Channel Estimation for Stacked Intelligent Metasurface-Assisted Wireless Networks
Open accessAbstract
Emerging technologies, such as holographic multiple-input multiple-output (HMIMO) and stacked intelligent metasurface (SIM), are driving the development of wireless communication systems. Specifically, the SIM is physically constructed by stacking multiple layers of metasurfaces and has an architecture similar to an artificial neural network (ANN), which can flexibly manipulate the electromagnetic waves that propagate through it at the speed of light. This architecture enables the SIM to achieve HMIMO precoding and combining in the wave domain, thus significantly reducing the hardware cost and energy consumption. In this letter, we investigate the channel estimation problem in SIM-assisted multi-user HMIMO communication systems. Since the number of antennas at the base station (BS) is much smaller than the number of meta-atoms per layer of the SIM, it is challenging to acquire the channel state information (CSI) in SIM-assisted multi-user systems. To address this issue, we collect multiple copies of the uplink pilot signals that propagate through the SIM. Furthermore, we leverage the array geometry to identify the subspace that spans arbitrary spatial correlation matrices. Based on partial CSI about the channel statistics, a pair of subspace-based channel estimators are proposed. Additionally, we compute the mean square error (MSE) of the proposed channel estimators and optimize the phase shifts of the SIM to minimize the MSE. Numerical results are illustrated to analyze the effectiveness of the proposed channel estimation schemes.
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Installing a SIM on a LEO satellite would significantly reduce the processing delay and computing load of the satellite compared to traditional digital beamforming methods.
“This would significantly reduce the processing delay and computing load of the satellite compared to traditional digital beamforming methods.”
From Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications (2026) · cites this paper as [91]
The Introduction states that an SIM greatly reduces precoding delay compared with its digital counterpart and decreases the number of RF chains. It does not address installation on a LEO satellite or establish a reduction in the satellite’s computing load; the system studied uses a base station and user equipment. (LLM, conf=0.87)
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Cites
All-optical machine learning using diffractive deep neural networks
Lin, X., Rivenson, Y., Yardimci, N. T., Veli, M., Luo, Y., Jarrahi, M., & Ozcan, A. (2018) · Science · doi:10.1126/science.aat8084 · Cited by 2,568 · see citing works
A programmable diffractive deep neural network based on a digital-coding metasurface array
Liu, C., Ma, Q., Luo, Z. J., Hong, Q. R., Xiao, Q., Zhang, H. C., Miao, L., Yu, W. M., Cheng, Q., Li, L., et al. (2022) · Nature Electronics · doi:10.1038/s41928-022-00719-9 · Cited by 633 · see citing works
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Research works printed but not linked: 22
- J. An, C. Yuen, L. Dai, M. Di Renzo, M. Debbah, and L. Hanzo, "Toward beamfocusing-aided near-field communications: Research advances, potential, and challenges," arXiv preprint arXiv:2309.09242, 2023. · arXiv
- C.-X. Wang, X. You, X. Gao et al., "On the road to 6G: Visions, requirements, key technologies and testbeds," IEEE Commun. Surv. Tutor., vol. 25, no. 2, pp. 905-974, Feb. 2023.
- F. Tang, X. Chen, M. Zhao, and N. Kato, "The roadmap of communication and networking in 6G for the metaverse," IEEE Wireless Commun., vol. 30, no. 4, pp. 72-81, Aug. 2023.
- J. An, C. Yuen, C. Huang et al., "A tutorial on holographic MIMO communications-part I: Channel modeling and channel estimation," IEEE Commun. Lett., vol. 27, no. 7, pp. 1664-1668, Jul. 2023.
- A. Pizzo, L. Sanguinetti, and T. L. Marzetta, "Fourier plane-wave series expansion for holographic MIMO communications," IEEE Trans. Wireless Commun., vol. 21, no. 9, pp. 6890-6905, Sep. 2022.
- J. An, C. Yuen, C. Xu, H. Li, D. W. K. Ng, M. Di Renzo, M. Debbah, and L. Hanzo, "Stacked intelligent metasurface-aided mimo transceiver design," arXiv preprint arXiv:2311.09814, 2023. · arXiv
- R. Deng, Y. Zhang, H. Zhang et al., "Reconfigurable holographic surface: A new paradigm to implement holographic radio," IEEE Veh. Technol. Mag., vol. 18, no. 1, pp. 20-28, Mar. 2023.
- C. Huang, S. Hu, G. C. Alexandropoulos et al., "Holographic MIMO surfaces for 6G wireless networks: Opportunities, challenges, and trends," IEEE Wireless Commun., vol. 27, no. 5, pp. 118-125, Oct. 2020.
- J. An, M. Di Renzo, M. Debbah, and C. Yuen, "Stacked intelligent metasurfaces for multiuser beamforming in the wave domain," in Proc. IEEE Int. Conf. Commun. (ICC), Rome, Italy, May. 2023, pp. 1-6.
- J. An, C. Xu, D. W. K. Ng et al., "Stacked intelligent metasurfaces for efficient holographic MIMO communications in 6G," IEEE J. Sel. Areas Commun., vol. 41, no. 8, pp. 2380-2396, Aug. 2023.
- J. An, M. Di Renzo, M. Debbah, H. V. Poor, and C. Yuen, "Stacked intelligent metasurfaces for multiuser downlink beamforming in the wave domain," arXiv preprint arXiv:2309.02687, 2023. · arXiv
- X. Peng, L. Zhao, Y. Jiang et al., "Channel estimation for extremely large-scale massive MIMO systems in hybrid-field channel," in 2023 IEEE/CIC International Conference on Communications in China (ICCC). IEEE, Aug. 2023, pp. 1-6.
- M. Di Renzo, A. Zappone, M. Debbah et al., "Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead," IEEE J. Sel. Areas Commun., vol. 38, no. 11, pp. 2450-2525, Nov. 2020.
- J. An, C. Yuen, Y. L. Guan, M. Di Renzo, M. Debbah, H. V. Poor, and L. Hanzo, "Two-dimensional direction-of-arrival estimation using stacked intelligent metasurfaces," arXiv preprint arXiv:2402.08224, 2024. · arXiv
- D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge university press, 2005.
- Ö. T. Demir, E. Björnson, and L. Sanguinetti, "Channel modeling and channel estimation for holographic massive MIMO with planar arrays," IEEE Wireless Commun. Lett., vol. 11, no. 5, pp. 997-1001, Feb. 2022.
- C. Wei, H. Jiang, J. Dang et al., "Accurate channel estimation for mmwave massive MIMO with partially coherent phase offsets," IEEE Commun. Lett., vol. 26, no. 9, pp. 2170-2174, Sep. 2022.
- E. Björnson and L. Sanguinetti, "Rayleigh fading modeling and channel hardening for reconfigurable intelligent surfaces," IEEE Wireless Commun. Lett., vol. 10, no. 4, pp. 830-834, Dec. 2020.
- M. Biguesh and A. B. Gershman, "Training-based MIMO channel estimation: A study of estimator tradeoffs and optimal training signals," IEEE Trans. Signal Process., vol. 54, no. 3, pp. 884-893, Mar. 2006.
- Q.-U.-A. Nadeem, J. An, and A. Chaaban, "Hybrid digital-wave domain channel estimator for stacked intelligent metasurface enabled multi-user MISO systems," arXiv preprint arXiv:2309.16204, Sep. 2023. · arXiv
- J. An, C. Xu, Q. Wu, D. W. K. Ng, M. D. Renzo, C. Yuen, and L. Hanzo, "Codebook-based solutions for reconfigurable intelligent surfaces and their open challenges," IEEE Wireless Communications, pp. 1-8, 2022, Early Access.
- J. An, C. Xu, L. Gan, and L. Hanzo, "Low-complexity channel estimation and passive beamforming for RIS-assisted MIMO systems relying on discrete phase shifts," IEEE Trans. Commun., vol. 70, no. 2, pp. 1245-1260, Feb. 2022.
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Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications
An, J., Debbah, M., Cui, T. J., Chen, Z. N., & Yuen, C. (2026) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2025.3571069 · Cited by 72 · see citing works
“To tackle this challenge, Yao et al. [91] investigated channel estimation for SIM-assisted multiuser HMIMO communication systems.”
Self-citationDarsena, D., Verde, F., Iudice, I., & Galdi, V. (2025) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2025.3526126 · Cited by 21 · see citing works
Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications
An, J., Debbah, M., Cui, T. J., Chen, Z. N., & Yuen, C. (2024) · arXiv · Cited by 72 · see citing works
“To tackle this challenge, Yao et al. [91] investigated channel estimation for SIM-assisted multiuser HMIMO communication systems.”
Self-citation
- Authors
- Yao, X., An, J., Gan, L., Di Renzo, M., & Yuen, C.
- Affiliations
- University of Electronic Science and Technology of China (CN)
- Nanyang Technological University (SG)
- Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, Gif-sur-Yvette, France
- Venue
- IEEE Wireless Communications Letters
- Published
- 2024-05
- Volume
- 13
- Issue
- 5
- Pages
- 1349-1353
- ISSN
- 2162-2337 (ISSN-L)
- 2162-2345
- OpenAlex
- W4392151992
- Cited by
- 61
- References
- 2
- Citations by year
- 2026: 19 · 2025: 37 · 2024: 5
- FWCI
- 6.33
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE Wireless Communications Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- DR-NTU (Nanyang Technological University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Sichuan Science and Technology Program (2023YFSY0008, 2023YFG0291)
- Yibin Science and Technology Program (YBP-002)
- Horizon Europe Projects (COVER-101086228, UNITE-101129618, INSTINCT-101139161)
- ANR Projects (NF-PERSEUS 22-PEFT-004, PASSIONATE ANR-23-CHR4-0003-01)
- Ministry of Education, Singapore, under its MOE Tier 2 (MOE-T2EP50220-0019)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Wireless Communication Technologies
- Physical Sciences › Engineering › Aerospace Engineering › Advanced Antenna and Metasurface Technologies
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Millimeter-Wave Propagation and Modeling
- Keywords
- stacked intelligent metasurfaces, channel estimation, holographic MIMO, multi-user MIMO, subspace-based estimation, spatial correlation matrix, phase shift optimization, channel state information
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