Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
139 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Bayes-Optimal Unsupervised Learning for Channel Estimation in Near-Field Holographic MIMO (2312.10438v2)

Published 16 Dec 2023 in eess.SP, cs.IT, and math.IT

Abstract: Holographic MIMO (HMIMO) is being increasingly recognized as a key enabling technology for 6G wireless systems through the deployment of an extremely large number of antennas within a compact space to fully exploit the potentials of the electromagnetic (EM) channel. Nevertheless, the benefits of HMIMO systems cannot be fully unleashed without an efficient means to estimate the high-dimensional channel, whose distribution becomes increasingly complicated due to the accessibility of the near-field region. In this paper, we address the fundamental challenge of designing a low-complexity Bayes-optimal channel estimator in near-field HMIMO systems operating in unknown EM environments. The core idea is to estimate the HMIMO channels solely based on the Stein's score function of the received pilot signals and an estimated noise level, without relying on priors or supervision that is not feasible in practical deployment. A neural network is trained with the unsupervised denoising score matching objective to learn the parameterized score function. Meanwhile, a principal component analysis (PCA)-based algorithm is proposed to estimate the noise level leveraging the low-rank near-field spatial correlation. Building upon these techniques, we develop a Bayes-optimal score-based channel estimator for fully-digital HMIMO transceivers in a closed form. The optimal score-based estimator is also extended to hybrid analog-digital HMIMO systems by incorporating it into a low-complexity message passing algorithm. The (quasi-) Bayes-optimality of the proposed estimators is validated both in theory and by extensive simulation results. In addition to optimality, it is shown that our proposal is robust to various mismatches and can quickly adapt to dynamic EM environments in an online manner thanks to its unsupervised nature, demonstrating its potential in real-world deployment.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (47)
  1. W. Yu, H. He, X. Yu, S. Song, J. Zhang, R. D. Murch, and K. B. Letaief, “Learning Bayes-optimal channel estimation for holographic MIMO in unknown EM environments,” arXiv preprint arXiv:2311.07908, 2023.
  2. A. Pizzo, T. L. Marzetta, and L. Sanguinetti, “Spatially-stationary model for holographic MIMO small-scale fading,” IEEE J. Sel. Areas Commun., vol. 38, no. 9, pp. 1964–1979, Sept. 2020.
  3. A. Pizzo, L. Sanguinetti, and T. L. Marzetta, “Fourier plane-wave series expansion for holographic MIMO communications,” IEEE Trans. Wireless Commun., vol. 21, no. 9, pp. 6890–6905, Sept. 2022.
  4. O. T. Demir, E. Bjornson, and L. Sanguinetti, “Channel modeling and channel estimation for holographic massive MIMO with planar arrays,” IEEE Wireless Commun. Lett., vol. 11, no. 5, pp. 997–1001, May 2022.
  5. L. Wei, C. Huang, G. C. Alexandropoulos, W. E. I. Sha, Z. Zhang, M. Debbah, and C. Yuen, “Multi-user holographic MIMO surfaces: Channel modeling and spectral efficiency analysis,” IEEE J. Sel. Topics Signal Process., vol. 16, no. 5, pp. 1112–1124, Aug. 2022.
  6. T. Wang, Y. Liu, M. Zhang, W. E. I. Sha, C. Ling, C. Li, and S. Wang, “Channel measurement for holographic MIMO: Benefits and challenges of spatial oversampling,” in IEEE Int. Conf. Commun., Rome, Italy, May-Jun. 2023, pp. 5036–5041.
  7. R. Deng, B. Di, H. Zhang, Y. Tan, and L. Song, “Reconfigurable holographic surface: Holographic beamforming for metasurface-aided wireless communications,” IEEE Trans. Veh. Technol., vol. 70, no. 6, pp. 6255–6259, Jun. 2021.
  8. 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.
  9. L. Wei, C. Huang, G. C. Alexandropoulos, Z. Yang, J. Yang, W. E. I. Sha, Z. Zhang, M. Debbah, and C. Yuen, “Tri-polarized holographic MIMO surfaces for near-field communications: Channel modeling and precoding design,” IEEE Trans. Wireless Commun., pp. 1–1, to appear, 2023.
  10. A. A. D’Amico, A. d. J. Torres, L. Sanguinetti, and M. Win, “Cramer-Rao bounds for holographic positioning,” IEEE Trans. Signal Process., vol. 70, pp. 5518–5532, Nov. 2022.
  11. A. Elzanaty, A. Guerra, F. Guidi, D. Dardari, and M.-S. Alouini, “Toward 6G holographic localization: Enabling technologies and perspectives,” IEEE Internet Things Mag., vol. 6, no. 3, pp. 138–143, Sept. 2023.
  12. H. Zhang, H. Zhang, B. Di, M. D. Renzo, Z. Han, H. V. Poor, and L. Song, “Holographic integrated sensing and communication,” IEEE J. Sel. Areas Commun., vol. 40, no. 7, pp. 2114–2130, Jul. 2022.
  13. W. Yu, Y. Ma, H. He, S. Song, J. Zhang, and K. B. Letaief, “AI-native transceiver design for near-field ultra-massive MIMO: Principles and techniques,” arXiv preprint arXiv:2309.09575, 2023.
  14. M. Cui and L. Dai, “Channel estimation for extremely large-scale MIMO: Far-field or near-field?” IEEE Trans. Commun., vol. 70, no. 4, pp. 2663–2677, Apr. 2022.
  15. Y. Liu, Z. Tan, H. Hu, L. J. Cimini, and G. Y. Li, “Channel estimation for OFDM,” IEEE Commun. Surv. Tut., vol. 16, no. 4, pp. 1891–1908, Fourthquarter, 2014.
  16. S. Liu, X. Yu, Z. Gao, and D. W. K. Ng, “DPSS-based codebook design for near-field XL-MIMO channel estimation,” arXiv preprint arXiv:2310.18180, 2023.
  17. H. Xie, F. Gao, and S. Jin, “An overview of low-rank channel estimation for massive MIMO systems,” IEEE Access, vol. 4, pp. 7313–7321, Nov. 2016.
  18. Y. Zhu, H. Guo, and V. K. N. Lau, “Bayesian channel estimation in multi-user massive MIMO with extremely large antenna array,” IEEE Trans. Signal Process., vol. 69, pp. 5463–5478, Sept. 2021.
  19. W. Yu, Y. Shen, H. He, X. Yu, S. Song, J. Zhang, and K. B. Letaief, “An adaptive and robust deep learning framework for THz ultra-massive MIMO channel estimation,” IEEE J. Sel. Topics Signal Process., vol. 17, no. 4, pp. 761–776, Jul. 2023.
  20. H. He, S. Jin, C.-K. Wen, F. Gao, G. Y. Li, and Z. Xu, “Model-driven deep learning for physical layer communications,” IEEE Wireless Commun., vol. 26, no. 5, pp. 77–83, Oct. 2019.
  21. E. Balevi, A. Doshi, A. Jalal, A. Dimakis, and J. G. Andrews, “High dimensional channel estimation using deep generative networks,” IEEE J. Sel. Areas Commun., vol. 39, no. 1, pp. 18–30, Jan. 2021.
  22. X. Zheng and V. K. N. Lau, “Online deep neural networks for mmwave massive MIMO channel estimation with arbitrary array geometry,” IEEE Trans. Signal Process., vol. 69, pp. 2010–2025, Mar. 2021.
  23. H. He, R. Wang, W. Jin, S. Jin, C.-K. Wen, and G. Y. Li, “Beamspace channel estimation for wideband millimeter-wave MIMO: A model-driven unsupervised learning approach,” IEEE Trans. Wireless Commun., vol. 22, no. 3, pp. 1808–1822, Mar. 2023.
  24. W. Yu, H. He, X. Yu, S. Song, J. Zhang, and K. B. Letaief, “Blind performance prediction for deep learning based ultra-massive MIMO channel estimation,” in Proc. IEEE Int. Conf. Commun., Rome, Italy, May-Jun. 2023.
  25. J. An, C. Yuen, C. Huang, M. Debbah, H. V. 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.
  26. H. He, C.-K. Wen, S. Jin, and G. Y. Li, “Model-driven deep learning for MIMO detection,” IEEE Trans. Signal Process., vol. 68, pp. 1702–1715, Feb. 2020.
  27. A. A. D’Amico, G. Bacci, and L. Sanguinetti, “DFT-based channel estimation for holographic MIMO,” in Proc. Asilomar Conf. Signals Syst. Comput., Pacific Grove, CA, USA, Nov. 2023.
  28. Z. Wan, Z. Gao, F. Gao, M. D. Renzo, and M.-S. Alouini, “Terahertz massive MIMO with holographic reconfigurable intelligent surfaces,” IEEE Trans. Commun., vol. 69, no. 7, pp. 4732–4750, Jul. 2021.
  29. E. Bjornson and L. Sanguinetti, “Rayleigh fading modeling and channel hardening for reconfigurable intelligent surfaces,” IEEE Wireless Commun. Lett., vol. 10, no. 4, pp. 830–834, Apr. 2021.
  30. Z. Dong and Y. Zeng, “Near-field spatial correlation for extremely large-scale array communications,” IEEE Commun. Lett., vol. 26, no. 7, pp. 1534–1538, Jul. 2022.
  31. A. Abdi, J. Barger, and M. Kaveh, “A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station,” IEEE Trans. Veh. Technol., vol. 51, no. 3, pp. 425–434, May 2002.
  32. A. de Jesus Torres, L. Sanguinetti, and E. Bjornson, “Electromagnetic interference in RIS-aided communications,” IEEE Wireless Commun. Lett., vol. 11, no. 4, pp. 668–672, Apr. 2022.
  33. J. Zhang, X. Yu, and K. B. Letaief, “Hybrid beamforming for 5G and beyond millimeter-wave systems: A holistic view,” IEEE Open J. Commun. Soc., vol. 1, pp. 77–91, Dec. 2019.
  34. G. Alain and Y. Bengio, “What regularized auto-encoders learn from the data-generating distribution,” J. Mach. Learn. Res., vol. 15, no. 1, pp. 3563–3593, Nov. 2014.
  35. Z. Gulgun and E. G. Larsson, “Massive MIMO with Cauchy noise: Channel estimation, achievable rate and data decoding,” IEEE Trans. Wireless Commun., pp. 1–1, to appear, 2023.
  36. M. Raphan and E. P. Simoncelli, “Least squares estimation without priors or supervision,” Neural Comput., vol. 23, no. 2, pp. 374–420, Feb. 2011.
  37. K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proc. IEEE Conf. Comput. Vis. Pattern Recog., Las Vegas, NV, USA, Jun. 2016.
  38. J. H. Lim, A. Courville, C. Pal, and C.-W. Huang, “AR-DAE: towards unbiased neural entropy gradient estimation,” in Proc. Int. Conf. Mach. Learn., Virtual, Jul. 2020.
  39. H. Lu, Y. Zeng, C. You, Y. Han, J. Zhang, Z. Wang, Z. Dong, S. Jin, C.-X. Wang, T. Jiang, X. You, and R. Zhang, “A tutorial on near-field XL-MIMO communications towards 6G,” arXiv preprint arXiv:2310.11044, 2023.
  40. S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality (complete samples),” Biometrika, vol. 52, no. 3/4, pp. 591–611, Dec. 1965.
  41. J. Ma and L. Ping, “Orthogonal AMP,” IEEE Access, vol. 5, pp. 2020–2033, Jan. 2017.
  42. Q. Zou and H. Yang, “A concise tutorial on approximate message passing,” arXiv preprint arXiv:2201.07487, 2022.
  43. K. Takeuchi, “Rigorous dynamics of expectation-propagation-based signal recovery from unitarily invariant measurements,” IEEE Trans. Inf. Theory, vol. 66, no. 1, pp. 368–386, Jan. 2020.
  44. J. P. Vila and P. Schniter, “Expectation-maximization Gaussian-mixture approximate message passing,” IEEE Trans. Signal Process., vol. 61, no. 19, pp. 4658–4672, Oct. 2013.
  45. O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Proc. Int. Conf. Med. Image Comput. Comput.-Assisted Intervention, Munich, Germany, Oct. 2015.
  46. A. Gallyas-Sanhueza and C. Studer, “Low-complexity blind parameter estimation in wireless systems with noisy sparse signals,” IEEE Trans. Wireless Commun., vol. 22, no. 10, pp. 7055–7071, Oct. 2023.
  47. H. He, C.-K. Wen, and S. Jin, “Bayesian optimal data detector for hybrid mmwave MIMO-OFDM systems with low-resolution ADCs,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 3, pp. 469–483, Jun. 2018.
Citations (4)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now