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Two-Dimensional Direction-of-Arrival Estimation Using Stacked Intelligent Metasurfaces (2402.08224v1)

Published 13 Feb 2024 in cs.IT, eess.SP, and math.IT

Abstract: Stacked intelligent metasurfaces (SIM) are capable of emulating reconfigurable physical neural networks by relying on electromagnetic (EM) waves as carriers. They can also perform various complex computational and signal processing tasks. A SIM is fabricated 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 a SIM for two-dimensional (2D) direction-of-arrival (DOA) estimation. In contrast to the conventional designs, an advanced SIM in front of the receiver array automatically carries out the 2D discrete Fourier transform (DFT) as the incident waves propagate through it. As a result, the receiver array directly observes the angular spectrum of the incoming signal. In this context, the DOA estimates can be readily obtained by using probes to detect the energy distribution on the receiver array. This avoids the need for power-thirsty radio frequency (RF) chains. To enable SIM to perform the 2D DFT, we formulate the optimization problem of minimizing the fitting error between the SIM's EM response and the 2D DFT matrix. Furthermore, a gradient descent algorithm is customized for iteratively updating the phase shift of each meta-atom in SIM. To further improve the DOA estimation accuracy, we configure the phase shift pattern in the zeroth 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 mean square error (MSE). Our numerical simulations verify the capability of a well-trained SIM to perform DOA estimation and corroborate our theoretical analysis. It is demonstrated that a SIM having an optical computational speed achieves an MSE of $10{-4}$ for DOA estimation.

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References (37)
  1. J. An, C. Yuen, M. Di Renzo, M. Debbah, H. V. Poor, and L. Hanzo, “Stacked intelligent metasurface performs a 2D DFT in the wave domain for DOA estimation,” arXiv preprint arXiv:2310.09861, 2023.
  2. R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276–280, Mar. 1986.
  3. R. Roy and T. Kailath, “ESPRIT-estimation of signal parameters via rotational invariance techniques,” IEEE Trans. Acoustics Speech Signal Process., vol. 37, no. 7, pp. 984–995, Jul. 1989.
  4. P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer-Rao bound,” IEEE Trans. Acoustics Speech Signal Process., vol. 37, no. 5, pp. 720–741, May 1989.
  5. B. Rao and K. Hari, “Performance analysis of root-MUSIC,” IEEE Trans. Acoustics Speech Signal Process., vol. 37, no. 12, pp. 1939–1949, Dec. 1989.
  6. S. Qin, Y. D. Zhang, and M. G. Amin, “Generalized coprime array configurations for direction-of-arrival estimation,” IEEE Trans. Signal Process., vol. 63, no. 6, pp. 1377–1390, Mar. 2015.
  7. Z. Yang, L. Xie, and C. Zhang, “Off-grid direction of arrival estimation using sparse bayesian inference,” IEEE Trans. Signal Process., vol. 61, no. 1, pp. 38–43, Jan. 2013.
  8. J. An, H. Li, D. W. K. Ng, and C. Yuen, “Fundamental detection probability vs. achievable rate tradeoff in integrated sensing and communication systems,” IEEE Trans. Wireless Commun., pp. 1–1, 2023.
  9. Z. Zheng, Y. Huang, W.-Q. Wang, and H. C. So, “Direction-of-arrival estimation of coherent signals via coprime array interpolation,” IEEE Signal Process. Lett., vol. 27, no. 3, pp. 585–589, Mar. 2020.
  10. H. Krim and M. Viberg, “Two decades of array signal processing research: the parametric approach,” IEEE Signal Process. Mag., vol. 13, no. 4, pp. 67–94, Jul. 1996.
  11. L. Godara, “Application of antenna arrays to mobile communications – Part II beam-forming and direction-of-arrival considerations,” Proc. IEEE, vol. 85, no. 8, pp. 1195–1245, Aug. 1997.
  12. J. An, C. Yuen, L. Dai, M. Di Renzo, M. Debbah, and L. Hanzo, “Toward beamfocusing-aided near-field communications: Research advances, potential, and challenges,” arXiv preprint arXiv:2309.09242, 2023.
  13. C. See and A. Gershman, “Direction-of-arrival estimation in partly calibrated subarray-based sensor arrays,” IEEE Trans. Signal Process., vol. 52, no. 2, pp. 329–338, Feb. 2004.
  14. Z.-M. Liu and Y.-Y. Zhou, “A unified framework and sparse bayesian perspective for direction-of-arrival estimation in the presence of array imperfections,” IEEE Trans. Signal Process., vol. 61, no. 15, pp. 3786–3798, Aug. 2013.
  15. Z.-M. Liu, C. Zhang, and P. S. Yu, “Direction-of-arrival estimation based on deep neural networks with robustness to array imperfections,” IEEE Trans. Antennas Propag., vol. 66, no. 12, pp. 7315–7327, Dec. 2018.
  16. S. Chakrabarty and E. A. P. Habets, “Multi-speaker DOA estimation using deep convolutional networks trained with noise signals,” IEEE J. Sel. Topics Signal Process., vol. 13, no. 1, pp. 8–21, Mar. 2019.
  17. L. Wu, Z.-M. Liu, and Z.-T. Huang, “Deep convolution network for direction of arrival estimation with sparse prior,” IEEE Signal Process. Lett., vol. 26, no. 11, pp. 1688–1692, Nov. 2019.
  18. J. An, C. Yuen, C. Xu, H. Li, D. W. K. Ng, M. Di Renzo, M. Debbah, and L. Hanzo, “Stacked intelligent metasurface-aided MIMO transceiver design,” arXiv preprint arXiv:2311.09814, 2023.
  19. X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science, vol. 361, no. 6406, pp. 1004–1008, Jul. 2018.
  20. A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science, vol. 343, no. 6167, pp. 160–163, Jan. 2014.
  21. M. Di Renzo, A. Zappone, M. Debbah, M.-S. Alouini, C. Yuen, J. de Rosny, and S. Tretyakov, “Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead,” IEEE J. Sel. Areas Commun., vol. 38, no. 11, pp. 2450–2525, Nov. 2020.
  22. J. An, C. Xu, L. Gan, and L. Hanzo, “Low-complexity channel estimation and passive beamforming for RIS-assisted MIMO systems relying on discrete phase shifts,” IEEE Trans. Commun., vol. 70, no. 2, pp. 1245–1260, Feb. 2022.
  23. J. An, C. Xu, Q. Wu, D. W. K. Ng, M. D. Renzo, C. Yuen, and L. Hanzo, “Codebook-based solutions for reconfigurable intelligent surfaces and their open challenges,” IEEE Wireless Commun., pp. 1–8, 2023, Early Access.
  24. T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light: Science & Applications, vol. 3, no. 10, pp. e218–e218, Oct. 2014.
  25. J. An, C. Xu, L. Wang, Y. Liu, L. Gan, and L. Hanzo, “Joint training of the superimposed direct and reflected links in reconfigurable intelligent surface assisted multiuser communications,” IEEE Trans. Green Commun. Netw., vol. 6, no. 2, pp. 739–754, Jun. 2022.
  26. C. Xu et al., “Channel estimation for reconfigurable intelligent surface assisted high-mobility wireless systems,” IEEE Trans. Veh. Technol., vol. 72, no. 1, pp. 718–734, Jan. 2023.
  27. W. Xu et al., “Algorithm-unrolling-based distributed optimization for ris-assisted cell-free networks,” IEEE Int. Things J., vol. 11, no. 1, pp. 944–957, Jan. 2024.
  28. C. Xu et al., “Antenna selection for reconfigurable intelligent surfaces: A transceiver-agnostic passive beamforming configuration,” IEEE Trans. Wireless Commun., vol. 22, no. 11, pp. 7756–7774, Nov. 2023.
  29. C. Liu, Q. Ma, Z. J. Luo, Q. R. Hong, Q. Xiao, H. C. Zhang, L. Miao, W. M. Yu, Q. Cheng, L. Li et al., “A programmable diffractive deep neural network based on a digital-coding metasurface array,” Nature Electronics, vol. 5, no. 2, pp. 113–122, Feb. 2022.
  30. J. An, C. Xu, D. W. K. Ng, G. C. Alexandropoulos, C. Huang, C. Yuen, and L. Hanzo, “Stacked intelligent metasurfaces for efficient holographic MIMO communications in 6G,” IEEE J. Sel. Areas Commun., vol. 41, no. 8, pp. 2380–2396, Aug. 2023.
  31. Q.-U.-A. Nadeem et al., “Hybrid digital-wave domain channel estimator for stacked intelligent metasurface enabled multi-user miso systems,” arXiv preprint arXiv:2309.16204, 2023.
  32. J. An, C. Yuen, C. Huang, M. Debbah, H. Vincent Poor, and L. Hanzo, “A tutorial on holographic MIMO communications—Part I: Channel modeling and channel estimation,” IEEE Commun. Lett., vol. 27, no. 7, pp. 1664–1668, Jul. 2023.
  33. J. An, M. Di Renzo, M. Debbah, and C. Yuen, “Stacked intelligent metasurfaces for multiuser beamforming in the wave domain,” in Proc. IEEE Int. Conf. Commun. (ICC), Rome, Italy, May 2023, pp. 1–6.
  34. J. An, M. Di Renzo, M. Debbah, H. V. Poor, and C. Yuen, “Stacked intelligent metasurfaces for multiuser downlink beamforming in the wave domain,” arXiv preprint arXiv:2309.02687, 2023.
  35. P. Heidenreich, A. M. Zoubir, and M. Rubsamen, “Joint 2-D DOA estimation and phase calibration for uniform rectangular arrays,” IEEE Trans. Signal Process., vol. 60, no. 9, pp. 4683–4693, Sep. 2012.
  36. E. S. Pearson, “Note on an approximation to the distribution of non-central χ2superscript𝜒2\chi^{2}italic_χ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT,” Biometrika, vol. 46, no. 3/4, pp. 364–364, 1959. [Online]. Available: http://www.jstor.org/stable/2333533
  37. E. B. Wilson and M. M. Hilferty, “The distribution of chi-square,” Proc. Natl. Acad. Sci. U.S.A., vol. 17, no. 12, pp. 684–688, Dec. 1931.
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