deep unfolding; GNN; LEO; Massive MIMO; WMMSE; Deep unfolding; Earth orbits; Graph neural networks; Low earth orbit; Massive multiple-input multipleoutput; Means square errors; Minimum mean squares; Multiple inputs; Unfoldings; Weighted minimum mean square error; Electrical and Electronic Engineering; Low earth orbit satellites; Precoding; Satellites; Satellite communications; Training; Heuristic algorithms; Artificial intelligence; Computational efficiency; eess.SP; Computer Science - Information Theory
Abstract :
[en] Low Earth Orbit (LEO) satellite communication is a critical component in the development of sixth generation (6G) networks. The integration of massive multiple-input multiple-output (MIMO) technology is being actively explored to enhance the performance of LEO satellite communications. However, the limited power of LEO satellites poses a significant challenge in improving communication energy efficiency (EE) under constrained power conditions. Artificial intelligence (AI) methods are increasingly recognized as promising solutions for optimizing energy consumption while enhancing system performance, thus enabling more efficient and sustainable communications. This paper proposes approaches to address the challenges associated with precoding in massive MIMO LEO satellite communications. First, we introduce an end-to-end graph neural network (GNN) framework that effectively reduces the computational complexity of traditional precoding methods. Next, we introduce a deep unfolding of the Dinkelbach algorithm and the weighted minimum mean square error (WMMSE) approach to achieve enhanced EE, transforming iterative optimization processes into a structured neural network, thereby improving convergence speed and computational efficiency. Furthermore, we incorporate the Taylor expansion method to approximate matrix inversion within the GNN, enhancing both the interpretability and performance of the proposed method. Numerical experiments demonstrate the validity of our proposed method in terms of complexity and robustness, achieving significant improvements over state-of-the-art methods.
Disciplines :
Electrical & electronics engineering
Author, co-author :
Zhou, Huibin ; Southeast University, National Mobile Communications Research Laboratory, Nanjing, China ; Purple Mountain Laboratories, Nanjing, China
Gong, Xinrui; Purple Mountain Laboratories, Nanjing, China
Tsinos, Christos G. ; National and Kapodistrian University of Athens, Department of Digital Industry Technologies, Athens, Greece
You, Li ; Southeast University, National Mobile Communications Research Laboratory, Nanjing, China ; Purple Mountain Laboratories, Nanjing, China
Gao, Xiqi ; Southeast University, National Mobile Communications Research Laboratory, Nanjing, China ; Purple Mountain Laboratories, Nanjing, China
OTTERSTEN, Björn ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > PI Ottersten
External co-authors :
yes
Language :
English
Title :
GNN-Enabled Precoding for Massive MIMO LEO Satellite Communications
Publication date :
2025
Journal title :
IEEE Transactions on Communications
ISSN :
0090-6778
eISSN :
1558-0857
Publisher :
Institute of Electrical and Electronics Engineers Inc.
National Natural Science Foundation of China for Outstanding Young Scholars Jiangsu Province Major Science and Technology Project Natural Science Foundation of Jiangsu Province Fundamental Research Funds for the Central Universities Civil Aerospace Technology Pre-research Project Luxembourg National Research Fund
Funding text :
Received 26 November 2024; revised 20 March 2025; accepted 30 April 2025. Date of publication 8 May 2025; date of current version 20 October 2025. This work was supported by the National Natural Science Foundation of China for Outstanding Young Scholars under Grant 62322104, the Jiangsu Province Major Science and Technology Project under Grant BG2024005, the Natural Science Foundation of Jiangsu Province under Grant BK20231415, the Fundamental Research Funds for the Central Universities under Grant 2242022k60007, and the Civil Aerospace Technology Pre-research Project under Grant D030301. The work of Bj\u00F6rn Ottersten was supported in part by the Luxembourg National Research Fund (FNR), grant reference INTER/MOBILITY/2023/IS/18014377/MCR. An earlier version of this paper was presented at the WCNC 2025 [DOI: 10.1109/WCNC61545.2025.10978590]. The associate editor coordinating the review of this article and approving it for publication was K. Dev. (Corresponding author: Li You.) Huibin Zhou, Li You, and Xiqi Gao are with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China, and also with Purple Mountain Laboratories, Nanjing 211100, China (e-mail: zhouhb@seu.edu.cn; lyou@seu.edu.cn; xqgao@seu.edu.cn).
H. Zhou, X. Gong, C. G. Tsinos, L. You, X. Gao, and B. Ottersten, “GNN-enabled deep unfolding for precoding in massive MIMO LEO satellite communications,” in Proc. IEEE Wireless Commun. Netw. Conf. (WCNC), Milan, Italy, Mar. 2025, pp. 1–6.
C.-X. Wang et al., “On the road to 6G: Visions, requirements, key technologies, and testbeds,” IEEE Commun. Surveys Tuts., vol. 25, no. 2, pp. 905–974, 2nd Quart., 2023.
R. Deng, B. Di, H. Zhang, H. V. Poor, and L. Song, “Holographic MIMO for LEO satellite communications aided by reconfigurable holographic surfaces,” IEEE J. Sel. Areas Commun., vol. 40, no. 10, pp. 3071–3085, Oct. 2022.
L. You et al., “Ubiquitous integrated sensing and communications for massive MIMO LEO satellite systems,” IEEE Internet Things Mag., vol. 7, no. 4, pp. 30–35, Jul. 2024.
E. Lagunas, S. Chatzinotas, and B. Ottersten, “Low-Earth orbit satellite constellations for global communication network connectivity,” Nature Rev. Electr. Eng., vol. 1, no. 10, pp. 656–665, Sep. 2024.
K.-X. Li et al., “Downlink transmit design for massive MIMO LEO satellite communications,” IEEE Trans. Commun., vol. 70, no. 2, pp. 1014–1028, Feb. 2022.
L. You, K.-X. Li, J. Wang, X. Gao, X.-G. Xia, and B. Ottersten, “Massive MIMO transmission for LEO satellite communications,” IEEE J. Sel. Areas Commun., vol. 38, no. 8, pp. 1851–1865, Aug. 2020.
Y. Zhu, L. You, Q. Kong, G. Seco-Granados, and X. Gao, “Robust precoding for massive MIMO LEO satellite localization systems,” IEEE Trans. Veh. Technol., vol. 74, no. 2, pp. 3434–3438, Feb. 2025.
C. G. Tsinos, S. Maleki, S. Chatzinotas, and B. Ottersten, “On the energy-efficiency of hybrid analog–digital transceivers for single- and multi-carrier large antenna array systems,” IEEE J. Sel. Areas Commun., vol. 35, no. 9, pp. 1980–1995, Sep. 2017.
Y. Liu, Y. Wang, J. Wang, L. You, W. Wang, and X. Gao, “Robust downlink precoding for LEO satellite systems with per-antenna power constraints,” IEEE Trans. Veh. Technol., vol. 71, no. 10, pp. 10694–10711, Oct. 2022.
L. You et al., “Hybrid analog/digital precoding for downlink massive MIMO LEO satellite communications,” IEEE Trans. Wireless Commun., vol. 21, no. 8, pp. 5962–5976, Aug. 2022.
T. Thi Thanh Le, N. Ul Hassan, X. Chen, M.-S. Alouini, Z. Han, and C. Yuen, “A survey on random access protocols in direct-access LEO satellite-based IoT communication,” IEEE Commun. Surveys Tuts., vol. 27, no. 1, pp. 426–462, Feb. 2025.
Z. Zhang et al., “User activity detection and channel estimation for grant-free random access in LEO satellite-enabled Internet of Things,” IEEE Internet Things J., vol. 7, no. 9, pp. 8811–8825, Sep. 2020.
N. U. Hassan, C. Huang, C. Yuen, A. Ahmad, and Y. Zhang, “Dense small satellite networks for modern terrestrial communication systems: Benefits, infrastructure, and technologies,” IEEE Wireless Commun., vol. 27, no. 5, pp. 96–103, Oct. 2020.
Y. Zhu, L. You, H. Zhou, Z. Jin, Q. Kong, and X. Gao, “Robust precoding for massive MIMO LEO satellite integrated communication and localization systems,” IEEE Commun. Lett., vol. 29, no. 1, pp. 21–25, Jan. 2025.
X. Xiao, L. You, K. Wang, and X. Gao, “Distortion-aware beamforming design for multi-beam satellite communications with nonlinear power amplifiers,” Sci. China Inf. Sci., vol. 67, no. 6, pp. 1415–1429, Jun. 2024.
X. Wang et al., “Robust beamforming with gradient-based liquid neural network,” IEEE Wireless Commun. Lett., vol. 13, no. 11, pp. 3020–3024, Nov. 2024.
L. You et al., “Integrated communications and localization for massive MIMO LEO satellite systems,” IEEE Trans. Wireless Commun., vol. 23, no. 9, pp. 11061–11075, Sep. 2024.
Y. Huang, L. You, C. G. Tsinos, W. Wang, and X. Gao, “QoS-aware precoding in downlink massive MIMO LEO satellite communications,” IEEE Commun. Lett., vol. 27, no. 6, pp. 1560–1564, Jun. 2023.
L. You et al., “Beam squint-aware integrated sensing and communications for hybrid massive MIMO LEO satellite systems,” IEEE J. Sel. Areas Commun., vol. 40, no. 10, pp. 2994–3009, Oct. 2022.
X. Gong, A. Lu, X. Liu, X. Fu, X. Gao, and X.-G. Xia, “Deep learning based fingerprint positioning for multi-cell massive MIMO-OFDM systems,” IEEE Trans. Veh. Technol., vol. 73, no. 3, pp. 3832–3849, Mar. 2024.
Z. Jin et al., “GDM4MMIMO: Generative diffusion models for massive MIMO communications,” 2024, arXiv:2412.18281.
C. Zhao, M. Chen, S. Feng, W. Zhu, and B. Qin, “Full-range feature extraction network based on quality–quantity-balance sample enhancement for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens., vol. 62, 2024, Art. no. 5514313.
C. Xie, L. You, Z. Jin, J. Tang, X. Gao, and X.-G. Xia, “CF-CGN: Channel fingerprints extrapolation for multi-band massive MIMO transmission based on cycle-consistent generative networks,” 2024, arXiv:2412.20885.
X. Gong, A.-A. Lu, X. Fu, X. Liu, X. Gao, and X.-G. Xia, “Semisupervised representation contrastive learning for massive MIMO fingerprint positioning,” IEEE Internet Things J., vol. 11, no. 8, pp. 14870–14885, Apr. 2024.
M. Chen et al., “Fractional Fourier-based frequency-spatial–Spectral prototype network for agricultural hyperspectral image open-set classification,” IEEE Trans. Geosci. Remote Sens., vol. 62, 2024, Art. no. 5514014.
Z. Jin, L. You, J. Wang, X.-G. Xia, and X. Gao, “An I2I inpainting approach for efficient channel knowledge map construction,” IEEE Trans. Wireless Commun., vol. 24, no. 2, pp. 1415–1429, Feb. 2025.
C. Fuchs, N. Perlot, J. Riedi, and J. Perdigues, “Performance estimation of optical LEO downlinks,” IEEE J. Sel. Areas Commun., vol. 36, no. 5, pp. 1074–1085, May 2018.
Y. Shi et al., “Machine learning for large-scale optimization in 6G wireless networks,” IEEE Commun. Surveys Tuts., vol. 25, no. 4, pp. 2088–2132, 4th Quart., 2023.
A. Chowdhury, G. Verma, C. Rao, A. Swami, and S. Segarra, “Unfolding WMMSE using graph neural networks for efficient power allocation,” IEEE Trans. Wireless Commun., vol. 20, no. 9, pp. 6004–6017, Sep. 2021.
Y. Shen, J. Zhang, S. H. Song, and K. B. Letaief, “Graph neural networks for wireless communications: From theory to practice,” IEEE Trans. Wireless Commun., vol. 22, no. 5, pp. 3554–3569, May 2023.
Y. Shen, Y. Shi, J. Zhang, and K. B. Letaief, “Graph neural networks for scalable radio resource management: Architecture design and theoretical analysis,” IEEE J. Sel. Areas Commun., vol. 39, no. 1, pp. 101–115, Jan. 2021.
M. Lee, G. Yu, and G. Y. Li, “Graph embedding-based wireless link scheduling with few training samples,” IEEE Trans. Wireless Commun., vol. 20, no. 4, pp. 2282–2294, Apr. 2021.
Y. Wang, Y. Li, Q. Shi, and Y.-C. Wu, “ENGNN: A general edge-update empowered GNN architecture for radio resource management in wireless networks,” IEEE Trans. Wireless Commun., vol. 23, no. 6, pp. 5330–5344, Jun. 2024.
Y. Peng, J. Guo, and C. Yang, “Learning resource allocation policy: Vertex-GNN or edge-GNN?,” IEEE Trans. Mach. Learn. Commun. Netw., vol. 2, pp. 190–209, 2024.
J. Guo and C. Yang, “A model-based GNN for learning precoding,” IEEE Trans. Wireless Commun., vol. 23, no. 7, pp. 6983–6999, Jul. 2024.
F. Zhu et al., “Robust beamforming for RIS-aided communications: Gradient-based manifold meta learning,” IEEE Trans. Wireless Commun., vol. 23, no. 11, pp. 15945–15956, Nov. 2024.
L. You et al., “Massive MIMO hybrid precoding for LEO satellite communications with twin-resolution phase shifters and nonlinear power amplifiers,” IEEE Trans. Commun., vol. 70, no. 8, pp. 5543–5557, Aug. 2022.
K. Kang, Q. Hu, Y. Cai, G. Yu, J. Hoydis, and Y. C. Eldar, “Mixed-timescale deep-unfolding for joint channel estimation and hybrid beamforming,” IEEE J. Sel. Areas Commun., vol. 40, no. 9, pp. 2510–2528, Sep. 2022.
Q. Hu, Y. Cai, Q. Shi, K. Xu, G. Yu, and Z. Ding, “Iterative algorithm induced deep-unfolding neural networks: Precoding design for multiuser MIMO systems,” IEEE Trans. Wireless Commun., vol. 20, no. 2, pp. 1394–1410, Feb. 2021.
F. P. Fontan, M. Vazquez-Castro, C. E. Cabado, J. P. Garcia, and E. Kubista, “Statistical modeling of the LMS channel,” IEEE Trans. Veh. Technol., vol. 50, no. 6, pp. 1549–1567, Nov. 2001.
R. Shafin, L. Liu, Y. Li, A. Wang, and J. Zhang, “Angle and delay estimation for 3-D massive MIMO/FD-MIMO systems based on parametric channel modeling,” IEEE Trans. Wireless Commun., vol. 16, no. 8, pp. 5370–5383, Aug. 2017.
S. Jaeckel, L. Raschkowski, K. Börner, L. Thiele, F. Burkhardt, and E. Eberlein, “QuaDRiGa—Quasi Deterministic Radio Channel Generator,” User Manual, v2.4, Fraunhofer Heinrich Hertz Inst., Berlin, Germany, 2019, p. 260. [Online]. Available: https://quadriga-channelmodel.de
A. Zappone and E. Jorswieck, “Energy efficiency in wireless networks via fractional programming theory,” Found. Trends Commun. Inf. Theory, vol. 11, nos. 3–4, pp. 185–396, 2015.
R. G. Ródenas, M. L. López, and D. Verastegui, “Extensions of Dinkelbach’s algorithm for solving non-linear fractional programming problems,” Top, vol. 7, no. 1, pp. 33–70, Jun. 1999.
Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, “An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,” IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4331–4340, Sep. 2011.
