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Two-Dimensional Direction-of-Arrival Estimation Using Stacked Intelligent Metasurfaces
Open accessAbstract
Stacked intelligent metasurfaces (SIMs) are capable of emulating reconfigurable physical neural networks by utilizing electromagnetic (EM) waves as carriers. They can also perform various complex computational and signal processing tasks. An SIM is constructed by densely integrating multiple metasurface layers, each consisting of a large number of small meta-atoms that can control the EM waves passing through it. In this paper, we harness an SIM for two-dimensional (2D) direction-of-arrival (DOA) estimation. In contrast to conventional designs, an advanced SIM in front of a receiver array can be designed to automatically compute the 2D discrete Fourier transform (DFT) as the incident waves propagate through it. As a result, a receiver array can directly observe the angular spectrum of the incoming signal, and it can estimate the DOA by simply using probes to detect the energy distribution on the receiver array. This avoids the need for power inefficient radio frequency chains. To enable an SIM to perform the 2D DFT in the wave domain, we formulate an optimization problem that minimizes the mean square error (MSE) between the SIM’s EM response and the 2D DFT matrix. Then, a gradient descent algorithm is customized for iteratively updating the phase shift applied by each meta-atom of the SIM. To further improve the DOA estimation accuracy, we configure the phase shifts of the input layer of the SIM to generate a set of 2D DFT matrices associated with orthogonal spatial frequency bins. Additionally, we analytically evaluate the performance of the proposed SIM-based DOA estimator by deriving a tight upper bound for the MSE. Extensive numerical simulations verify the capability of an optimized SIM to perform DOA estimation and corroborate the theoretical analysis. Specifically, we show that an SIM is capable of performing DOA estimation with an MSE of the order of$10^{-4}$.
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“Recent prototypes have demonstrated SIMs with impressive capabilities for applications such as MIMO beamforming [25], radar sensing [26], and image classification [27].”
From Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications (2026) · cites this paper as [26]
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“By properly configuring the transmission coefficients of the meta-atoms on each metasurface, a SIM becomes capable of automatically accomplishing various advanced computation and signal processing tasks as EM waves propagate through the layered structure at the speed of light [25], [26].”
From Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications (2026) · cites this paper as [26]
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“The field response impinging on each layer is the weighted sum of the diffracted fields from the meta-atoms on the previous layer, with the weight coefficient determined by the product of the complex-valued transmission coefficients and corresponding propagation coefficients [25], [26].”
From Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications (2026) · cites this paper as [26]
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“Numerical simulations have confirmed that an optimized SIM can perform DOA estimation with remarkable speed and accuracy, achieving an MSE of -40 dB.”
From Emerging Technologies in Intelligent Metasurfaces: Shaping the Future of Wireless Communications (2026) · cites this paper as [26]
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Metadata
- Authors
- An, J., Yuen, C., Guan, Y. L., Renzo, M. D., Debbah, M., Poor, H. V., & Hanzo, L.
- Affiliations
- Nanyang Technological University (SG)
- Centre National de la Recherche Scientifique (FR)
- Center for 6G Technology, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates
- Princeton University (US)
- University of Southampton (GB)
- ORCID
- Venue
- IEEE Journal on Selected Areas in Communications
- Published
- 2024-10
- Volume
- 42
- Issue
- 10
- Pages
- 2786-2802
- ISSN
- 0733-8716 (ISSN-L)
- 1558-0008
- OpenAlex
- W4399666068
- Cited by
- 125
- References
- 39
- Citations by year
- 2026: 37 · 2025: 65 · 2024: 23
- FWCI
- 21.57
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE Journal on Selected Areas in Communications (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- ePrints Soton (University of Southampton) (submittedVersion)
- DR-NTU (Nanyang Technological University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Ministry of Education, Singapore, under its MOE Tier 2 (MOE-T2EP50220-0019)
- National Research Foundation Singapore
- Infocomm Media Development Authority under its Future Communications Research and Development Program
- European Commission through the Horizon Europe projects titled COVER (101086228)
- Università degli Studi di Teramo (101129618)
- INSTINCT (101139161)
- Agence Nationale de la Recherche (ANR) through the France 2030 Project titled ANR-PEPR Networks of the Future (NF-YACARI 22-PEFT-0005)
- CHIST-ERA Project titled PASSIONATE (CHIST-ERA-22-WAI-04, ANR-23-CHR4-0003-01)
- National Science Foundation (CNS-2128448)
- Engineering and Physical Sciences Research Council (EP/W016605/1, EP/X01228X/1, EP/Y026721/1, EP/W032635/1)
- European Research Council’s Advanced Fellow Grant QuantCom (789028)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Antenna and Metasurface Technologies
- Physical Sciences › Computer Science › Signal Processing › Direction-of-Arrival Estimation Techniques
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Wireless Communication Technologies
- Keywords
- stacked intelligent metasurfaces, direction of arrival estimation, two-dimensional DOA estimation, two-dimensional discrete Fourier transform, receiver array, angular spectrum, reconfigurable neural networks, meta-atoms
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