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REVIEW 4 major objections 5 minor 40 references

Channel Customization for Low-Complexity CSI Acquisition in Multi-RIS-Assisted MIMO Systems

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2411.14088 v1 pith:YUQCB5NP submitted 2024-11-21 cs.IT eess.SPmath.IT

Weicong Chen , Yu Han , Chao-Kai Wen , Xiao Li , Shi Jin This is my paper · ORCID
classification cs.ITeess.SPmath.IT
keywords reconfigurableintelligentsurfaceMIMOchannelestimationcustomizationsparsificationpositioning-basedpilotoverheadreductionNewtonizedorthogonalmatchingpursuitmillimeter-wavecommunications
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

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.

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 (4)
  1. [Section IV-A, Eq. (27); Appendix A, Eqs. (63)-(64)]
  2. [Section IV-C, Eqs. (40)-(46)]
  3. [Section IV-B, Algorithm 1 and Eq. (29)]
  4. [Section IV-C, Eq. (40)]
minor comments (5)
  1. [Eq. (24)]
  2. [Notation, Section II]
  3. [Appendix A, Eq. (54)]
  4. [Section V-A, Fig. 6]
  5. [Section V-D, Fig. 12]

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the sparse-channel approximation is derived from first principles in Appendix A, and no fitted input is renamed as a prediction.

full rationale

The paper's derivation chain is self-contained with respect to its central claim. Equation (26) defines the RIS reflection vector from LoS angle parameters, and Appendix A computes the expected power of each cascaded path, showing in (63)-(64) that for large M_k the LoS cascaded component dominates in expectation. Equation (27) is used as an approximation, not as an equality forced by definition; the residual H - A_b,e Ξ_e A_u,e^H is a modeling error that is evaluated by Monte Carlo simulations in Figs. 6 and 11-13. The downlink single-path estimator (42)-(45) does not fit a parameter to the downlink data and then call that fit a prediction; it estimates the LoS angle and gain from the customized channel model. Uplink LoS parameters are used to configure the RIS, and the downlink angles are re-estimated, so the downlink result is not statistically forced by the uplink fit. Self-citations [10], [13], and [40] concern prior channel-customization frameworks, but the present derivation does not rely on them as unverified premises: the array response decomposition in (27) is stated explicitly and the dominance claim is proven in Appendix A using the paper's own assumptions. The gap between the average-power statement in (63)-(64) and the instantaneous use of (27) is a correctness and statistical issue (the NLoS residual is not bounded per realization), not a circularity in the derivation chain.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The method introduces no new physical entities. The free parameters are algorithmic design choices (τ, KL, grid oversampling factors) rather than fitted physical constants. The main burden is carried by four modeling axioms, most importantly the average-power-to-instantaneous sparsity approximation that supports Eq. (27).

free parameters (3)
  • Stopping threshold τ = not specified
    Used in Algorithm 1 to decide when the estimated AoAs match the positioning-based LoS angles; the value affects how many NOMP iterations run and the accuracy/complexity trade-off, but no value is given.
  • Number of positioning RISs KL = not specified (must be ≥ 3)
    The positioning step requires selecting KL out of K RISs for triangulation; the paper assumes a LoS subset KL but does not state how KL is chosen or its value in simulations.
  • Oversampling factors ηb, ηu, ηh,k, ηv,k = not specified
    These grid oversampling factors control the complexity formula in (21) and the resolution of parameter extraction; they are algorithmic choices not fitted to data, but they affect the reported complexity comparisons.
assumptions (4)
  • standard math The fast reflection matrix F is a DFT matrix satisfying F^T F^* = KF I (Section III-A, Eq. (13)).
    Used to separate channel components by multiplying the received signal by F^*; standard property of DFT matrices.
  • domain assumption Far-field planar wave propagation and geometric multipath model with known LoS angles for the fixed RIS-BS links (Section II-A, Eqs. (3)-(7)).
    The array response structure and the known B_k,0 LoS path used in extraction and customization depend on far-field and known geometry.
  • domain assumption All RISs are perfectly synchronized with the BS via GNSS (footnote 1).
    The joint fast reflection patterns require coordinated timing across RISs; the paper explicitly sets synchronization out of scope.
  • ad hoc to paper The reflection channel can be replaced by the LoS-only term H ≈ A_{b,e} Ξ_e A_{u,e}^H in (27) because the expected power of the LoS cascaded path dominates for large M_k (Appendix A, Eqs. (63)-(64)).
    This is the load-bearing sparsification premise; it is an average-power statement applied to instantaneous channel estimation and downlink reconstruction.

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Cite this review

Pith. "Pith review of Channel Customization for Low-Complexity CSI Acquisition in Multi-RIS-Assisted MIMO Systems." pith.science (2026). https://pith.science/paper/YUQCB5NP

@misc{pith2026241114088,
  author       = {Pith},
  title        = {Pith review of: Channel Customization for Low-Complexity CSI Acquisition in Multi-RIS-Assisted MIMO Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YUQCB5NP}},
  note         = {Machine review of arXiv:2411.14088}
}
read the original abstract

The deployment of multiple reconfigurable intelligent surfaces (RISs) enhances the propagation environment by improving channel quality, but it also complicates channel estimation. Following the conventional wireless communication system design, which involves full channel state information (CSI) acquisition followed by RIS configuration, can reduce transmission efficiency due to substantial pilot overhead and computational complexity. This study introduces an innovative approach that integrates CSI acquisition and RIS configuration, leveraging the channel-altering capabilities of the RIS to reduce both the overhead and complexity of CSI acquisition. The focus is on multi-RIS-assisted systems, featuring both direct and reflected propagation paths. By applying a fast-varying reflection sequence during RIS configuration for channel training, the complex problem of channel estimation is decomposed into simpler, independent tasks. These fast-varying reflections effectively isolate transmit signals from different paths, streamlining the CSI acquisition process for both uplink and downlink communications with reduced complexity. In uplink scenarios, a positioning-based algorithm derives partial CSI, informing the adjustment of RIS parameters to create a sparse reflection channel, enabling precise reconstruction of the uplink channel. Downlink communication benefits from this strategically tailored reflection channel, allowing effective CSI acquisition with fewer pilot signals. Simulation results highlight the proposed methodology's ability to accurately reconstruct the reflection channel with minimal impact on the normalized mean square error while simultaneously enhancing spectral efficiency.

Figures

Figures reproduced from arXiv: 2411.14088 by the authors.

Figure 1
Figure 1. Multi-RIS-assisted MIMO system, where lines of dif [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Frame structure for the uplink channel estimation. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Overview of the parameter extraction process for the UE–RIS [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Overall flowchart of the proposed scheme. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: NMSE of the decoupled signal components. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 7
Figure 7. Figure 7: NME of parameters extracted in the uplink. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 6
Figure 6. Figure 6: Power ratio of channel components: (a) with and [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 9
Figure 9. Figure 9: NME of Θˇ ur,D 0 extracted in the downlink. set to −30 dB, [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 8
Figure 8. Figure 8: NME of Φˆ ur,A 0 extracted in the uplink. 8(b), the estimation accuracy of LoS paths improves with a higher Rician factor. Building on the customized sparse channel concept in￾troduced in Section IV-C, we show that downlink channel estimation can be achieved with a sim…
Figure 11
Figure 11. Figure 11: NMSE performance comparison of different schemes [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 10
Figure 10. Figure 10: Mean positioning error in the uplink. respectively [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 14
Figure 14. Figure 14: averaged SE in the downlink with different CSI. [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]
Figure 13
Figure 13. Figure 13: Impacts of the Rician factor in the UE–RISs channel. -60 -58 -56 -54 -52 -50 SNR (dB) 0 1 2 3 4 5 6 7 8 9 Averaged SE [bits/s/Hz] The perfect CSI The estimated CSI by the NOMP The estimated CSI by the proposal (a) averaged SE versus SNR 0 2 4 6 8 10 12 14 Rician facto…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.