Parametric Holographic MIMO Channel Modeling and Its Bayesian Estimation

YUAN Zhengdao; GUO Yabo; GAO Dawei; GUO Qinghua; HUANG Chongwen; LIAO Guisheng

doi:10.11999/JEIT250436

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YUAN Zhengdao, GUO Yabo, GAO Dawei, GUO Qinghua, HUANG Chongwen, LIAO Guisheng. Parametric Holographic MIMO Channel Modeling and Its Bayesian Estimation[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250436

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YUAN Zhengdao, GUO Yabo, GAO Dawei, GUO Qinghua, HUANG Chongwen, LIAO Guisheng. Parametric Holographic MIMO Channel Modeling and Its Bayesian Estimation[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250436

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Parametric Holographic MIMO Channel Modeling and Its Bayesian Estimation

doi: 10.11999/JEIT250436 cstr: 32379.14.JEIT250436

1.
School of Artificial Intelligence , Henan Open University, Zhengzhou 450000, China
2.
School of Information Science, Henan University of Technology, Zhengzhou 450000, China
3.
Hangzhou Institute of Technology, Xidian University, Hangzhou 311200, China
4.
University of Wollongong, Wollongong, NSW 2522, Australia
5.
College of Information science Electronic Engineering, Zhejiang University, Hangzhou 310027, China

Funds: The National Natural Science Foundation of China(62301394, 62331023, 62394292), Science and Technology Research Project of Henan Province(252102210228), China National Key R and D Program (2021YFA1000500, 2023YFB2904804)

Received Date: 2025-05-20
Available Online: 2025-09-08

Abstract

Abstract

Objective Holographic Multiple-Input Multiple-Output (HMIMO), based on continuous-aperture antennas and programmable metasurfaces, is regarded as a cornerstone of 6G wireless communication. Its potential to overcome the limitations of conventional massive MIMO is critically dependent on accurate channel modeling and estimation. Three major challenges remain: (1) oversimplified electromagnetic propagation models, such as far-field approximations, cause severe mismatches in near-field scenarios; (2) statistical models fail to characterize the coupling between channel coefficients, user positions, and random orientations; and (3) the high dimensionality of parameter spaces results in prohibitive computational complexity. To address these challenges, a hybrid parametric–Bayesian framework is proposed in which neural networks, factor graphs, and convex optimization are integrated. Precise channel estimation, user position sensing, and angle decoupling in near-field HMIMO systems are thereby achieved. The methodology provides a pathway toward high-capacity 6G applications, including Integrated Sensing And Communication (ISAC). Methods A hybrid channel estimation method is proposed to decouple the “channel–coordinate–angle” parameters and to enable joint estimation of channel coefficients, coordinates, and angles under random user orientations. A neural network is first employed to capture the nonlinear relationship between holographic channel characteristics and the relative coordinates of the base station and user. The trained network is then embedded into a factor graph, where global optimization is performed. The neural network is dynamically approximated through Taylor expansion, allowing bidirectional message propagation and iterative refinement of parameter estimates. To address random user orientations, Euler angle rotation theory is introduced. Finally, convex optimization is applied to estimate the rotation mapping matrix, resulting in the decoupling of coordinate and angle parameters and accurate channel estimation. Results and Discussions The simulations evaluate the performance of different algorithms under varying key parameters, including Signal-to-Noise Ratio (SNR), pilot length L, and base station antenna number M. Two performance metrics are considered: Normalized Mean Square Error (NMSE) of channel estimation and user positioning accuracy, with the Cramér–Rao Lower Bound (CRLB) serving as the theoretical benchmark. At an SNR of 10 dB, the proposed method achieves a channel NMSE below −40 dB, outperforming Least Squares (LS) estimation and approximate model-based approaches. Under high SNR conditions, the NMSE converges toward the CRLB, confirming near-optimal performance (Fig. 5a). The proposed channel model demonstrates superior performance over “approximate methods” due to its enhanced characterization of real-world channels. Moreover, the positioning error gap between the proposed method and the “parallel bound” narrows to nearly 3 dB at high SNR, confirming the accuracy of angle estimation and the effectiveness of parameter decoupling (Fig. 5b). Moreover, the proposed method maintains performance close to the theoretical bounds when system parameters, such as user antenna number N, base station antenna number M, and pilot length L, are varied, demonstrating strong robustness (Figs. 6–8). These results also show that the Euler angle rotation–based estimation effectively compensates for coordinate offsets induced by random user orientations. Conclusions This study proposes a framework for HMIMO channel estimation by integrating neural networks, factor graphs, and convex optimization. The main contributions are threefold. First, Euler angles and coordinate mapping are incorporated into the parameterized channel model through factorization and factor graphs, enabling channel modeling under arbitrary user antenna orientations. Second, neural networks and convex optimization are embedded as factor nodes in the graph, allowing nonlinear function approximation and global optimization. Third, bidirectional message passing between neural network and convex optimization nodes is realized through Taylor expansion, thereby achieving joint decoupling and estimation of channel parameters, coordinates, and angles. Simulation results confirm that the proposed framework achieves higher accuracy—exceeding benchmarks by more than 3 dB—and demonstrates strong robustness across a range of scenarios. Future work will extend the method to multi-user environments, incorporate polarization diversity, and address hardware impairments such as phase noise, with the aim of supporting practical deployment in 6G systems.
- Holographic Multiple-Input Multiple-Output (HMIMO),
- neural networks,
- Bayesian estimation,
- Euler angle rotation,
- message-passing algorithm.

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References(19)

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