Extremely large-scale MIMO channel estimation in hybrid field based on adaptive gradient matching pursuit algorithm

doi:10.11772/j.issn.1001-9081.2024121805

Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (12): 3931-3938.DOI: 10.11772/j.issn.1001-9081.2024121805

• Network and communications • Previous Articles Next Articles

Extremely large-scale MIMO channel estimation in hybrid field based on adaptive gradient matching pursuit algorithm

Zhanjun LIU¹^,², Yunpeng SONG¹^,², Shengbao WANG¹^,²

^1.School of Communications and Information Engineering，Chongqing University of Posts and Telecommunications，Chongqing 400065，China
^2.Chongqing Key Laboratory of Mobile Communication Technology （Chongqing University of Posts and Telecommunications），Chongqing 400065，China

Received:2024-12-24 Revised:2025-03-21 Accepted:2025-03-25 Online:2025-04-22 Published:2025-12-10
Contact: Yunpeng SONG
About author:LIU Zhanjun， born in 1975， Ph. D.， professor. His research interests include wireless mobile communication.
SONG Yunpeng， born in 1999， M. S. candidate. His research interests include physical layer algorithms for mobile communication， channel estimation.
WANG Shengbao， born in 2001， M. S. candidate. His research interests include physical layer algorithms for mobile communication， channel estimation.
Supported by:
Innovation and Development Joint Fund of Chongqing Natural Science Foundation （China Satellite Network）(CSTB2023NSCQ-LZX0114)

基于自适应梯度匹配追踪算法的超大规模多输入多输出混合场信道估计

刘占军¹^,², 宋云鹏¹^,², 王盛宝¹^,²

^1.重庆邮电大学通信与信息工程学院，重庆 400065
^2.移动通信技术重庆市市级重点实验室（重庆邮电大学），重庆 400065

通讯作者: 宋云鹏
作者简介:刘占军（1975—），男，河北保定人，教授，博士，主要研究方向：无线移动通信
宋云鹏（1999—），男，山东济南人，硕士研究生，主要研究方向：移动通信物理层算法、信道估计
王盛宝（2001—），男，湖北荆门人，硕士研究生，主要研究方向：移动通信物理层算法、信道估计。
基金资助:
重庆市自然科学基金创新发展联合基金（中国星网）资助项目(CSTB2023NSCQ-LZX0114)

Abstract

Abstract:

In response to the problem of high complexity and low accuracy in hybrid-field channel estimation faced by eXtremely Large-scale Multiple-Input Multiple-Output （XL-MIMO） systems in 6th Generation wireless communication technology （6G） networks， an Adaptive Gradient Matching Pursuit （AGMP） algorithm was proposed. Firstly， the angular-domain transformation matrix was used to estimate far-field components， and the polar-domain transformation matrix was used to estimate near-field components， thereby transforming the channel estimation problem into a sparse reconstruction problem. Then， during the component estimation process， the Least Mean Square （LMS） algorithm was combined with an adaptive gradient search strategy to optimize path component estimation through dynamic adjustment of step-size parameters， and the Minimum Mean Squared Error （MMSE） target was approximated iteratively， thereby optimizing the channel estimation process. Finally， the complete hybrid-field channel was reconstructed by using angular-domain and polar-domain transformation matrices， thereby achieving accurate hybrid-field channel estimation. Simulation results demonstrate that in low-Signal-to-Noise Ratio （SNR） environments， the proposed algorithm improves the achievable rate by 20.46% approximately compared to Orthogonal Matching Pursuit （OMP） algorithm. Furthermore， as the number of User Equipment （UE） antennas increases， the Normalized Mean Squared Error （NMSE） of the proposed algorithm is reduced by 1.2 dB approximately compared to that of OMP algorithm in multi-antenna environment. It can be seen that the proposed algorithm achieves superior estimation performance in low-SNR and multi-antenna UE environments.

Key words: eXtremely Large-scale Multiple-Input Multiple-Output (XL-MIMO), channel estimation, hybrid field, adaptive search, gradient descent

摘要：

针对第六代无线通信技术（6G）网络中超大规模多输入多输出（XL-MIMO）系统在混合场信道估计中面临的高复杂度和低精度问题，提出一种自适应梯度匹配追踪（AGMP）算法。首先，利用角域变换矩阵估计远场分量，并利用极域变换矩阵估计近场分量，从而将信道估计问题转化为稀疏重构问题；其次，在估计分量的过程中，采用最小均方（LMS）算法，并结合自适应梯度搜索策略，通过动态调整步长参数优化路径分量估计，并迭代逼近最小均方误差（MMSE）目标，从而优化信道估计过程；最后，通过角域和极域变换矩阵重建整个混合场信道，从而完成混合场信道的精确估计。仿真实验结果表明，在低信噪比（SNR）环境下，与正交匹配追踪（OMP）算法相比，所提算法的可达速率提升了约20.46%。此外，随着用户设备（UE）天线数量的增加，在多天线环境下，所提算法的归一化均方误差（NMSE）相较于OMP算法降低了约1.2 dB。可见，所提算法在低SNR和多天线UE环境下能获得更好的估计性能。

关键词: 超大规模多输入多输出, 信道估计, 混合场, 自适应搜索, 梯度下降

CLC Number:

TN929.5

Zhanjun LIU, Yunpeng SONG, Shengbao WANG. Extremely large-scale MIMO channel estimation in hybrid field based on adaptive gradient matching pursuit algorithm[J]. Journal of Computer Applications, 2025, 45(12): 3931-3938.

刘占军, 宋云鹏, 王盛宝. 基于自适应梯度匹配追踪算法的超大规模多输入多输出混合场信道估计[J]. 《计算机应用》唯一官方网站, 2025, 45(12): 3931-3938.

Figures/Tables 8

Fig. 1 Hybrid field system model of XL-MIMO

Fig. 2 Hybrid field channel model

Fig. 3 Block diagram of channel estimation system

Tab. 1 Simulation parameters

参数	变量符号	值
基站天线数	$N b$	256
用户天线数	$N u$	［1，10］
载波波长/m	$λ$	0.01
载波频率/GHz	$f$	30
总路径数	$L$	10
导频长度	$τ$	1
路径增益因子	$k$	10
稀疏度因子	$γ$	（0， 1）
步长参数	$μ$	［0.1， 0.6］
信道稀疏度参数	$β$	0.08
基站到用户设备的距离/m	$d R, 0$ / $d T, 0$	（10， 500）
基站与用户设备之间角度	$θ R, 0$ / $θ T, 0$	（-1， 1）

Tab. 1 Simulation parameters

参数	变量符号	值
基站天线数	$N b$	256
用户天线数	$N u$	［1，10］
载波波长/m	$λ$	0.01
载波频率/GHz	$f$	30
总路径数	$L$	10
导频长度	$τ$	1
路径增益因子	$k$	10
稀疏度因子	$γ$	（0， 1）
步长参数	$μ$	［0.1， 0.6］
信道稀疏度参数	$β$	0.08
基站到用户设备的距离/m	$d R, 0$ / $d T, 0$	（10， 500）
基站与用户设备之间角度	$θ R, 0$ / $θ T, 0$	（-1， 1）

Fig. 4 Comparison of achievable rates of channel estimation algorithms at different SNRs

Fig. 5 NMSE performance of channel estimation algorithms with different numbers of user transmit antennas

Fig. 6 NMSE performance of channel estimation algorithms with different numbers of paths

Fig. 7 NMSE performance of channel estimation algorithms with different sparsity factors

References 22

[1]	ZUO W， TANG P， MIAO H， et al. Analysis of spatial non-stationary characteristics for 6G XL-MIMO communication［C］// Proceedings of the 2024 IEEE 99th Vehicular Technology Conference. Piscataway： IEEE， 2024： 1-6.
[2]	ZHANG H， SHLEZINGER N， GUIDI F， et al. Beam focusing for near-field multiuser MIMO communications［J］. IEEE Transactions on Wireless Communications， 2022， 21（9）： 7476-7490.
[3]	GONG T， GAVRIILIDIS P， JI R， et al. Holographic MIMO communications： theoretical foundations， enabling technologies， and future directions［J］. IEEE Communications Surveys and Tutorials， 2024， 26（1）： 196-257.
[4]	YU W， SHEN Y， HE H， et al. An adaptive and robust deep learning framework for THz ultra-massive MIMO channel estimation［J］. IEEE Journal of Selected Topics in Signal Processing， 2023， 17（4）： 761-776.
[5]	XIAO J， WANG J， CHEN Z， et al. U-MLP-based hybrid-field channel estimation for XL-RIS assisted millimeter-wave MIMO systems［J］. IEEE Wireless Communications Letters， 2023， 12（6）： 1042-1046.
[6]	CUI M， DAI L. Channel estimation for extremely large-scale MIMO： far-field or near-field？［J］. IEEE Transactions on Communications， 2022， 70（4）： 2663-2677.
[7]	WEI X， DAI L. Channel estimation for extremely large-scale massive MIMO： far-field， near-field， or hybrid-field？［J］. IEEE Communications Letters， 2022， 26（1）： 177-181.
[8]	NAYIR H， KARAKOCA E， GÖRÇIN A， et al. Hybrid-field channel estimation for massive MIMO systems based on OMP cascaded convolutional autoencoder［C］// Proceedings of the 2022 IEEE 96th Vehicular Technology Conference. Piscataway： IEEE， 2022： 1-6.
[9]	CHEN Y， YAN L， HAN C. Hybrid spherical-and planar-wave modeling and DCNN-powered estimation of Terahertz ultra-massive MIMO channels［J］. IEEE Transactions on Communications， 2021， 69（10）： 7063-7076.
[10]	YANG W， LI M， LIU Q. A practical channel estimation strategy for XL-MIMO communication systems［J］. IEEE Communications Letters， 2023， 27（6）： 1580-1583.
[11]	李汀，张春洁，夏雨婷. 超大规模混合场MIMO去伪峰信道估计技术［J］. 信号处理， 2023， 39（6）： 1131-1140.
	LI T， ZHANG C J， XIA Y T. Channel estimation technique for eliminating spurious peaks in ultra-massive hybrid-field MIMO［J］. Journal of Signal Processing， 2023， 39（6）： 1131-1140.
[12]	王丹，方杰宁，谢长江. 基于均匀线性阵列的超大规模MIMO混合场信道估计算法［J］. 计算机应用研究， 2024， 41（10）： 3124-3128.
	WANG D， FANG J N， XIE C J. Hybrid field channel estimation algorithm for extremely large-scale MIMO based on uniform linear array［J］. Application Research of Computers， 2024， 41（10）： 3124-3128.
[13]	HU Z， CHEN C， JIN Y， et al. Hybrid-field channel estimation for extremely large-scale massive MIMO system［J］. IEEE Communications Letters， 2023， 27（1）： 303-307.
[14]	PENG X， ZHAO L， JIANG Y， et al. Channel estimation for extremely large-scale massive MIMO systems in hybrid-field channel［C］// Proceedings of the 2023 IEEE/CIC International Conference on Communications in China. Piscataway： IEEE， 2023： 1-6.
[15]	LU Y， DAI L. Near-field channel estimation in mixed LoS/NLoS environments for extremely large-scale MIMO systems［J］. IEEE Transactions on Communications， 2023， 71（6）： 3694-3707.
[16]	WU Z， DAI L. Multiple access for near-field communications： SDMA or LDMA？［J］. IEEE Journal on Selected Areas in Communications， 2023， 41（6）： 1918-1935.
[17]	王亿，杨柳，张痛快. RIS辅助毫米波系统中基于压缩感知的信道估计［J］. 计算机应用， 2022， 42（12）： 3870-3875.
	WANG Y， YANG L， ZHANG T K. Channel estimation based on compressive sensing in RIS-assisted millimeter wave system［J］. Journal of Computer Applications， 2022， 42（12）： 3870-3875.
[18]	HUANG C， LIU L， YUEN C， et al. Iterative channel estimation using LSE and sparse message passing for mmWave MIMO systems［J］. IEEE Transactions on Signal Processing， 2019， 67（1）： 245-259.
[19]	XU P Z， XIANG W， YU Q Y. DFrFT-based near-field channel estimation for extremely large-scale MIMO systems［J］. IEEE Communications Letters， 2024， 28（8）： 1914-1918.
[20]	WANG Z， ZHANG J， AI B， et al. Uplink performance of cell-free massive MIMO with multi-antenna users over jointly-correlated Rayleigh fading channels［J］. IEEE Transactions on Wireless Communications， 2022， 21（9）： 7391-7406.
[21]	LIU Z， ZHANG J， LIU Z， et al. Double-layer power control for mobile cell-free XL-MIMO with multi-agent reinforcement learning［J］. IEEE Transactions on Wireless Communications， 2024， 23（5）： 4658-4674.
[22]	LIN Y M， CHEN Y， HUANG N S， et al. Low-complexity stochastic gradient pursuit algorithm and architecture for robust compressive sensing reconstruction［J］. IEEE Transactions on Signal Processing， 2017， 65（3）： 638-650.

Extremely large-scale MIMO channel estimation in hybrid field based on adaptive gradient matching pursuit algorithm

基于自适应梯度匹配追踪算法的超大规模多输入多输出混合场信道估计

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 8

References 22

Related Articles 15

Recommended Articles

Metrics

[1]	Huahua WANG, Changjiang XIE, Jiening FANG. Fast beam training on extremely large-scale multiple-input multiple-output system [J]. Journal of Computer Applications, 2025, 45(5): 1625-1631.
[2]	Dan WANG, Wenhao ZHANG, Lijuan PENG. Channel estimation of reconfigurable intelligent surface assisted communication system based on deep learning [J]. Journal of Computer Applications, 2025, 45(5): 1613-1618.
[3]	Shufen ZHANG, Benjian TANG, Zikun TIAN, Xiaoyang QING. Survey of federated learning based on differential privacy [J]. Journal of Computer Applications, 2025, 45(10): 3221-3230.
[4]	Fang LEI, Yongcai NIU. Channel estimation method for low earth orbit satellite MIMO-OTFS system based on improved generalized orthogonal matching pursuit [J]. Journal of Computer Applications, 2024, 44(8): 2514-2520.
[5]	Ye TIAN, Jinjin CHEN, Xingyi ZHANG. Hybrid optimizer combining evolutionary computation and gradient descent for constrained multi-objective optimization [J]. Journal of Computer Applications, 2024, 44(5): 1386-1392.
[6]	Yu ZHANG, Ying CAI, Jianyang CUI, Meng ZHANG, Yanfang FAN. Gradient descent with momentum algorithm based on differential privacy in convolutional neural network [J]. Journal of Computer Applications, 2023, 43(12): 3647-3653.
[7]	Lei TIAN, Lina GE. Advertising recommendation algorithm based on differential privacy [J]. Journal of Computer Applications, 2023, 43(11): 3346-3350.
[8]	Yi WANG, Liu YANG, Tongkuai ZHANG. Channel estimation based on compressive sensing in RIS-assisted millimeter wave system [J]. Journal of Computer Applications, 2022, 42(12): 3870-3875.
[9]	CHEN Chengrui, SUN Ning, HE Shibiao, LIAO Yong. Deep learning-based joint channel estimation and equalization algorithm for C-V2X communications [J]. Journal of Computer Applications, 2021, 41(9): 2687-2693.
[10]	JING Xinghong, SUN Guodong, HE Shibiao, LIAO Yong. Time-varying channel estimation method based on sliding window filtering and polynomial fitting [J]. Journal of Computer Applications, 2021, 41(9): 2699-2704.
[11]	WANG Jinkai, JIA Xu. Vein recognition algorithm based on Siamese nonnegative matrix factorization with transferability [J]. Journal of Computer Applications, 2021, 41(3): 898-903.
[12]	WANG Jinkai, JIA Xu. Vehicle face recognition algorithm based on NMF with weighted and orthogonal constraints [J]. Journal of Computer Applications, 2020, 40(4): 1050-1055.
[13]	CHENG Qiwei, CHEN Qimai, HE Chaobo, LIU Hai. Overlapping community detection method based on improved symmetric binary nonnegative matrix factorization [J]. Journal of Computer Applications, 2020, 40(11): 3203-3210.
[14]	DING Ning, GUAN Xinrong, YANG Weiwei, LI Tongkai, WANG Jianshe. Performance analysis of wireless key generation with multi-bit quantization under imperfect channel estimation condition [J]. Journal of Computer Applications, 2020, 40(1): 143-147.
[15]	ZHOU Zhen, YUAN Zhengdao. Efficient communication receiver design for Internet of things environment [J]. Journal of Computer Applications, 2020, 40(1): 202-206.