Design of Stacked Intelligent Metasurfaces With Reconfigurable Amplitude and Phase for Multiuser Downlink Beamforming
Open accessAbstract
A novel technology based on stacked intelligent metasurfaces (SIM) has recently emerged. This platform involves cascading multiple metasurfaces, each acting as a digitally programmable physical layer within a diffractive neural network. SIM enable the implementation of signal-processing transformations directly in the electromagnetic wave domain, eliminating the need for expensive, high-precision, and power-intensive digital platforms. However, existing studies employing SIM in wireless communication applications rely solely on nearly passive structures that control only the phase of the meta-atoms in each layer. In this study, we propose a SIM-aided downlink multiuser transmission scheme, where the SIM at the base station (BS) end is designed by combining nearly passive layers with phase-only reconfiguration capabilities and active layers integrated with amplifier chips to enable amplitude control. Our optimal design aims at maximizing the sum rate for the best group of users by jointly optimizing the transmit power allocation at the BS and the wave-based beamforming at the SIM. In addition to the standard sum-power constraint at the BS, our optimization framework includes two additional constraints: (i) a per-stream power preserving constraint to prevent propagation losses across the SIM, and (ii) an amplitude constraint to account for power limitations for each active layer. To further reduce the complexity of the optimal beamforming solution, we explore a simple yet suboptimal zero-forcing (ZF) beamforming design, where the wave-based transformation implemented by the SIM is selected to eliminate interference among user streams. Finally, extensive Monte Carlo simulations demonstrate that incorporating both nearly passive and active layers within the SIM significantly enhances capacity compared to previously reported phase-only coding SIM. Additionally, the numerical results reveal that low-complexity ZF beamforming approaches optimality in terms of maximum sum rate even for a relatively small number of users.
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Darsena et al. enhanced channel capacity by inserting active layers with amplifier chips to tune both phase and amplitude.
“Additionally, Darsena et al. [82] enhanced channel capacity by inserting active layers with amplifier chips to tune both phase and amplitude.”
From Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications (2026) · cites this paper as [82]
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LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126 · see citing works
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601 · see citing works
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 25,760 · see citing works
Fundamentals of Wireless Communication
Tse, D., & Viswanath, P. (2005) · doi:10.1017/cbo9780511807213 · Cited by 13,162 · see citing works
Energy and spectral efficiency of very large multiuser MIMO systems
Ngo, H. Q., Larsson, E. G., & Marzetta, T. L. (2013) · IEEE Transactions on Communications · doi:10.1109/tcomm.2013.020413.110848 · Cited by 3,173 · see citing works
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
On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming
Taesa, & Goldsmith, A. J. (2006) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2005.862421 · Cited by 2,118 · see citing works
Marzetta, T. L., Larsson, E. G., Yang, H. B., & Ngo, H. Q. (2016) · Cambridge University Press eBooks · doi:10.1017/cbo9781316799895 · Cited by 1,725 · see citing works
Wu, Q., & Zhang, R. (2019) · IEEE Transactions on Communications · doi:10.1109/tcomm.2019.2958916 · Cited by 1,295 · see citing works
Why future supercomputing requires optics
Caulfield, H. J., & Dolev, S. (2010) · Nature Photonics · doi:10.1038/nphoton.2010.94 · Cited by 772 · 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
Sum Power Iterative Water-Filling for Multi-Antenna Gaussian Broadcast Channels
Jindal, N., Rhee, W., Vishwanath, S., Jafar, S. A., & Goldsmith, A. J. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.844082 · Cited by 617 · see citing works
Introduction to Fourier Optics
Goodman, J. W., & Cox, M. E. (1969) · Physics Today · doi:10.1063/1.3035549 · Cited by 467 · see citing works
On the Duality of Gaussian Multiple-Access and Broadcast Channels
Jindal, N., Vishwanath, S., & Goldsmith, A. J. (2004) · IEEE Transactions on Information Theory · doi:10.1109/tit.2004.826646 · Cited by 443 · see citing works
Stacked Intelligent Metasurfaces for Efficient Holographic MIMO Communications in 6G
An, J., Xu, C., Ng, D. W. K., Alexandropoulos, G. C., Huang, C., Yuen, C., & Hanzo, L. (2023) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2023.3288261 · Cited by 358 · see citing works
Introduction to Nonlinear Optimization
Beck, A. (2014) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611973655 · Cited by 298 · see citing works
Two-Dimensional Direction-of-Arrival Estimation Using Stacked Intelligent Metasurfaces
An, J., Yuen, C., Guan, Y. L., Renzo, M. D., Debbah, M., Poor, H. V., & Hanzo, L. (2024) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2024.3414613 · Cited by 125 · see citing works
Stacked Intelligent Metasurfaces for Multiuser Beamforming in the Wave Domain
An, J., Renzo, M. D., Debbah, M. A., & Yuen, C. (2023) · International Conference on Communications · doi:10.1109/icc45041.2023.10279173 · Cited by 106 · see citing works
Efficient Asymmetric Transmission of Elastic Waves in Thin Plates with Lossless Metasurfaces
Li, B., Hu, Y., Chen, J., Su, G., Liu, Y., Zhao, M., & Li, Z. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.14.054029 · Cited by 97 · see citing works
Liao, J., Guo, S., Yuan, L., Ji, C., Huang, C. H., & Luo, X. (2021) · Advanced Optical Materials · doi:10.1002/adom.202101551 · Cited by 95 · see citing works
Stacked Intelligent Metasurface Enabled LEO Satellite Communications Relying on Statistical CSI
Lin, S., An, J., Gan, L., Debbah, M. A., & Yuen, C. (2024) · IEEE Wireless Communications Letters · doi:10.1109/lwc.2024.3368238 · Cited by 80 · see citing works
Nerini, M., & Clerckx, B. (2024) · IEEE Communications Letters · doi:10.1109/lcomm.2024.3401580 · Cited by 76 · see citing works
Channel Estimation for Stacked Intelligent Metasurface-Assisted Wireless Networks
Yao, X., An, J., Gan, L., Di Renzo, M., & Yuen, C. (2024) · IEEE Wireless Communications Letters · doi:10.1109/lwc.2024.3369874 · Cited by 61 · see citing works
Stacked Intelligent Metasurfaces for Wireless Communications: Applications and Challenges
Liu, H., An, J., Jia, X., Gan, L., Karagiannidis, G. K., Clerckx, B., Bennis, M., Debbah, M., & Cui, T. J. (2024) · arXiv · doi:10.48550/arxiv.2407.03566 · Cited by 57 · see citing works
Efficient Beamforming and Radiation Pattern Control Using Stacked Intelligent Metasurfaces
Hassan, N. U., An, J., Di Renzo, M., Debbah, M., & Yuen, C. (2024) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2023.3349155 · Cited by 55 · see citing works
Review of diffractive deep neural networks
Sun, Y., Dong, M., Yu, M., Liu, X., & Zhu, L. (2023) · Journal of the Optical Society of America B · doi:10.1364/josab.497148 · Cited by 40 · see citing works
DRL-Based Orchestration of Multi-User MISO Systems with Stacked Intelligent Metasurfaces
Liu, H., An, J., Ng, D. W. K., Alexandropoulos, G. C., & Gan, L. (2024) · International Conference on Communications · doi:10.1109/icc51166.2024.10622385 · Cited by 36 · see citing works
Menzel, C., Sperrhake, J., & Pertsch, T. (2016) · Physical Review A · doi:10.1103/physreva.93.063832 · Cited by 32 · see citing works
Lim, Q. J., Ross, C., Ghosh, A., Vook, F. W., Gradoni, G., & Peng, Z. (2023) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2023.3298134 · Cited by 31 · see citing works
DRL-Based Orchestration of Multi-User MISO Systems with Stacked Intelligent Metasurfaces
Liu, H., An, J., Ng, D. W. K., Alexandropoulos, G. C., & Gan, L. (2024) · arXiv · doi:10.48550/arxiv.2402.09006
Flagged first, then by citations
Research works printed but not linked: 1
- [23][23] S.M. Kay, Fundamentals of Statistical Signal Processing, Vol. 2: Detection Theory . Prentice Hall PTR, 1998. -
Cited by
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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
“In addition, Darsena et al. [82] enhanced the channel capacity by inserting active layers with amplifier chips to tune both phase and amplitude.”
Arnaoutoglou, D. G., Empliouk, T. M., Kaifas, T. N. F., Zekios, C. L., & Kyriacou, G. A. (2025) · Future Internet · doi:10.3390/fi17060249 · Cited by 22 · see citing works
Renzo, M. D. (2025) · European Conference on Antennas and Propagation · doi:10.23919/eucap63536.2025.10999805 · Cited by 10 · see citing works
Max-Min Fairness for Stacked Intelligent Metasurface-Assisted Multi-User MISO Systems
Ginige, N., Dharmawansa, P., de Sena, A. S., Mahmood, N. H., Rajatheva, N., & Latva‐aho, M. (2025) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2025.3583850 · Cited by 5 · see citing works
SIM-Enabled Hybrid Digital-Wave Beamforming for Fronthaul-Constrained Cell-Free Massive MIMO Systems
Park, E., Park, S.-H., Simeone, O., Renzo, M. D., & Shamai, S. S. (2025) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2025.3628306 · Cited by 5 · see citing works
SIM-IPS: Stacked Intelligent Metasurface-Based Indoor Positioning System
Javed, A., Hassan, N. U., Renzo, M. D., & Yuen, C. (2025) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2025.3559946 · Cited by 4 · see citing works
Stacked Intelligent Metasurface-Enabled Satellite Integrated Sensing and Communications Systems
Jiang, C., Yuan, H., Zhang, C., An, J., Huang, C., & Yuen, C. (2025) · IEEE Wireless Communications Letters · doi:10.1109/lwc.2025.3639287 · Cited by 4 · see citing works
Jia, X., Liu, H., Niu, H., Li, J., Ding, X., & Gan, L. (2026) · IEEE Wireless Communications · doi:10.1109/mwc.2026.3670305 · Cited by 4 · see citing works
An, J., Yuen, C., Renzo, M. D., Bennis, M., Debbah, M. A., & Hanzo, L. (2026) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2026.3720502 · Cited by 4 · see citing works
Stacked Intelligent Metasurfaces-Based Electromagnetic Wave Domain Interference-Free Precoding
Wang, H., Cao, Y., Lv, T., Wang, J., Wei, N., An, J., & Yuen, C. (2026) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2026.3656012 · Cited by 3 · see citing works
Transmit Power Minimization in Stacked Intelligent Metasurface-Aided Multi-User Systems
Niu, H., An, J., Lin, S., Gan, L., Matthaiou, M., & Chatzinotas, S. (2025) · Globecom · doi:10.1109/globecom59602.2025.11432150 · Cited by 1 · 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
“In addition, Darsena et al. [82] enhanced the channel capacity by inserting active layers with amplifier chips to tune both phase and amplitude.”
Intelligent Transmission Control Scheme for 5G mmWave Networks Employing Hybrid Beamforming
Hatamleh, H., Alnaser, A. M. A., Aloglah, R. M. A., Bani-Ata, T. J., Ramadan, A. M., & Alzoubi, O. R. A. (2025) · Future Internet · doi:10.3390/fi17070277
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Kaifas, T. N. F., Babas, D. G., Boursianis, A. D., & Sahalos, J. N. (2025) · International Conference on Modern Circuits and Systems Technologies · doi:10.1109/mocast65744.2025.11083731
Remote Signal DOA Estimation Using Active Stacked-Intelligent-Metasurface
Jiang, G., Chen, S., Wu, W., & Wang, W. (2026) · IEEE Communications Letters · doi:10.1109/lcomm.2026.3677209
Optimization of Active RIS Configurations in SIM Architectures With Mutual Coupling
Mandalika, H., Singh, S., Rosyidah, A., Singh, K. K., & Shin, H. (2026) · IEEE Wireless Communications Letters · doi:10.1109/lwc.2026.3677379
Pattern Reconfigurable Intelligent Surfaces to Enable "Circuits-in-the-air" for Wireless Radios
Liao, S., Pandey, D., Chi, T., Swami, A., & Sabharwal, A. (2025) · Asilomar Conference on Signals, Systems and Computers (ACSSC) · doi:10.1109/ieeeconf67917.2025.11443676
AI-Driven Design of Stacked Intelligent Metasurfaces for Software-Defined Radio Applications
Iudice, I., Gelli, G., & Darsena, D. (2026) · IEEE Aerospace Conference (AERO) · doi:10.1109/aero66936.2026.11519851
Self-citationOpportunistic beamforming with space-time stacked intelligent metasurfaces under partial CSI
Darsena, D., Iudice, I., Galdi, V., & Verde, F. (2026) · International Conference on Communications · doi:10.1109/icc59461.2026.11587089
Self-citationMustafa, M. I., & Osman Nuri, U. C. A. N. (2026) · Discover Computing · doi:10.1007/s10791-026-10407-3
Niu, H., An, J., Shi, E., Li, Z., Gan, L., Zhang, J., Chatzinotas, S., & Yuen, C. (2026) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2026.3729450
Wang, S., Song, X., An, J., Song, T., Soong, B., Yang, Y., & Yuen, C. (2026) · IEEE Transactions on Communications · doi:10.1109/tcomm.2026.3731768
Sun, Y., Wang, L., Meng, F., Li, B., Lu, W., & Li, C. (2026) · Mobile Networks and Applications · doi:10.1007/s11036-026-02551-3
- Authors
- Darsena, D., Verde, F., Iudice, I., & Galdi, V.
- Affiliations
- University of Naples Federico II (IT)
- Italian Aerospace Research Centre (IT)
- University of Sannio (IT)
- Venue
- IEEE Open Journal of the Communications Society
- Published
- 2025
- Volume
- 6
- Pages
- 531-550
- ISSN
- 2644-125X (ISSN-L)
- OpenAlex
- W4406046883
- Cited by
- 21
- References
- 29
- Citations by year
- 2026: 10 · 2025: 11
- FWCI
- 4.73
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- IEEE Open Journal of the Communications Society (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- Funders
- European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on ``Telecommunications of the Future" (PE00000001 - program ``RESTART")
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Wireless Communication Technologies
- Physical Sciences › Engineering › Aerospace Engineering › Advanced Antenna and Metasurface Technologies
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- stacked intelligent metasurfaces, transmit power allocation, sum rate maximization, zero-forcing beamforming, interference cancellation, diffractive neural networks, wireless communication capacity
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