近三十年来，无线通信业务量剧增，第五代移动通信（The 5th Generation Mobile Communication，5G）应运而生。毫米波、大规模多输入多输出（Massive Multiple-Input Multiple-Output，Massive MIMO）和波束赋形是5G三大核心技术。其中全数字波束赋形（Digital Beamforming，DBF）性能理想，硬件成本和能耗较高。全模拟波束赋形（Analog Beamforming，ABF）硬件成本低，性能表现差。而混合波束赋形（Hybrid Beamforming，HBF）技术能够实现期望性能和硬件成本间的折衷，但其在模拟域的处理存在恒模约束，系统不能获得全部天线增益，存在性能损失。其次，移动通信中传统的正交多址（Orthogonal Multiple Access，OMA）技术中存在一个资源块被单用户独占的问题。因此，本文结合毫米波通信、Massive MIMO技术和波束赋形技术，分别针对混合波束赋形的性能损失和OMA技术中一个资源块被单用户独占的问题，研究了毫米波Massive MIMO系统的混合波束赋形算法。

针对混合波束赋形性能损失的问题，基于部分连接架构下的毫米波Massive MIMO系统，以最大化系统频谱效率为目标，提出一种混合波束赋形算法。首先基于奇异值分解得到最优全数字波束赋形，然后利用矩阵特性交替更新模拟和数字波束赋形，将非凸问题转化为凸优化子问题，在小范围内求解模拟域的元素相位增量。仿真结果显示该算法在所考虑的信噪比（Signal to Noise Ratio，SNR）范围内的平均频谱效率分别是部分连接架构下的经典算法、全模拟波束赋形、全连接架构下经典算法和全数字波束赋形的108.8%、168.1%、98.7%和97.6%。即，所提算法性能优于部分连接架构下的经典算法和全模拟波束赋形的性能，与最优全数字波束赋形及全连接架构下经典算法的性能接近，但硬件复杂度和功耗更低。

针对OMA技术中一个资源块被单用户独占的问题，引入非正交多址（Non-Orthogonal Multiple Access，NOMA）技术，提出了两种用户分组、功率分配和混合波束赋形方案。首先，基于K均值聚类算法，根据用户间的信道相关性，提出了一种用户分组方案。在此基础上，提出了一个功率分配和混合波束赋形的联合优化问题。然后，将信漏噪比（Signal to Leakage plus Noise Ratio，SLNR）作为性能目标，可将原问题的两个变量解耦从而迭代地求解。然后，基于初始波束赋形矩阵，通过引入辅助正实变量，将功率分配问题转化为一个凸问题，再基于卡罗需-库恩-塔克（Karush-Kuhn-Tucker，KKT）条件和拉格朗日（Lagrange）乘子法解得最优功率分配闭式解。最后，基于广义特征值分解（Generalized Eigenvalue Decomposition，GED）求得最优全数字波束赋形矩阵的闭式解。基于此矩阵，根据对模拟域和数字域的不同优化方法，设计两种混合波束赋形算法。仿真结果显示在所考虑的信噪比范围内，经典的NOMA方案的平均频谱效率和平均能量效率分别是所提方案2的24.8%和24.7%，分别是所提方案1的32.8%和32.7%。经典的OMA方案的频谱效率和能量效率分别是所提方案2的0.45%和1.17%，分别是所提方案1的0.61%和1.55%。即，所提出的两种用户分组、功率分配和混合波束赋形的联合方案频谱效率和能量效率优于经典的NOMA方案和OMA方案。

In the past three decades, with the rapid growth of wireless communication traffic, 5G emerges as the times require. Millimeter wave, Massive MIMO and beamforming are the three core technologies of 5G. Due to the DBF can achieve the best performance, but the hardware cost and energy consumption are high, and ABF has low hardware cost and poor performance, HBF technology can achieve the tradeoff between the ideal performance and hardware cost, but its processing in the analog domain has constant modulus constraint, so the system can not obtain all the antenna gain and has performance loss. Secondly, the traditional OMA technology in mobile communication has the problem that a resource block is monopolized by a single user. Therefore, combining with millimeter wave communication, Massive MIMO technology and beamforming technology, this paper studies the hybrid beamforming algorithms for millimeter wave Massive MIMO system, aiming at the performance loss of hybrid beamforming and the problem that a resource block in OMA technology is monopolized by a single user.

Aiming at the problem of performance loss of hybrid beamforming, this paper proposes a hybrid beamforming algorithm based on partially-connected Massive MIMO system with millimeter wave to maximize the system spectral efficiency. Firstly, the optimal DBF is obtained based on singular value decomposition. Then, the matrix characteristics are used to update the analog and digital beamforming alternately. The nonconvex problem is transformed into a convex optimization subproblem, and the element phase increment in the analog domain is solved in a small range. The simulation results show that the average spectral efficiency of the proposed algorithm in the considered SNR range is 108.8%, 168.1%, 98.7% and 97.6% of the classical algorithm with partially-connected architecture, full analog beamforming, classical algorithm with fully-connected architecture and full digital beamforming, respectively. In other words, the performance of the algorithm is better than that of the classical algorithm with partially-connected architecture and the full analog beamforming , and is close to that of optimal full digital beamforming and that of the and classical algorithms with fully-connected architecture, but the hardware complexity and power consumption are lower.

Aiming at the problem that a resource block in OMA technology is monopolized by a single user, this paper introduces NOMA technology and proposes two schemes of user grouping, power allocation and hybrid beamforming. Firstly, based on the K-means clustering algorithm, a user grouping scheme is proposed according to the channel correlation between users. On this basis, a joint optimization problem of power allocation and hybrid beamforming is proposed. Then, taking SLNR as the performance objective, the two variables of the original problem can be decoupled and solved iteratively. Then, based on the initial beamforming matrix, the power allocation problem is transformed into a convex problem by introducing an auxiliary-positive real variable, and the optimal closed-form solution of power allocation is obtained based on KKT condition and Lagrange multiplier method. Finally, the optimal closed-form solution of optimal full digital beamforming can be obtained based on GED. Based on this matrix, two hybrid beamforming algorithms can be designed according to the different optimization methods in analog domain and digital domain. The simulation results show that the average spectral efficiency and average energy efficiency of the classic NOMA scheme in the considered SNR range are 24.8% and 24.7% of the proposed scheme 2, and 32.8% and 32.7% of the proposed scheme 1, respectively. The spectral efficiency and energy efficiency of the classical OMA scheme are 0.45% and 1.17% of the proposed scheme 2, and 0.61% and 1.55% of the proposed scheme 1, respectively. In other words, the spectrum efficiency and energy efficiency of the proposed joint schemes of user grouping, power allocation and hybrid beamforming are better than those of the classic NOMA schemes and OMA schemes.

[1]Henry S, Alsohaily A, Sousa E S. 5G is real: Evaluating the compliance of the 5G new r- adio system with the ITU IMT-2020 requirements[J]. IEEE Access, 2020, 8: 42828-42840.

[2]IMT-2020 (5G) 推进组发布 5G 技术白皮书[J]. 中国无线电, 2015 (5): 6.

[3]Li J, Zhang X. Deep Reinforcement Learning-Based Joint Scheduling of eMBB and URLLC in 5G Networks[J]. IEEE Wireless Communications Letters, 2020, 9(9): 1543-1546.

[4]Dong L, Zhao H, Chen Y, et al. Introduction on IMT-2020 5G trials in China[J]. IEEE journal on selected areas in communications, 2017, 35(8): 1849-1866.

[5]Annamalai P, Bapat J, Das D. A novel frequency allocation scheme for in band full duplex systems in 5G networks[J]. IEEE Wireless Communications Letters, 2018, 8(2): 364-367.

[6]Al-Rubaye S, Al-Dulaimi A, Cosmas J, et al. Call admission control for non-standalone 5G ultra-dense networks[J]. IEEE Communications Letters, 2018, 22(5): 1058-1061.

[7]Bai T, Heath R W. Coverage and rate analysis for millimeter-wave cellular networks[J]. IEEE Transactions on Wireless Communications, 2014, 14(2): 1100-1114.

[8]Hu Y, Hong W, Yu C, et al. A digital multibeam array with wide scanning angle and enhanced beam gain for millimeter-wave massive MIMO applications[J]. IEEE Transactions on Antennas and Propagation, 2018, 66(11): 5827-5837.

[9]Zhang P, Yang B, Yi C, et al. Measurement-based 5G millimeter-wave propagation characterization in vegetated suburban macrocell environments[J]. IEEE Transactions on Antennas and Propagation, 2020, 68(7): 5556-5567.

[10]Ullah H, Tahir F A. A high gain and wideband narrow-beam antenna for 5G millimeter-wave applications[J]. IEEE Access, 2020, 8: 29430-29434.

[11]Taheri M M S, Abdipour A, Zhang S, et al. Integrated millimeter-wave wideband end-fire 5G beam steerable array and low-frequency 4G LTE antenna in mobile terminals[J]. IEEE Transactions on Vehicular Technology, 2019, 68(4): 4042-4046.

[12]Han C, Duan S. Impact of atmospheric parameters on the propagated signal power of millimeter-wave bands based on real measurement data[J]. IEEE Access, 2019, 7: 113626-113641.

[13]Andrews J G, Bai T, Kulkarni M N, et al. Modeling and analyzing millimeter wave cellular systems[J]. IEEE Transactions on Communications, 2016, 65(1): 403-430.

[14]Yu C, Jing J, Shao H, et al. Full-angle digital predistortion of 5G millimeter-wave massive MIMO transmitters[J]. IEEE Transactions on Microwave Theory and Techniques, 2019, 67(7): 2847-2860.

[15]Yang B, Yu Z, Lan J, et al. Digital beamforming-based massive MIMO transceiver for 5G millimeter-wave communications[J]. IEEE Transactions on Microwave Theory and Techniques, 2018, 66(7): 3403-3418.

[16]Marcano A S, Christiansen H L. Impact of NOMA on network capacity dimensioning for 5G HetNets[J]. Ieee Access, 2018, 6: 13587-13603.

[17]Kumaresan S P, Tan C K, Ng Y H. Efficient User Clustering Using a Low-Complexity Artificial Neural Network (ANN) for 5G NOMA Systems[J]. IEEE Access, 2020, 8: 179307-179316.

[18]Qian J, Lops M, Zheng L, et al. Joint system design for coexistence of MIMO radar and MIMO communication[J]. IEEE Transactions on Signal Processing, 2018, 66(13): 3504-3519.

[19]Marzetta T L. Noncooperative cellular wireless with unlimited numbers of base station antennas[J]. IEEE transactions on wireless communications, 2010, 9(11): 3590-3600.

[20]Ding Q, Deng Y, Gao X, et al. Hybrid precoding for mmWave massive MIMO systems with different antenna arrays[J]. China Communications, 2019, 16(10): 45-55.

[21]Rusek F, Persson D, Lau B K, et al. Scaling up MIMO: Opportunities and challenges with very large arrays[J]. IEEE signal processing magazine, 2012, 30(1): 40-60.

[22]Wang W, Zhang W. Orthogonal Projection-Based Channel Estimation for Multi-Panel Millimeter Wave MIMO[J]. IEEE Transactions on Communications, 2020, 68(4): 2173-2187.

[23]Choi J, Lee G, Evans B L. Two-stage analog combining in hybrid beamforming systems with low-resolution ADCs[J]. IEEE Transactions on Signal Processing, 2019, 67(9): 2410-2425.

[24]Han S, Chih-Lin I, Xu Z, et al. Reference signals design for hybrid analog and digital beamforming[J]. IEEE communications letters, 2014, 18(7): 1191-1193.

[25]Ni W, Dong X, 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.

[26]Nair S S, Bhashyam S. Hybrid beamforming in MU-MIMO using partial interfering beam feedback[J]. IEEE Communications Letters, 2020, 24(7): 1548-1552.

[27]Song X, Kühne T, Caire G. Fully/partially-connected hybrid beamforming architectures for mmWave MU-MIMO[J]. IEEE Transactions on Wireless Communications, 2019, 19(3): 1754-1769.

[28]Zhang Q, Liu Y, Xie G, et al. An efficient hybrid diagonalization for multiuser mmwave massive MIMO systems[C]//2018 11th Global Symposium on Millimeter Waves (GSMM). IEEE, 2018: 1-6.

[29]Busari S A, Huq K M S, Mumtaz S, et al. Generalized hybrid beamforming for vehicular connectivity using THz massive MIMO[J]. IEEE Transactions on Vehicular Technology, 2019, 68(9): 8372-8383.

[30]Soleimani M, Elliott R C, Krzymień W A, et al. Hybrid Beamforming for mmWave Massive MIMO Systems Employing DFT-Assisted User Clustering[J]. IEEE Transactions on Vehicular Technology, 2020, 69(10): 11646-11658.

[31]Tsai T H, Chiu M C, Chao C. Sub-system SVD hybrid beamforming design for millimeter wave multi-carrier systems[J]. IEEE Transactions on Wireless Communications, 2018, 18(1): 518-531.

[32]Stirling-Gallacher R A, Rahman M S. Linear MU-MIMO pre-coding algorithms for a millimeter wave communication system using hybrid beam-forming[C]//2014 IEEE International Conference on Communications (ICC). IEEE, 2014: 5449-5454.

[33]Liao W H, Huang C C. SF-MAC: A spatially fair MAC protocol for underwater acoustic sensor networks[J]. IEEE Sensors Journal, 2011, 12(6): 1686-1694.

[34]Amjad M, Musavian L, Aïssa S. NOMA versus OMA in Finite Blocklength Regime: Link-Layer Rate Performance[J]. IEEE Transactions on Vehicular Technology, 2020, 69(12): 16253 - 16257.

[35]Zhu L, Zhang J, Xiao Z, et al. Millimeter-wave NOMA with user grouping, power allocation and hybrid beamforming[J]. IEEE Transactions on Wireless Communications, 2019, 18(11): 5065-5079.

[36]Ding J, Cai J. Two-side coalitional matching approach for joint MIMO-NOMA clustering and BS selection in multi-cell MIMO-NOMA systems[J]. IEEE Transactions on Wireless Communications, 2019, 19(3): 2006-2021.

[37]Wei Z, Ng D W K, Yuan J. NOMA for hybrid mmwave communication systems with beamwidth control[J]. IEEE Journal of Selected Topics in Signal Processing, 2019, 13(3): 567-583.

[38]Ahmed I, Khammari H, Shahid A, et al. A survey on hybrid beamforming techniques in 5G: Architecture and system model perspectives[J]. IEEE Communications Surveys & Tutorials, 2018, 20(4): 3060-3097.

[39]Li N, Wei Z, Geng J, et al. Multiuser hybrid beamforming for max-min SINR problem under 60 GHz wireless channel[C]//2014 IEEE 25th Annual International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC). IEEE, 2014: 123-128.

[40]Ni W, Dong X. Hybrid block diagonalization for massive multiuser MIMO systems[J]. IEEE transactions on communications, 2015, 64(1): 201-211.

[41]Wang Z, Li M, Tian X, et al. Iterative hybrid precoder and combiner design for mmWave multiuser MIMO systems[J]. IEEE Communications Letters, 2017, 21(7): 1581-1584.

[42]Payami S, Ghoraishi M, Dianati M. Hybrid beamforming for large antenna arrays with phase shifter selection[J]. IEEE Transactions on Wireless Communications, 2016, 15(11): 7258-7271.

[43]Man Y, Zhang C, Li Z, et al. Massive MIMO pre-coding algorithm based on improved Newton iteration[C]//2017 IEEE 85th Vehicular Technology Conference (VTC Spring). IEEE, 2017: 1-5.

[44]Rusu C, Méndez-Rial R, González-Prelcicy N, et al. Low complexity hybrid sparse precoding and combining in millimeter wave MIMO systems[C]//2015 IEEE International Conference on Communications (ICC). IEEE, 2015: 1340-1345.

[45]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.

[46]Yu X, 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.

[47]Kim T, Park J, Seol J Y, et al. Tens of Gbps support with mmWave beamforming systems for next generation communications[C]//2013 IEEE Global Communications Conference (GLOBECOM). IEEE, 2013: 3685-3690.

[48]Cui M, Zou W. Joint hybrid precoding based on orthogonal codebook in millimeter wave systems[C]//2018 15th International Symposium on Wireless Communication Systems (ISWCS). IEEE, 2018: 1-6.

[49]Dai L, Gao X, Quan J, et al. Near-optimal hybrid analog and digital precoding for downlink mmWave massive MIMO systems[C]//2015 IEEE International Conference on Communications (ICC). IEEE, 2015: 1334-1339.

[50]Utschick W, Stöckle C, Joham M, et al. Hybrid LISA precoding for multiuser millimeter-wave communications[J]. IEEE Transactions on Wireless Communications, 2017, 17(2): 752-765.

[51]Lin H, Gao F, Jin S, et al. A new view of multi-user hybrid massive MIMO: Non-orthogonal angle division multiple access[J]. IEEE Journal on Selected Areas in Communications, 2017, 35(10): 2268-2280.

[52]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.

[53]Han S, Chih-Lin I, Xu Z, et al. Large-scale antenna systems with hybrid analog and digital beamforming for millimeter wave 5G[J]. IEEE Communications Magazine, 2015, 53(1): 186-194.

[54]Alluhaibi O, Ahmed Q Z, Wang J, et al. Hybrid digital-to-analog precoding design for mm-wave systems[C]//2017 IEEE International Conference on Communications (ICC). IEEE, 2017: 1-6.

[55]Gao X, Dai L, Han S, et al. Energy-efficient hybrid analog and digital precoding for mmWave MIMO systems with large antenna arrays[J]. IEEE Journal on Selected Areas in Communications, 2016, 34(4): 998-1009.

[56]Xu Z, Han S, Pan Z, et al. Alternating beamforming methods for hybrid analog and digital MIMO transmission[C]//2015 IEEE International Conference on Communications (ICC). IEEE, 2015: 1595-1600.

[57]Wu Z, Lu K, Jiang C, et al. Comprehensive study and comparison on 5G NOMA schemes[J]. IEEE Access, 2018, 6: 18511-18519.

[58]Chung K. NOMA for correlated information sources in 5G systems[J]. IEEE Communications Letters, 2021, 25(2): 422-426.

[59]de Sena A S, Lima F R M, da Costa D B, et al. Massive MIMO-NOMA networks with imperfect SIC: Design and fairness enhancement[J]. IEEE Transactions on Wireless Communications, 2020, 19(9): 6100-6115.

[60]Zeng M, Yadav A, Dobre O A, et al. Capacity comparison between MIMO-NOMA and MIMO-OMA with multiple users in a cluster[J]. IEEE Journal on Selected Areas in Communications, 2017, 35(10): 2413-2424.

[61]Liu F, Mähönen P, Petrova M. Proportional fairness-based user pairing and power allocation for non-orthogonal multiple access[C]//2015 IEEE 26th annual international symposium on personal, indoor, and mobile radio communications (PIMRC). IEEE, 2015: 1127-1131.

[62]Sun Q, Han S, Chin-Lin I, et al. On the ergodic capacity of MIMO NOMA systems[J]. IEEE Wireless Communications Letters, 2015, 4(4): 405-408.

[63]Al-Abbasi Z Q, So D K C. Power allocation for sum rate maximization in non-orthogonal multiple access system[C]//2015 IEEE 26th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC). IEEE, 2015: 1649-1653.

[64]Hojeij M R, Nour C A, Farah J, et al. Waterfilling-based proportional fairness scheduler for downlink non-orthogonal multiple access[J]. IEEE wireless communications letters, 2017, 6(2): 230-233.

[65]Oviedo J A, Sadjadpour H R. A fair power allocation approach to NOMA in multiuser SISO systems[J]. IEEE Transactions on Vehicular Technology, 2017, 66(9): 7974-7985.

[66]Chinnadurai S, Selvaprabhu P, Lee M H. A novel joint user pairing and dynamic power allocation scheme in MIMO-NOMA system[C]//2017 International Conference on Information and Communication Technology Convergence (ICTC). IEEE, 2017: 951-953.

[67]Fang F, Zhang H, Cheng J, et al. Energy-efficient resource allocation for downlink non-orthogonal multiple access network[J]. IEEE Transactions on Communications, 2016, 64(9): 3722-3732.

[68]Wang B, Dai L, Wang Z, et al. Spectrum and energy-efficient beamspace MIMO-NOMA for millimeter-wave communications using lens antenna array[J]. IEEE Journal on Selected Areas in Communications, 2017, 35(10): 2370-2382.

[69]Wang H, Fu Y, Song R, et al. Power minimization precoding in uplink multi-antenna NOMA systems with jamming[J]. IEEE Transactions on Green Communications and Networking, 2019, 3(3): 591-602.

[70]Ding Z, Fan P, Poor H V. Random beamforming in millimeter-wave NOMA networks[J]. IEEE access, 2017, 5: 7667-7681.

[71]Hao W, Zeng M, Chu Z, et al. Energy-efficient power allocation in millimeter wave massive MIMO with non-orthogonal multiple access[J]. IEEE Wireless Communications Letters, 2017, 6(6): 782-785.

[72]Kim H, Chen J, Yoon J. Joint User Clustering and Beamforming in Non-Orthogonal Multiple Access Networks[J]. IEEE Access, 2020, 8: 111355-111367.

[73]Hanif M F, Ding Z, Ratnarajah T, et al. A minorization-maximization method for optimizing sum rate in the downlink of non-orthogonal multiple access systems[J]. IEEE Transactions on Signal Processing, 2015, 64(1): 76-88.

[74]Park S, Truong A Q, Nguyen T H. Power control for sum spectral efficiency optimization in MIMO-NOMA systems with linear beamforming[J]. IEEE Access, 2019, 7: 10593-10605.

[75]Badrudeen A A, Leow C Y, Won S H. Performance Analysis of Hybrid Beamforming Precoders for Multiuser Millimeter Wave NOMA Systems[J]. IEEE Transactions on Vehicular Technology, 2020, 69(8): 8739-8752.

[76]Xiao Z, Zhu L, Choi J, et al. Joint power allocation and beamforming for non-orthogonal multiple access (NOMA) in 5G millimeter wave communications[J]. IEEE Transactions on Wireless Communications, 2018, 17(5): 2961-2974.

[77]Zhu L, Zhang J, Xiao Z, et al. Joint power control and beamforming for uplink non-orthogonal multiple access in 5G millimeter-wave communications[J]. IEEE Transactions on Wireless Communications, 2018, 17(9): 6177-6189.

[78]Dai L, Wang B, Peng M, et al. Hybrid precoding-based millimeter-wave massive MIMO-NOMA with simultaneous wireless information and power transfer[J]. IEEE Journal on Selected Areas in Communications, 2018, 37(1): 131-141.

[79]Yang K, Yan X, Wang Q, et al. Joint Power Allocation and Relay Beamforming Optimization for Weighted Sum-Rate Maximization in NOMA AF Relay System[J]. IEEE Communications Letters, 2020, 25(1): 219-223.

[80]Lei L, Yuan D, Ho C K, et al. Power and channel allocation for non-orthogonal multiple access in 5G systems: Tractability and computation[J]. IEEE Transactions on Wireless Communications, 2016, 15(12): 8580-8594.

[81]Fu Y, Zhang M, Salaün L, et al. Zero-Forcing Oriented Power Minimization for Multi-Cell MISO-NOMA Systems: A Joint User Grouping, Beamforming, and Power Control Perspective[J]. IEEE Journal on Selected Areas in Communications, 2020, 38(8): 1925-1940.

[82]Cui J, Liu Y, Ding Z, et al. Optimal user scheduling and power allocation for millimeter wave NOMA systems[J]. IEEE Transactions on Wireless Communications, 2017, 17(3): 1502-1517.

[83]Wu W, Liu D. Non-orthogonal multiple access based hybrid beamforming in 5G mmWave systems[C]//2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC). IEEE, 2017: 1-7.

[84]Yoshida S, Suzuki Y, Ta T T, et al. A 60-GHz band planar dipole array antenna using 3-D SiP structure in small wireless terminals for beamforming applications[J]. IEEE transactions on antennas and propagation, 2013, 61(7): 3502-3510.

[85]Zhang Y, Zhang J, Chu X, et al. Effects of Wall Reflection on the Per-Antenna Power Distribution of ZF-Precoded ULA for Indoor mmWave MU-MIMO Transmissions[J]. IEEE Communications Letters, 2021, 25(1): 13-17.

[86]Sultan Q, Khan M S, Cho Y S. Fast 3D Beamforming Technique for Millimeter-Wave Cellular Systems With Uniform Planar Arrays[J]. IEEE Access, 2020, 8: 123469-123482.

[87]Amani N, Glazunov A A, Ivashina M V, et al. Per-antenna power distribution of a zero-forcing beamformed ULA in pure LOS MU-MIMO[J]. IEEE Communications Letters, 2018, 22(12): 2515-2518.

[88]Zhang R, Zhou J, Lan J, et al. A high-precision hybrid analog and digital beamforming transceiver system for 5G millimeter-wave communication[J]. IEEE Access, 2019, 7: 83012-83023.

[89]Li M. Generalized Lagrange multiplier method and KKT conditions with an application to distributed optimization[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2018, 66(2): 252-256.

[90]Yang M S, Sinaga K P. A feature-reduction multi-view k-means clustering algorithm[J]. IEEE Access, 2019, 7: 114472-114486.

[91]Park S, Park J, Yazdan A, et al. Optimal user loading in massive MIMO systems with regularized zero forcing precoding[J]. IEEE Wireless Communications Letters, 2016, 6(1): 118-121.

[92]Ho K C, Tsai S H. A Novel Multiuser Beamforming System With Reduced Complexity and Beam Optimizations[J]. IEEE Transactions on Wireless Communications, 2019, 18(9): 4544-4557.

[93]Golub G H, Van Loan C F. Matrix computations[M]. JHU press, 2013.