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 capabilities for MIMO beamforming, radar sensing, and image classification.
“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]
The paper studies SIM-based direction-of-arrival estimation, which is relevant to radar sensing. Its radar discussion describes probing ground targets as a potential application, while the performance section reports simulations; it does not demonstrate a radar-sensing prototype. The separate MIMO and image-classification citations are not attributed to this source. (LLM, conf=0.87)
Experimental — accuracy not yet measuredBy properly configuring the transmission coefficients of the meta-atoms on each metasurface, a SIM can automatically accomplish various advanced computation and signal processing tasks as electromagnetic waves propagate through the layered structure at the speed of light.
“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]
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.
“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]
Numerical simulations have confirmed that an optimized SIM can perform DOA estimation with remarkable speed and accuracy, achieving an MSE of -40 dB.
“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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Self-citationWireless Localization With Space–Time-Coded Reconfigurable Intelligent Surfaces
Gholami, M., Khajavi, S., Neshat, M., Tewes, S., & Sezgin, A. (2025) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2025.3569392 · Cited by 6 · see citing works
Fu, Y., Li, Y., Fu, X., Xu, L. T., Liu, Y., Zhou, Q. Y., Yang, J. G., Han, C. Z., Dai, J. Y., Cheng, Q., et al. (2025) · Engineering · doi:10.1016/j.eng.2025.08.040 · Cited by 6 · see citing works
Tang, A., Wang, J.-B., Pan, Y., Zeng, C., Chen, Y., Yu, H., Xiao, M., de Lamare, R. C., & Wang, J. (2025) · IEEE Transactions on Communications · doi:10.1109/tcomm.2025.3564724 · Cited by 6 · see citing works
Continuous-Aperture Array for Integrated Sensing and Communication: Rate-CRB Tradeoff
Zhang, Y., Shan, H., Ouyang, C., Liu, Y., Shi, Z., Dong, L. R., & Hou, F. (2025) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2025.3609401 · Cited by 5 · see citing works
Nerini, M., & Clerckx, B. (2025) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2025.3641053 · Cited by 5 · see citing works
Multi-Layer RIS on Edge: Communication, Computation and Wireless Power Transfer
Chen, S., Jia, J., Zhang, B., Hui, Y., Qin, Y., Meng, W., & Xu, T. (2025) · IEEE Internet of Things Magazine · doi:10.1109/iotm.001.2400191 · Cited by 5 · see citing works
Zhao, H., Shi, Y., He, W., Sun, H., Wang, H., Liu, J., & Gui, L. (2025) · Digital Signal Processing · doi:10.1016/j.dsp.2025.105619 · Cited by 5 · see citing works
Efficient and Physically Consistent Modeling of Reconfigurable Electromagnetic Structures
Stutz-Tirri, A., Schwan, G., & Studer, C. (2025) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2025.3542621 · Cited by 5 · see citing works
Near-Field Localization With Limited RF Chains: An Array Partitioning Approach
Teng, B., Yuan, X., & Wang, R. (2024) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2024.3457241 · Cited by 4 · see citing works
B, A. G. A., & Babu, N. V. (2025) · International Conference on Integrated Circuits and Communication Systems (ICICACS) · doi:10.1109/icicacs65178.2025.10967677 · Cited by 4 · see citing works
Aliyu, K. N., Lawal, A., Alawsh, S. A., Zerguine, A., Muqaibel, A. H., & Iqbal, N. (2025) · Arabian Journal for Science and Engineering · doi:10.1007/s13369-025-10203-z · Cited by 4 · see citing works
Hu, C., Zhang, R., Chen, G., Luo, X., Guan, X., & Yuen, C. (2025) · IEEE Wireless Communications Letters · doi:10.1109/lwc.2025.3598026 · Cited by 4 · see citing works
Self-citationStacked Intelligent Metasurface for Simultaneous Wireless Information and Power Transfer
Amiri, M. P., Javadi, S., Zarini, H., Mili, M. R., An, J., Sookhak, M., & Krikidis, I. (2025) · International Conference on Communications · doi:10.1109/icc52391.2025.11161741 · Cited by 4 · see citing works
Self-citationOn the Orchestration of SIM and UAV
Zarini, H., Kazemi, S. M., An, J., Sookhak, M., & Choi, J. (2025) · International Conference on Communications · doi:10.1109/icc52391.2025.11161971 · Cited by 4 · see citing works
Self-citationGuo, S., Zhang, Q., Fu, X., Zheng, G., & Zhou, H. (2025) · Digital Signal Processing · doi:10.1016/j.dsp.2025.105627 · 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
Self-citationDownlink Sum-Rate Maximization for Joint Active and Passive Stacked Intelligent Metasurfaces
Darsena, D., Verde, F., Iudice, I., & Galdi, V. (2024) · IEEE Virtual Conference on Communications (VCC) · doi:10.1109/vcc63113.2024.10914484 · Cited by 3 · see citing works
Stacked Intelligent Metasurfaces: Key Technologies, Scenario Adaptation, and Future Directions
Liu, J., & Kong, J. (2026) · Electronics · doi:10.3390/electronics15020274 · Cited by 3 · see citing works
Generative AI-Enhanced Low-Altitude UAV-Mounted Stacked Intelligent Metasurfaces
Sun, G., Fan, M., Zhang, L., Pan, H., Li, J., Zhang, C., Li, L., Zhao, C., & Yuen, C. (2026) · IEEE Transactions on Cognitive Communications and Networking · doi:10.1109/tccn.2026.3656419 · Cited by 3 · see citing works
Self-citationMutual Coupling-Aware Hybrid Beamforming for Densely Packed MIMO Metasurface
Guo, Y., Guo, X., & Wang, Y. (2026) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2026.3663602 · Cited by 3 · see citing works
Efficient Localization with Base Station-Integrated Beyond Diagonal RIS
Raeisi, M., Chen, H., Wymeersch, H., & Başar, E. (2025) · International Conference on Communications · doi:10.1109/icc52391.2025.11162032 · Cited by 3 · see citing works
Over-the-Air Electromagnetic Signal Processing: From fundamentals to emerging paradigms
Dardari, D., Torcolacci, G., Pasolini, G., & Decarli, N. (2026) · IEEE Signal Processing Magazine · doi:10.1109/msp.2025.3622001 · Cited by 3 · see citing works
Adaptive Weighted Access Point Technique for Robust Dynamic Indoor Positioning
Mazlan, A. B., & Ng, Y. H. (2024) · IEEE Access · doi:10.1109/access.2024.3501304 · Cited by 3 · see citing works
User Localization for Reconfigurable Intelligent Surface-Assisted mmWave MIMO-OFDM Systems
Sheng, M., Li, Y., Cai, W., Qi, Q., Wu, Z., & Wu, Y. (2024) · IEEE Communications Letters · doi:10.1109/lcomm.2024.3509621 · Cited by 3 · see citing works
Vehicle Localization Based on Bayesian Tensor Decomposition in Intelligent Transportation Systems
Yu, W., Du, J., Chen, Y., Jin, L., Li, X., & Yuen, C. (2025) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2025.3582038 · Cited by 2 · see citing works
Self-citationReal-Time Wireless Sensing and Positioning Through Reconfigurable Intelligent Surfaces
Tang, W., Meng, S., Zhou, Q. Y., Xu, Y., Li, H., Dai, J. Y., Yang, J., Wong, K., Jin, S., Cheng, Q., et al. (2025) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2025.3589272 · Cited by 2 · see citing works
Sparse Bayesian Learning Based Channel Estimation for SIM-Assisted Near-Field Communications
Yao, X., An, J., Gan, L., Clerckx, B., & Renzo, M. D. (2025) · International Conference on Communications · doi:10.1109/icc52391.2025.11161340 · Cited by 2 · see citing works
Self-citationAbrardo, A., Bartoli, G., Toccafondi, A., & Renzo, M. D. (2025) · European Signal Processing Conference (EUSIPCO) · doi:10.23919/eusipco63237.2025.11226149 · Cited by 2 · see citing works
Self-citationKhatun, H., & Chowdhury, M. Z. (2025) · Results in Engineering · doi:10.1016/j.rineng.2025.107460 · Cited by 2 · see citing works
Zhang, Q., Liu, J., Get, Y., Zhao, Y., Khan, W. U., Dong, Z., Guan, Y. L., & Yuen, C. (2026) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2026.3661858 · Cited by 2 · see citing works
Self-citationRSMA-Assisted Fluid Antenna ISAC via Hierarchical Deep Reinforcement Learning
Sheraz, M., Chuah, T. C., & Lee, I. E. (2026) · Telecom · doi:10.3390/telecom7020041 · Cited by 2 · see citing works
Rufo, S., Aguiar-Castillo, L., Rufo, J., & Pérez‐Jiménez, R. (2024) · Electronics · doi:10.3390/electronics13101828 · Cited by 2 · see citing works
Modern Base Station Architecture: Enabling Passive Beamforming With Beyond Diagonal RISs
Raeisi, M., Chen, H., Wymeersch, H., & Başar, E. (2025) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2025.3641612 · Cited by 2 · see citing works
Chen, Z., Liu, L., & Yu, Z. (2024) · IEEE Signal Processing Letters · doi:10.1109/lsp.2024.3429272 · Cited by 2 · see citing works
Direction finding by learning-assisted programmable metasurface
Meftah, N., Ratni, B., Korso, M. N. E., & Burokur, S. N. (2025) · Journal of Applied Physics · doi:10.1063/5.0278818 · Cited by 1 · see citing works
Abrardo, A., Bartoli, G., Toccafondi, A., & Renzo, M. D. (2025) · IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC) · doi:10.1109/apwc65665.2025.11190469 · Cited by 1 · see citing works
Self-citationHui, Y., Chen, S., Liu, X., & Meng, W. (2025) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2025.3622205 · Cited by 1 · see citing works
Zheng, B., Jiang, X., Yu, K., Li, L., Yu, C., Li, N., & Zhang, Y. (2025) · IEEE Antennas and Wireless Propagation Letters · doi:10.1109/lawp.2025.3628338 · Cited by 1 · see citing works
Interplay of STAR-RIS and SIM: Joint Computing and Communication for Full-Space Coverage
Zarini, H., Kazemi, S. M., An, J., Sookhak, M., & Yilmazer, N. (2025) · IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) · doi:10.1109/pimrc62392.2025.11275106 · Cited by 1 · see citing works
Self-citationOn the Application of Active RIS to Stacked Intelligent Metasurface Systems
Zarini, H., Kazemi, S. M., An, J., Movaghar, A., Sookhak, M., & Yilmazer, N. (2025) · IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) · doi:10.1109/pimrc62392.2025.11274698 · Cited by 1 · see citing works
Self-citationQoE-Driven Resource Allocation for Stacked Intelligent Metasurface Systems
Zarini, H., Kazemi, S. M., An, J., Movaghar, A., Sookhak, M., & Yilmazer, N. (2025) · IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) · doi:10.1109/pimrc62392.2025.11275274 · Cited by 1 · see citing works
Self-citationMinimization of Secrecy Outage Probability for ARIS-Aided ISAC Systems
Liu, M., Zhou, Z., Shi, Q., Lei, X., & Fan, P. (2026) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2026.3657807 · Cited by 1 · see citing works
Zhang, H., Cui, Y., Liu, S., & Wang, S. (2025) · International Conference on Communication Technology and Information Technology (ICCTIT) · doi:10.1109/icctit68197.2025.11406452 · Cited by 1 · see citing works
Intelligent Programmable Metasurfaces for Robust Spatiotemporal 3D Human Pose Estimation
Wang, Y., Zheng, Y. N., Li, Y., Qi, Z., He, S., Shi, H. T., Chen, X. Q., Zhang, L., & Cui, T. J. (2026) · Advanced Materials Technologies · doi:10.1002/admt.71241 · Cited by 1 · see citing works
Baseband-Free End-to-End Communication System Based on Diffractive Deep Neural Network
Teng, X., Tang, W., Li, X., & Jin, S. (2025) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2025.3632886 · Cited by 1 · 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
Self-citationAnalog Computing With Hybrid Couplers and Phase Shifters
Nerini, M., Liu, X., & Clerckx, B. (2026) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2026.3721382 · Cited by 1 · see citing works
Ibrahim, M., Mezghani, A., & Hossain, E. (2026) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2026.3696550 · Cited by 1 · see citing works
A review of reconfigurable metasurfaces for radar applications
Qian, B., Chu, H., Guo, Y.-X., & Zhao, Z. (2026) · iScience · doi:10.1016/j.isci.2026.116348 · Cited by 1 · see citing works
The Role of Excitation Schemes in the Functionality of Metasurface-based Antennas
Rezvani, M., Ataloglou, V. G., Adve, R. S., Eleftheriades, G. V., Sediq, A. B., & El‐Keyi, A. (2026) · International Conference on Communications · doi:10.1109/icc59461.2026.11588234 · 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 recent years, several advanced SIM architectures have been reported to demonstrate impressive capabilities for various emerging applications, such as hologram generation [73], image classification [27], and matrix operations [25], [26].”
InfluentialSelf-citationChannel Model for Estimating Received Power Variations at a Mobile Terminal in a Cellular Network
Moreno, K. V., Lupera, P., Chiguano, R., Álvarez, R., Llugsi, R., & Palma, G. (2025) · Electronics · doi:10.3390/electronics14153077
A Multidimensional Matrix Completion Method for 2-D DOA Estimation with L-Shaped Array
Zhang, H., Shi, J., Li, Z., & Shi, S. (2025) · Sensors · doi:10.3390/s25175583
Positioning via Probabilistic Graphical Models in RIS-Aided Systems with Channel Estimation Errors
Terças, L., & Juntti, M. J. (2025) · International Conference on Communications · doi:10.1109/icc52391.2025.11161755
Abrardo, A., & Toccafondi, A. (2025) · IEEE Radio and Antenna Days of the Indian Ocean (RADIO) · doi:10.1109/radio65825.2025.11296372
Pan, W., Li, P., Cheng, Z., Xie, R., Xu, R., Gao, J., & Chu, H. (2025) · International Conference on Signal Processing Systems (ICSPS) · doi:10.1109/icsps66615.2025.11347792
- 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 › Aerospace 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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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