave systems, the setting the paper's customization scheme extends and simplifies."},{"cited_title":"A statistical model for indoor multipath propagation,","cited_arxiv_id":null,"evidence_quote":"Provides the geometric multipath channel model used for the NLoS components of the UE-RIS and RIS-BS channels."},{"cited_title":"Channel customization for limited feedback in RIS-assisted FDD systems,","cited_arxiv_id":null,"evidence_quote":"Earlier channel-customization concept for RIS-assisted FDD systems, extended here to joint estimation and configuration in multi-RIS TDD systems."},{"cited_title":"Localization and channel reconstruction for extra large RIS-assisted massive MIMO systems,","cited_arxiv_id":null,"evidence_quote":"Motivates the positioning-based channel reconstruction direction by showing how localization can replace exhaustive channel parameter search in RIS-assisted massive MIMO."}],"review_version":1}