Efficient Beamforming and Radiation Pattern Control Using Stacked Intelligent Metasurfaces
Open accessAbstract
In this paper, we consider a stacked intelligent metasurface (SIM) with the ability to perform beamforming in the electromagnetic (EM) wave domain. We develop a path-loss model that allows us to compute the received power of the signal after passing through the SIM. Based on the proposed path-loss model, we formulate an optimization problem to maximize the power at a desired target location in space. We develop a gradient ascent algorithm that can be applied when the phases of the meta-atoms of the SIM can be continuously varied. Also, we develop an alternating optimization (AO) algorithm for the same problem when the meta-atoms can only apply discrete phase shifts. In addition, we formulate an optimization problem whose objective is to produce a given target radiation pattern on a 2D plane located at a certain distance from the center of the SIM. The corresponding algorithms for the continuous and discrete values for the transmission coefficients applied by the SIM are provided. We show that, thanks to the use of multiple layers, complex target radiation patterns in a 2D plane are easily generated. For continuous-valued transmission coefficients, more than 90% of the radiated power is concentrated at the desired points with only three layers. For discrete-valued transmission coefficients with two phase shifts, we show, on the other hand, that nine layers are required to concentrate 90% of the power towards the desired locations. Compared to a single-layer SIM, notably, the power ratio increases by almost 50% by using only three layers.
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Niu et al. [107]'s simulation results confirmed the effectiveness of SIM in achieving PLS with low complexity.
“Simulation results confirmed the effectiveness of SIM in achieving PLS with low complexity.”
From Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications (2026) · cites this paper as [107]
The Simulation Results and Conclusion report that simulations demonstrated SIM's ability to control radiated power. They do not report a physical-layer security (PLS) outcome, and the paper notes that computational complexity increases with the number of discrete meta-atom states. Thus, the claimed PLS effectiveness with low complexity is not established by this source. (LLM, conf=0.84)
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Research works printed but not linked: 22
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Cited by
Sorted by citations
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, it requires further investigation to characterize the fundamental tradeo ff between the power loss of EM signals as they pass through the multiple metasurface layers and the benefit of increased depth.”
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
“In addition, it requires further investigation to characterize the fundamental tradeo ff between the power loss of EM signals as they pass through the multiple metasurface layers and the benefit of increased depth.”
Self-citation
- Authors
- Hassan, N. U., An, J., Di Renzo, M., Debbah, M., & Yuen, C.
- Affiliations
- Lahore University of Management Sciences (PK)
- Nanyang Technological University (SG)
- Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systemes, Gif-sur-Yvette, France
- Computer & Communication Engineering Department, College of Computing and Mathematical Sciences, Khalifa University of Science and Technology, Abu Dhabi, UAE
- Venue
- IEEE Open Journal of the Communications Society
- Published
- 2024
- Volume
- 5
- Pages
- 599-611
- ISSN
- 2644-125X (ISSN-L)
- OpenAlex
- W4390491928
- Cited by
- 55
- References
- 2
- Citations by year
- 2026: 16 · 2025: 28 · 2024: 11
- FWCI
- 9.50
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- IEEE Open Journal of the Communications Society (publishedVersion, cc-by-nc-nd)
- HAL (submittedVersion, cc-by-nc-nd)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- DR-NTU (Nanyang Technological University) (submittedVersion, cc-by-nc-nd)
- Funders
- Ministry of Education, Singapore, under its MOE Tier 2 (MOE-T2EP50220-0019)
- Science and Engineering Research Council of Agency for Science, Technology and Research (A*STAR), Singapore (M22L1b0110)
- LUMS Faculty Initiative Fund
- European Commission through the Horizon Europe Project titled COVER (101086228)
- Horizon Europe Project titled UNITE (101129618)
- Horizon Europe Project titled INSTINCT (101139161)
- Agence Nationale de la Recherche through the France 2030 Project titled ANR-PEPR Networks of the Future (NF-SYSTERA 22-PEFT-0006)
- ANR-CHISTERA Project titled PASSIONATE (ANR-23-CHR4-0003-01)
- Topics
- Physical Sciences › Engineering › Aerospace Engineering › Advanced Antenna and Metasurface Technologies
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Wireless Communication Technologies
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- stacked intelligent metasurfaces, beamforming, radiation pattern control, path loss model, received power maximization, gradient ascent algorithm, alternating optimization, discrete phase shifts, continuous phase shift, meta-atoms
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