基于互质阵列的堆叠智能超表面及二维DOA估计

  • 赖欣 ,
  • 陈小瑜 ,
  • 张小飞
展开
  • 1. 南京航空航天大学
    2. 香港科技大学
    3. 泉州师范学院
    4. 南京航空航天大学,电子信息工程学院,通信与信息系统专业

收稿日期: 2026-04-28

  修回日期: 2026-07-29

  网络出版日期: 2026-07-30

基金资助

国家自然科学基金;国家自然科学基金

Coprime Array Stacked Intelligent Meta-surfaces for Two-Dimensional Di-rection of Arrival Estimation

  • LAI Xin ,
  • CHEN Xiao-Yu ,
  • ZHANG Xiao-Fei
Expand

Received date: 2026-04-28

  Revised date: 2026-07-29

  Online published: 2026-07-30

摘要

堆叠智能超表面(Stacked Intelligent Metasurface, SIM)通过在衍射超原子层间模拟电磁波传播,能够在射频前端以光速实现波域信号处理,为突破传统数字方法的高延迟与高能耗瓶颈提供了新范式。针对二维波达方向估计问题(Two Dimensional Direction of Arrival, 2D-DOA),本文提出一种基于互质阵列的堆叠智能超表面(Coprime Array Stacked Intelligent Meta-surface, CA-SIM)与角度估计方法。CA-SIM由两个单元间距满足互质关系的级联子SIM构成,在相同超表面单元数量下有效扩展了阵列孔径。在相位优化阶段,采用自适应动量估计方法分别优化各子SIM中间层的相位分布,使其端到端响应精确逼近二维离散傅里叶变换(Two Dimensional Discrete Fourier Transform, 2D-DFT)估计器。在角度估计阶段,利用输入层可重构超表面(Reconfigurable Intelligent meta-Surface, RIS)的相位旋转实现空间谱的精细化搜索,并基于互质特性唯一消除子SIM估计的模糊角度估计。仿真结果表明,所提CA-SIM架构在优化收敛速度与二维DOA估计精度上均具有显著优势。

本文引用格式

赖欣 , 陈小瑜 , 张小飞 . 基于互质阵列的堆叠智能超表面及二维DOA估计[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2026.33782

Abstract

Stacked intelligent metasurface (SIM) enables wave-domain signal processing at the speed of light by emulating elec-tromagnetic wave propagation across diffractive meta-atom layers, offering a new paradigm to overcome the high latency and energy consumption bottlenecks of conventional digital methods. Aiming at two-dimensional direction-of-arrival (2D-DOA) estimation, this paper proposes a coprime array stacked intelligent metasurface (CA-SIM) architec-ture. The proposed architecture consists of two cascaded sub-SIMs whose element spacings satisfy a coprime rela-tionship, effectively extending the array aperture without increasing the number of meta-atoms. In the optimization phase, an adaptive momentum estimation method is employed to optimize the phase distributions of the intermediate layers in each sub-SIM, enabling their end-to-end responses to accurately approximate two-dimensional discrete Fou-rier transform (2D-DFT) estimators. In the estimation phase, phase rotations of the reconfigurable intelligent surface (RIS) input layer are utilized to perform refine spatial spectrum searching, while the coprime property uniquely re-solves the ambiguous angle estimates from the sub-SIMs. Simulation results demonstrate that the proposed CA-SIM architecture achieves significant advantages in both optimization convergence speed and 2D-DOA estimation accura-cy.

参考文献

[1] 张小飞,李建峰,徐大专,等.阵列信号处理及MATLAB实现[M].电子工业出版社,2023. [2] LIU W, HAARDT M, GRECO M, et al. Twenty-Five Years of Sensor Array and Multichannel Signal Pro-cessing: A Review of Progress to Date and Potential Research Directions[J]. IEEE Signal Processing Mag-azine, 2023, 40(4):80–91. [3] STOCIA P, NEHORAI A. MUSIC, Maximum Likeli-hood, and Cramer-Rao Bound[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989, 37(5):720–741. [4] Roy R, Paulraj A, Kailath T. ESPRIT–A Subspace Rotation Approach to Estimation of Parameters of Cisoids in Noise[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1986, 34(5):1340–1342. [5] Zhang X, Xu L, Xu L, et al. Direction of Departure (DOD) and Direction of Arrival (DOA) Estimation in MIMO Radar with Reduced-Dimension MUSIC[J]. IEEE Communications Letters, 2010, 14(12):1161-1163. [6] Dong X, Zhang X, Zhao J, et al. Multi-Maneuvering Sources DOA Tracking With Improved Interactive Multi-Model Multi-Bernoulli Filter for Acoustic Vec-tor Sensor (AVS) Array[J]. IEEE Transactions on Ve-hicular Technology, 2021,70(8):7825-7838. [7] 文方青,罗祥波,师俊朋.一种基于平行因子分解的电磁矢量传感器MIMO雷达测向算法[J].数据采集与处理, 2024, 39(6):1333-1344. WEN F, LUO X, SHI J. A Direction-Finding Algo-rithm for Electromagnetic Vector Sensor MIMO Ra-dar Based on Parallel Factor Decomposition[J]. Jour-nal of Data Acquisition and Processing, 2024,39(6):1333-1344 (in Chinese). [8] XIE Q, WANG Z, WEN F, et al. Coarray Tensor Trai Decomposition for Bistatic MIMO Radar With Uniform Planar Array[J]. IEEE Transactions on An-tennas and Propagation, 2025, 73(8):5310-5323. [9] LI J, ZHANG X. Unitary Reduced-Dimensional Esti-mation of Signal Parameters via Rotational in Vari-ance Techniques for Angle Estimation in Monostatic Multiple-Input–Multiple-Output Radar with Rectan-gular Arrays[J]. IET Radar, Sonar & Navigation, 2014, 8(6):575–584. [10] WANG X, WANG L, LI X, et al. Nuclear Norm Min-imization Rramework for DOA Estimation in MIMO Radar[J]. Signal Processing, 2017, 135:147–152. [11] VAIDYANATHAN P, PAL P. Sparse Sensing With Co-Prime Samplers and Arrays[J]. IEEE Transactions on Signal Processing, 2011, 59(2):573–586. [12] 张宇乐,周豪,胡国平,等.稀疏阵列结构设计及波达方向估计研究进展[J].信号处理, 2024, 40(10):1773-1790. ZHANG Yule, ZHOU Hao, HU Guoping, et al. Re-search Progress on Sparse Array Design and Direction of Arrival Estimation[J]. Journal of Signal Processing, 2024, 40(10): 1773-1790 (in Chinese). [13] 刘永祥,师俊朋,黎湘.稀疏阵列MIMO雷达参数估计研究进展[J].中国科学:信息科学, 2022, 40(10) :1560-1576. LIU Y, SHI J, LI X. Research Progress on Sparse Ar-ray MIMO Radar Parameter Estimation, Sci SinIn-form, 2022, 40(10) :1560-1576 (in Chinese). [14] ZHENG W, ZHANG X, WANG Y, et al. Padded Coprime Arrays for Improved DOA Estimation: Ex-ploiting Hole Representation and Filling Strategies[J]. IEEE Transactions on Signal Processing, 2020, 68:4597-4611. [15] SHI J, HU G, ZHANG X, et al. Sparsity-Based Two-Dimensional DOA Estimation for Coprime Array: From Sum–Difference Coarray Viewpoint[J]. IEEE Transactions on Signal Processing, 2017, 65(21):5591-5604. [16] WU Q, SUN F, LAN P, et al. Two-Dimensional Direc-tion-of-Arrival Estimation for Co-Prime Planar Arrays: A Partial Spectral Search Approach[J]. IEEE Sensors Journal, 2016, 16(14):5660-5670. [17] LAI X, ZHANG X, LIU W, et al. Sparse Enhance-ment of MIMO Radar Exploiting Moving Transmit and Receive Arrays for DOA Estimation: From the Perspective of Synthetic Coarray[J]. IEEE Transac-tions on Signal Processing, 2024, 72:4022-4036. [18] SHI Z, ZHOU C, GU Y, et al. Source Estimation Us-ing Coprime Array: A Sparse Reconstruction Perspec-tive[J]. IEEE Sensors Journal, 2017, 17(3):755–765 [19] LAI X, ZHANG X, ZHENG W, et al. Spatially Smoothed Tensor-Based Method for Bistatic Co-Prime MIMO Radar With Hole-Free Sum-Difference Co-Array[J]. IEEE Transactions on Vehicular Tech-nology, 2022, 71(4):3889–3899. [20] 杨杰,廖桂生. 基于空域稀疏性的嵌套MIMO雷达DOA估计算法[J]. 电子与信息学报, 2014, 36(11):2698–2705. YANG J, LIAO G. A Spatial Sparsity-based DOA Es-timation Method in Nested MIMO Radar[J]. Journal of Electronics & Information Technology, 2014, 36(11): 2698-2705 (in Chinese). [21] ZHENG H, ZHOU C, VOROBOVV S, et al. Decom-posed CNN for Sub-Nyquist Tensor-Based 2-D DOA Estimation[J]. IEEE Signal Processing Letters, 2023, 30:708-712. [22] LIU W. Super Resolution DOA Estimation Based on Deep Neural Network [J]. Scientific Report, 2020, 10(1):19. [23] SU X, LIU Z, HU P, et al. Real-Valued Deep Unfolded Networks for Off-Grid DOA Estimation via Nested Array[J]. IEEE Transactions on Aerospace and Elec-tronic Systems, 2023, 59(4):4049-4062. [24] LIN X, RIVENSION Y, YARDIMCI N, et al. All-Optical Machine Learning Using Diffractive Deep Neural Networks [J]. Science, 2018, 361(6406):1004-1008. [25] ALEXANADRE S, et al. Performing Mathematical Operations with Meta Materials [J]. Science, 2014, 343:160-163. [26] LIU C, MA Q, LUO Z, et al. A Programmable Diffrac-tive Deep Neural Network Based on A Digital-coding Metasurface Array [J]. Nature Electronics, 2022, 5:113-122. [27] AN J, et al. Stacked Intelligent Metasurface-Aided MIMO Transceiver Design [J]. IEEE Wireless Com-munication, 2024, 31(4):123-131. [28] NIU H, AN J, PARAZAFEIROPOULOS A, et al. Stacked Intelligent Metasurfaces for Integrated Sens-ing and Communications [J]. IEEE Wireless Commu-nication, 2024, 31(4):123-131. [29] AN J, et al. Two-Dimensional Direction-of-Arrival Estimation Using Stacked Intelligent Metasurfaces[J]. IEEE Journal of Selected Area on Communications, 2024, 42(10):2786-2802. [30] AN J, et al. Stacked Intelligent Metasurface-Aided MIMO Transceiver Design [J]. IEEE Wireless Com-munication, 2024, 31(4):123-131. [31] LI J, HE Y, MA P, et al. Direction of Arrival Estima-tion Using Sparse Nested Arrays with Coprime Dis-placement[J]. IEEE Sensors Journal, 2020, 4(21):5282-5291. [32] Kingma P, Jimmy B. Adam: A Method for Stochastic Optimization[C]. International Conference on Learn-ing Representations, 2015. [33] ZINKEVICH M. Online Convex Programming and Generalized Infinitesimal Gradient Ascent[C]. ICML, 2003. [34] CAO R, LIU B, GAO F, et al. A Low-Complex One-Snapshot DOA Estimation Algorithm with Massive ULA[J]. IEEE Communications Letters, 2017, 21(5):1071–1074. [35] LAI X, CHEN W, LI B, et al. Improved DFT Method for DOA Estimation with Extended Coprime Array: Based on Large Difference Coarray[J]. International Journal of Electronics, 2022, 109(5):733–747. [36] STOICA P, GERSHMAN A. Maximum-Likelihood DOA Estimation by Data-Supported Grid Search[J]. IEEE Signal Processing Letters, 1999, 6(10):273–275.
Options
文章导航

/