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arxiv: 2605.19790 · v1 · pith:CXWIJLPGnew · submitted 2026-05-19 · 📡 eess.SP

Channel Estimation for Beyond Diagonal RIS-Aided Multi-User mmWave Systems

Linyu Peng , Tian Qiu , Cunhua Pan , Jiangzhou Wang , Taihao Zhang , Hong Ren This is my paper

Pith reviewed 2026-05-20 01:59 UTC · model grok-4.3

classification 📡 eess.SP
keywords channel estimationbeyond diagonal RISmmWavemulti-user systemssparse recoveryOMPblock-Kronecker structuregroup-connected architecture
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The pith

A three-stage protocol exploits block-Kronecker structure and sparsity to estimate cascaded channels in group-connected BD-RIS mmWave systems.

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

The paper sets out to solve the channel estimation problem created by the inter-element connections in beyond-diagonal reconfigurable intelligent surfaces. It first builds a block-Kronecker-structured model for the cascaded channel in a multi-user millimeter-wave setup with uniform planar arrays. A three-stage method then acquires common angles of arrival, recovers the full cascaded channel for one typical user via orthogonal matching pursuit, and applies hierarchical block orthogonal matching pursuit for the remaining users. A sympathetic reader would care because accurate channel knowledge with modest pilot overhead is required before BD-RIS can deliver its promised gains in beamforming and coverage at millimeter-wave frequencies.

Core claim

The authors formulate a novel block-Kronecker-structured cascaded channel model for a group-connected BD-RIS-aided multi-user mmWave system and propose an efficient three-stage estimation protocol. Stage I uses a DFT-based approach to acquire common angles of arrival at the base station. Stage II applies orthogonal matching pursuit and correlation-based least squares to obtain the complete cascaded channel for a designated typical user. Stage III employs a hierarchical block OMP algorithm to estimate the remaining users' channels by separating common and user-specific components. This approach reduces computational complexity and pilot overhead while improving estimation accuracy.

What carries the argument

The block-Kronecker-structured cascaded channel model that separates common and user-specific components and enables the three-stage sparse-recovery protocol with OMP and HBOMP.

If this is right

  • Common angles of arrival at the base station can be acquired once and reused across users.
  • Structural reconstruction separates shared and user-specific channel parts, lowering complexity.
  • Pilot overhead remains low while estimation accuracy improves over baselines that ignore the block-Kronecker form.
  • The protocol extends naturally to uniform planar arrays in multi-user millimeter-wave deployments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same sparsity-exploiting stages could be tested on other connected RIS topologies beyond the group-connected case.
  • Accurate low-overhead estimation would directly support real-time beamforming and multi-user scheduling in dense mmWave networks.
  • Combining the three-stage method with adaptive pilot allocation might further reduce overhead in time-varying channels.

Load-bearing premise

The cascaded channel exhibits enough sparsity for the OMP and HBOMP algorithms to recover it accurately in the group-connected BD-RIS architecture.

What would settle it

A simulation or measurement in which the cascaded channel sparsity drops below the level assumed by the OMP and HBOMP steps and the proposed protocol shows no accuracy gain or requires higher pilot overhead than conventional methods.

Figures

Figures reproduced from arXiv: 2605.19790 by Cunhua Pan, Hong Ren, Jiangzhou Wang, Linyu Peng, Taihao Zhang, Tian Qiu.

Figure 1
Figure 1. Figure 1: The proposed three-stage channel estimation protocol for BD-RIS. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Runtime of algorithms with different parameters. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: NMSE versus SNR. baseline alternatives. By estimating the cascaded channel in se￾quential stages, our approach effectively avoids the extremely large search grid that affects the conventional Direct-OMP and iterative SBL algorithms [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: NMSE versus pilot overhead. 1 2 3 4 J 10-5 10-4 10-3 10-2 10-1 100 101 102 NMSE Proposed-full,SNR=0dB,T=28,G=4 Proposed-full,SNR=0dB,T=14,G=4 Proposed-full,SNR=0dB,T=28,G=9 Proposed-full,SNR=0dB,T=14,G=9 Direct-OMP,SNR=0dB,T=28,G=4 Direct-OMP,SNR=0dB,T=14,G=4 SBL,SNR=0dB,T=14,G=4 SBL,SNR=0dB,T=28,G=4 [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: NMSE versus the number of user-RIS link J with SNR = 0 dB. The impact of the average number of pilot symbols T on the NMSE is depicted in [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
read the original abstract

Beyond diagonal reconfigurable intelligent surface (BD-RIS) represents a promising architecture for advancing millimeter-wave (mmWave) communications. However, its intricate inter-element connections invalidate the conventional decoupled mathematical structure, thereby severely complicating cascaded channel estimation. In this paper, we formulate a novel block-Kronecker-structured cascaded channel model for a \textit{group-connected} BD-RIS-aided multi-user (MU) mmWave system equipped with uniform planar arrays (UPAs). By exploiting the cascaded channel sparsity, an efficient three-stage estimation protocol is proposed. Specifically, Stage I acquires the common angles of arrival (AoAs) at the base station (BS) via a discrete Fourier transform (DFT)-based approach. Stage II leverages the block-Kronecker structure alongside orthogonal matching pursuit (OMP) and correlation-based least squares (LS) to extract the complete cascaded channel for a designated typical user. Finally, Stage III utilizes a Hierarchical Block OMP (HBOMP) algorithm to estimate the other users' channels. This structurally reconstructs the common and user-specific components, which fundamentally reduces the computational complexity and substantially reduces the pilot overhead. Numerical simulations verify that the proposed protocol yields improved channel estimation accuracy while maintaining a relatively low pilot overhead.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript formulates a block-Kronecker-structured cascaded channel model for a group-connected BD-RIS-aided multi-user mmWave system with UPAs and proposes a three-stage estimation protocol: Stage I uses DFT to acquire common BS AoAs, Stage II applies OMP and correlation-based LS to recover the full cascaded channel for a typical user, and Stage III employs HBOMP to estimate the remaining users' channels by reconstructing common and user-specific components. The central claim is that this sparsity-exploiting protocol improves channel estimation accuracy while keeping pilot overhead relatively low.

Significance. If the performance gains hold, the work would advance practical channel estimation for BD-RIS architectures, which suffer from complex inter-element connections that break conventional decoupled models. The explicit use of the block-Kronecker structure and hierarchical OMP for multi-user reconstruction is a constructive contribution that could reduce complexity; the simulations appear to demonstrate the overhead reduction under the tested conditions.

major comments (2)
  1. [§III] §III (Proposed Estimation Protocol), Stage II description: the OMP recovery on the block-Kronecker model assumes the cascaded channel remains sufficiently sparse after group connections; no analytical bound or RIP-style guarantee is provided on the minimum number of paths or maximum group size for which exact recovery holds, which is load-bearing for the claimed pilot-overhead reduction.
  2. [§IV] §IV (Numerical Simulations): the NMSE and overhead curves are generated with fixed sparsity levels and ideal UPA responses; without additional results for overlapping user angles, reduced SNR, or higher inter-group connectivity that could increase effective paths and degrade block separability, the generalization of the accuracy gain over conventional methods remains unestablished.
minor comments (2)
  1. The abstract states 'relatively low pilot overhead' without a quantitative comparison (e.g., percentage reduction versus LS or standard OMP baselines); adding one sentence with the exact overhead numbers from the simulations would improve clarity.
  2. [§II] Notation for the group-connected BD-RIS response matrix could be introduced earlier with an explicit equation reference to aid readers unfamiliar with the architecture.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help improve the clarity and robustness of our work. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [§III] §III (Proposed Estimation Protocol), Stage II description: the OMP recovery on the block-Kronecker model assumes the cascaded channel remains sufficiently sparse after group connections; no analytical bound or RIP-style guarantee is provided on the minimum number of paths or maximum group size for which exact recovery holds, which is load-bearing for the claimed pilot-overhead reduction.

    Authors: We acknowledge that a rigorous RIP-style guarantee for exact recovery under the block-Kronecker structure would provide stronger theoretical support. Deriving such bounds is complicated by the group-connection matrix and the cascaded nature of the channel; this analysis is left for future work. In the revised manuscript we have added a paragraph in §III-B discussing the sparsity preservation properties of the model and the practical conditions (maximum group size and path count) under which the OMP step succeeds, supported by additional numerical validation of recovery probability versus group size. revision: partial

  2. Referee: [§IV] §IV (Numerical Simulations): the NMSE and overhead curves are generated with fixed sparsity levels and ideal UPA responses; without additional results for overlapping user angles, reduced SNR, or higher inter-group connectivity that could increase effective paths and degrade block separability, the generalization of the accuracy gain over conventional methods remains unestablished.

    Authors: We agree that broader simulation scenarios would better demonstrate robustness. The revised §IV now includes three new sets of results: (i) performance under partially overlapping user AoAs, (ii) NMSE curves at lower SNR regimes (down to 0 dB), and (iii) cases with increased inter-group connectivity (larger effective path counts). These experiments confirm that the proposed three-stage protocol retains its accuracy and overhead advantages relative to the benchmarks. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the three-stage estimation protocol

full rationale

The paper derives a block-Kronecker-structured cascaded channel model for the group-connected BD-RIS architecture and applies standard DFT-based AoA estimation, OMP, correlation-based LS, and HBOMP to exploit assumed sparsity. These steps use established compressive sensing tools on the new structure without any quoted reduction of a prediction to a fitted parameter by construction, without load-bearing self-citations, and without renaming known results as novel derivations. The central claims rest on the stated sparsity assumption and numerical verification rather than self-referential definitions or imported uniqueness theorems from the same authors. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the sparsity of the cascaded channel and the validity of the group-connected BD-RIS architecture; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption The cascaded channel in the group-connected BD-RIS system exhibits sparsity that can be exploited by compressive sensing algorithms.
    Invoked to justify the use of OMP and HBOMP in stages II and III.

pith-pipeline@v0.9.0 · 5760 in / 1206 out tokens · 30950 ms · 2026-05-20T01:59:29.504057+00:00 · methodology

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Reference graph

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