毫米波MIMO系统中基于自适应梯度算法的混合预编码

doi:10.11959/j.issn.1000-436x.2021207

Abstract

Abstract:

To reduce the complexity of existing hybrid precoding algorithms based on alternating minimization (AltMin) and online learning via gradient descent with momentum in mmWave MIMO systems, aiming at the single-user scenario, the problem of designing the hybrid precoder was reconsidered and an equivalent single hidden layer neural network was proposed.Under the new architecture, the elements of the digital and analog precoder were equivalent to the connecting weights of a single hidden layer neural network, and their optimal solution could be obtained via the weights training method.Inspired by the back propagation (BP) algorithm in feed forward neural networks, an adaptive gradient (AG)-based BP algorithm for hybrid precoding was proposed.Furthermore, the proposed algorithm was extended to the multi-user scenario.The numerical results show that the proposed algorithm achieves approximately the same spectral efficiency as the fully-digital precoding in both the single-user and multi-user scenarios, while has lower complexity than the existing AltMin-based hybrid precoding algorithms and online learning hybrid precoding based on gradient descent with momentum.

Key words: mmWave, hybrid precoding, neural network, adaptive gradient

CLC Number:

TN92

Yu ZHANG, Zhi ZHANG, Xiaodai DONG. Adaptive gradient algorithm for hybrid precoding in mmWave MIMO system[J]. Journal on Communications, 2021, 42(10): 95-105.

Figures/Tables 11

操作	复数乘法和除法个数
计算 ${y}_{n = 1}^{N_{d}}$	$N_{d} N_{t} N_{S}$
计算 ${b_{q}^{n}}_{n = 1}^{N_{d}}$	$N_{d} N_{t}^{RF} N_{S}$
计算 ${{\hat{y}}_{p}^{n}}_{n = 1}^{N_{d}}$	$N_{d} N_{t} N_{t}^{RF}$
更新a_p,q	$(4 N_{d} +2) N_{t} N_{t}^{RF}$
重构a_p,q	$2 N_{t} N_{t}^{RF}$
更新d_q,u	$2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF})$

算法	复数乘法和除法个数
算法1	$N_{iter} ((5 N_{d} +4) N_{t} N_{t}^{RF} + N_{d} N_{t} N_{S} + N_{d} N_{t}^{RF} N_{S} +$
	$2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF}))$
CG-AltMin	$N_{iter}^{i} (2(N_{t})^{2} N_{t}^{RF} N_{S} + 11 N_{t} N_{t}^{RF} + 1) +$
	$N_{iter}^{o} (2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF}))$
BB-AltMin	$N_{iter}^{i} (2(N_{t})^{2} N_{t}^{RF} N_{S} + 8 N_{t} N_{t}^{RF} + 1) +$
	$N_{iter}^{o} (2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF}))$
GP-AltMin	$N_{iter}^{i} (2(N_{t})^{2} N_{t}^{RF} N_{S} + 2 N_{t} N_{t}^{RF} + 1) +$
	$N_{iter}^{o} (2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF}))$
GDM	$N_{iter}^{GDM} ((5 N_{d} +4) N_{t} N_{t}^{RF} + N_{d} N_{t} N_{S} + N_{d} N_{t}^{RF} N_{S} +$
	$2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF})$

N_RF	本文算法		CG			BB			GP		GDM
N_RF	本文算法	$N_{iter}^{o}$		$N_{iter}^{i}$	$N_{iter}^{o}$		$N_{iter}^{i}$	$N_{iter}^{o}$		$N_{iter}^{i}$	$N_{iter}^{GDM}$
2	314.503	3.644		80.213	3.727		102.717	3.846		63.102	2 000
3	453.824	4.016		111.852	3.981		187.170	4.715		126.886	2 000
4	192.281	3.720		104.735	3.755		249.381	3.992		113.690	1 955.35
5	81.701	3.565		94.382	3.604		231.386	3.679		124.113	1 547.26
6	56.548	3.391		86.065	3.427		220.753	3.528		190.989	1 236.19

References 33

[1]	RAPPAPORT T S , SUN S , MAYZUS R ,et al. Millimeter wave mobile communications for 5G cellular:it will work![J]. IEEE Access, 2013,1: 335-349.
[2]	ROH W , SEOL J Y , PARK J ,et al. Millimeter-wave beamforming as an enabling technology for 5G cellular communications:theoretical feasibility and prototype results[J]. IEEE Communications Magazine, 2014,52(2): 106-113.
[3]	SHAFI M , MOLISCH A F , SMITH P J ,et al. 5G:a tutorial overview of standards,trials,challenges,deployment,and practice[J]. IEEE Journal on Selected Areas in Communications, 2017,35(6): 1201-1221.
[4]	RANGAN S , RAPPAPORT T S , ERKIP E . Millimeter-wave cellular wireless networks:potentials and challenges[J]. Proceedings of the IEEE, 2014,102(3): 366-385.
[5]	SALOUS S , ESPOSTI V D , FUSCHINI F ,et al. Millimeter-wave propagation:characterization and modeling toward fifth-generation systems[J]. IEEE Antennas and Propagation Magazine, 2016,58(6): 115-127.
[6]	HEATH R W , GONZáLEZ-PRELCIC N , RANGAN S ,et al. An overview of signal processing techniques for millimeter wave MIMO systems[J]. IEEE Journal of Selected Topics in Signal Processing, 2016,10(3): 436-453.
[7]	AYACH O E , RAJAGOPAL S , ABU-SURRA S , ,et al. Spatially sparse precoding in millimeter wave MIMO systems[J]. IEEE Transactions on Wireless Communications, 2014,13(3): 1499-1513.
[8]	LEE Y Y , WANG C H , HUANG Y H . A hybrid RF/baseband precoding processor based on parallel-index-selection matrix-inversion- bypass simultaneous orthogonal matching pursuit for millimeter wave MIMO systems[J]. IEEE Transactions on Signal Processing, 2015,63(2): 305-317.
[9]	ZHANG Y , HUANG Y Z , QIN X Q ,et al. Low complexity hybrid precoding based on ORLS for mmWave massive MIMO systems[C]// Proceedings of 2018 IEEE Wireless Communications and Networking Conference (WCNC). Piscataway:IEEE Press, 2018: 1-6.
[10]	HUNG W L , CHEN C H , LIAO C C ,et al. Low-complexity hybrid precoding algorithm based on orthogonal beamforming codebook[C]// Proceedings of 2015 IEEE Workshop on Signal Processing Systems (SiPS). Piscataway:IEEE Press, 2015: 1-5.
[11]	廖勇, 杨馨怡, 杜洁汝 . 基于两阶段的毫米波大规模MIMO低复杂度混合预编码算法[J]. 电子学报, 2021,49(7): 1298-1304.
	LIAO Y , YANG X Y , DU J R . A two-stage based low complexity hy-brid precoding algorithm for millimeter-wave massive MIMO[J]. Acta Electronica Sinica, 2021,49(7): 1298-1304.
[12]	刘剑飞, 何利平, 陶颖 ,等. 大规模MIMO系统中低复杂度的码本搜索方法[J]. 通信学报, 2019,40(1): 79-86.
	LIU J F , HE L P , TAO Y ,et al. Low complexity codebook search me-thod in massive MIMO system[J]. Journal on Communications, 2019,40(1): 79-86.
[13]	YU X H , SHEN J C , ZHANG J ,et al. Alternating minimization algorithms for hybrid precoding in millimeter wave MIMO systems[J]. IEEE Journal of Selected Topics in Signal Processing, 2016,10(3): 485-500.
[14]	NI W H , DONG X D , LU W S . Near-optimal hybrid processing for massive MIMO systems via matrix decomposition[J]. IEEE Transactions on Signal Processing, 2017,65(15): 3922-3933.
[15]	MULLA M , ULUSOY A H , RIZANER A ,et al. Barzilai-borwein gradient algorithm based alternating minimization for single user millimeter wave systems[J]. IEEE Wireless Communications Letters, 2020,9(4): 508-512.
[16]	CHEN J C . Gradient projection-based alternating minimization algorithm for designing hybrid beamforming in millimeter-wave MIMO systems[J]. IEEE Communications Letters, 2019,23(1): 112-115.
[17]	RUSU C , MèNDEZ-RIAL R , GONZáLEZ-PRELCIC N . Low complexity hybrid precoding strategies for millimeter wave communication systems[J]. IEEE Transactions on Wireless Communications, 2016,15(12): 8380-8393.
[18]	ALKHATEEB A , LEUS G , HEATH R W . Limited feedback hybrid precoding for multi-user millimeter wave systems[J]. IEEE Transactions on Wireless Communications, 2015,14(11): 6481-6494.
[19]	NGUYEN D H N , LE L B , LE-NGOC T . Hybrid MMSE precoding for mmWave multiuser MIMO systems[C]// Proceedings of 2016 IEEE International Conference on Communications (ICC). Piscataway:IEEE Press, 2016: 1-6.
[20]	NI W H , DONG X D . Hybrid block diagonalization for massive multiuser MIMO systems[J]. IEEE Transactions on Communications, 2016,64(1): 201-211.
[21]	HUANG H J , SONG Y W , YANG J ,et al. Deep-learning-based millimeter-wave massive MIMO for hybrid precoding[J]. IEEE Transactions on Vehicular Technology, 2019,68(3): 3027-3032.
[22]	CHEN K , YANG J , GE X H ,et al. Complex-BP-neural-network-based hybrid precoding for millimeter wave multiuser massive MIMO systems[C]// Proceedings of 2019 Computing,Communications and IoT Applications (ComComAp). Piscataway:IEEE Press, 2019: 100-105.
[23]	SIDHARTH C , HIREMATH S M , PATRA S K . Deep learning based hybrid precoding for mmwave massive MIMO system using comcepnet[C]// Proceedings of 2020 International Conference on Communication and Signal Processing (ICCSP). Piscataway:IEEE Press, 2020: 1317-1321.
[24]	BAO X L , FENG W J , ZHENG J L ,et al. Deep CNN and equivalent channel based hybrid precoding for mmWave massive MIMO systems[J]. IEEE Access, 2020,8: 19327-19335.
[25]	ELBIR A M . A deep learning framework for hybrid beamforming without instantaneous CSI feedback[J]. IEEE Transactions on Vehicular Technology, 2020,69(10): 11743-11755.
[26]	ELBIR A M , PAPAZAFEIROPOULOS A K . Hybrid precoding for multiuser millimeter wave massive MIMO systems:a deep learning approach[J]. IEEE Transactions on Vehicular Technology, 2020,69(1): 552-563.
[27]	CHAI M Y , TANG S H , ZHAO M ,et al. HPNet:a compressed neural network for robust hybrid precoding in multi-user massive MIMO systems[C]// Proceedings of GLOBECOM 2020 - 2020 IEEE Global Communications Conference. Piscataway:IEEE Press, 2020: 1-7.
[28]	MA W Y , QI C H , ZHANG Z C ,et al. Sparse channel estimation and hybrid precoding using deep learning for millimeter wave massive MIMO[J]. IEEE Transactions on Communications, 2020,68(5): 2838-2849.
[29]	章坚武, 王路鑫, 孙玲芬 ,等. 人工智能在 5G 系统中的应用综述[J]. 电信科学, 2021,37(5): 14-31.
	ZHANG J W , WANG L X , SUN L F ,et al. An survey on application of artificial intelligence in 5G system[J]. Telecommunications Science, 2021,37(5): 14-31.
[30]	ALKHATEEB A , EL AYACH O , LEUS G ,et al. Channel estimation and hybrid precoding for millimeter wave cellular systems[J]. IEEE Journal of Selected Topics in Signal Processing, 2014,8(5): 831-846.
[31]	LEUNG H , HAYKIN S . The complex backpropagation algorithm[J]. IEEE Transactions on Signal Processing, 1991,39(9): 2101-2104.
[32]	DUCHI J , HAZAN E , SINGER Y . Adaptive subgradient methods for online learning and stochastic optimization[J]. Journal of Machine Learning Research, 2011,12: 2121-2159.
[33]	SOHRABI F , YU W . Hybrid digital and analog beamforming design for large-scale antenna arrays[J]. IEEE Journal of Selected Topics in Signal Processing, 2016,10(3): 501-513.

Metrics

Recommended 0

No Suggested Reading articles found!

Adaptive gradient algorithm for hybrid precoding in mmWave MIMO system

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 11

References 33

Related Articles 15

Metrics

Recommended 0

[1]	Jinyin CHEN, Haiyang XIONG, Haonan MA, Yayu ZHENG. CLB-Defense: based on contrastive learning defense for graph neural network against backdoor attack [J]. Journal on Communications, 2023, 44(4): 154-166.
[2]	Jianfeng LI, Zheyu LIU, Yang RONG, Zhan LI, Bolin LIAO, Linxi QU, Zhijie LIU, Kunhuang LIN. Zeroing neural network for time-varying convex quadratic programming with linear noise [J]. Journal on Communications, 2023, 44(4): 226-233.
[3]	Yun LIN, Huaitao XU, Sen WANG, Sicheng ZHANG, Long ZHUANG. Objective assessment of communication speech interference effect based on feature fusion [J]. Journal on Communications, 2023, 44(3): 105-116.
[4]	Hongyu YANG, Haiyun YANG, Liang ZHANG, Xiang CHENG. Feature dependence graph based source code loophole detection method [J]. Journal on Communications, 2023, 44(1): 103-117.
[5]	Shiwen HE, Jun YUAN, Zhenyu AN, Min ZHANG, Yongming HUANG, Yaoxue ZHANG. GNN-based optimization algorithm for joint user scheduling and beamforming [J]. Journal on Communications, 2022, 43(7): 73-84.
[6]	Tao LENG, Lijun CAI, Aimin YU, Ziyuan ZHU, Jian’gang MA, Chaofei LI, Ruicheng NIU, Dan MENG. Review of threat discovery and forensic analysis based on system provenance graph [J]. Journal on Communications, 2022, 43(7): 172-188.
[7]	Gangcan SUN, Xinli WU, Wanming HAO, Zhengyu ZHU. Hybrid precoding and power allocation for mmWave NOMA systems based on time delay line arrays [J]. Journal on Communications, 2022, 43(6): 179-188.
[8]	Yurong LIAO, Haining WANG, Cunbao LIN, Yang LI, Yuqiang FANG, Shuyan NI. Research progress of deep learning-based object detection of optical remote sensing image [J]. Journal on Communications, 2022, 43(5): 190-203.
[9]	Fan ZHANG, Yun HUANG, Zizhuo FANG, Wei GUO. Lost-minimum post-training parameter quantization method for convolutional neural network [J]. Journal on Communications, 2022, 43(4): 114-122.
[10]	Zhengyu ZHU, Gengwang HOU, Chongwen HUANG, Gangcan SUN, Wanming HAO, Jing LIANG. Systems resource allocation algorithm for RIS-assisted D2D secure communication based on parallel CNN [J]. Journal on Communications, 2022, 43(3): 172-179.
[11]	Junyan HUO, Danni WANG, Yanzhuo MA, Shuai WAN, Fuzheng YANG. Efficient cross-component prediction for H.266/VVC based on lightweight fully connected networks [J]. Journal on Communications, 2022, 43(2): 143-155.
[12]	Hua LONG, Zhangheng HUANG, Yubin SHAO, Qingzhi DU, Shumeng SU. Research on language recognition algorithm based on improved CFCC feature extraction [J]. Journal on Communications, 2022, 43(12): 211-221.
[13]	Zhengyu ZHU, Pengfei CHEN, Zixuan WANG, Kexian GONG, Di WU, Zhongyong WANG. Short wave protocol signals recognition based on Swin-Transformer [J]. Journal on Communications, 2022, 43(11): 127-135.
[14]	Zhenyu XIAO, Ke LIU, Lipeng ZHU. Millimeter-wave array enabled UAV-to-UAV communication technology [J]. Journal on Communications, 2022, 43(10): 196-209.
[15]	Lei ZHANG, Qin WANG. Hybrid precoding based on distributed partially-connected structure for multiuser massive MIMO [J]. Journal on Communications, 2022, 43(1): 104-116.