随着无线通信的飞速发展，通信系统的功率消耗急速增加，排放的二氧化碳等温室气体也逐渐增加。为了满足绿色通信的需求，系统的能效研究成为5G通信研究的热点问题之一。大规模MIMO技术作为5G的关键技术之一，由于其在基站端配置大量的天线，从而显著提高通信系统的容量。然而，随着天线数目的增加，系统消耗的总能量也在增加，从而导致系统的总能效下降。因此，对大规模MIMO系统能效的研究成为无线通信领域的重要研究内容。本文针对单小区多用户大规模MIMO上行通信系统，以最大化系统能效为优化目标进行资源分配方案的研究，其主要的研究内容如下所述：
本文研究联合基站发射天线数和用户发射功率对系统能效性能的影响，提出一种基于能效优化的资源分配算法。所提算法在满足每个用户最低通信速率和用户终端续航的约束条件下，以最大化系统能效为准则建立优化模型。首先证明能效是关于用户发射功率的凸函数，并采用Lambert W函数分析得到用户最佳发射功率的闭式表达式；其次根据分式规划理论提出一种迭代天线选择算法用于求解使系统能效最佳的最优基站发射天线数；最后利用二次变换的性质，通过联合调整基站端的发射天线数和用户的发射功率来优化能效函数。仿真结果表明，与现有算法相比该算法能效提高5.2%，频谱效率提高6.05%。
本文研究在系统信道状态信息未知的条件下，提出一种基于能效最优的资源分配算法。所提算法在采用导频信号估计得到信道状态信息的情况下，以最大化系统能效为准则，同时考虑用户服务质量和信道估计误差要求，通过调整导频序列长度、数据功率和导频功率来优化能效函数。根据分式规划性质，把原始的分式最优化问题转化成减式的形式，进而采用块坐标下降算法，通过联合调整数据功率和导频功率来交替迭代优化能效函数。仿真结果表明，与现有算法相比该算法能效提高5.31%，频谱效率提高5.34%。

With the rapid development of wireless communication, the power consumption of the communication system is rapidly increasing, and the emission of carbon dioxide and other greenhouse gases is also gradually increasing. In order to meet the needs of green communication, the energy efficiency research of the system has become one of the hot issues in 5G communication research. As one of the key technologies of 5G, massive MIMO technology has a large number of antennas at the base station, thereby significantly increasing the capacity of the communication system. However, as the number of antennas increases, the total energy consumed by the system also increases, resulting in a reduction in the total energy efficiency of the system. Therefore, the research on the energy efficiency of massive MIMO systems has become an important research content in the field of wireless communication. This thesis considers the single-cell multi-user massive MIMO uplink communication system, and studies the resource allocation scheme with the goal of maximizing energy efficiency. The main research contents are as follows:
An energy-efficient resource allocation scheme is proposed in this thesis,considering the impact of the number of base station antennas and user transmit power on the energy efficiency performance. A mathematical formulation of optimization issue is provided with the objective of maximizing system energy efficiency under the minimum data rate requirement of user and the endurance of the user terminal, meanwhile the base station uses zero-forcing precoding. First, it is proved that energy efficiency is a convex function of the user's transmit power,a closed-form expression using the Lambert W function is proposed to obtain the user's optimal transmit power. An iterative algorithm is proposed to solve the optimal number of base station transmitting antennas.Then the properties of the quadratic transformation and an iterative optimization algorithm are used to maximize the energy efficiency. Specifically, both the number of antennas and the user's transmit power are adjusted. Simulation results show that compared with the existing algorithm, the energy efficiency of the algorithm is increased by 5.2%, and the spectrum efficiency is increased by 6.05%.
An resource allocation algorithm is proposed based on optimal energy efficiency in this thesis, under the condition that the channel state information of the system is unknown. Since most of the existing energy efficiency studies assume that the base station has known channel state information, it is difficult to obtain accurate channel state information in an actual communication system. A mathematical formulation of optimization issue is provided with the objective of maximizing system energy efficiency under user service quality and channel estimation error requirements, meanwhile the case of using pilot signal estimation to obtain channel state information, the pilot sequence length, data power and pilot power are adjusted synchronously. By transforming the originally fractional optimization problem into an equivalent subtractive form using the properties of the fractional planning, then the block coordinate descent algorithm is adopted to alternately optimize the energy efficiency function by adjusting the data power and pilot power jointly. The simulation results show that compared with the existing algorithm, the energy efficiency of the algorithm is increased by 5.31%, and the spectral efficiency is increased by 5.34%.

[1]Isabona J, Srivastava V M. Downlink massive MIMO systems: Achievable sum rates and energy efficiency perspective for future 5G systems[J]. Wireless Personal Commu- nications, 2017, 96(2): 2779-2796.

[2]Al-Nahari A, Sakran H, Su W, et al. Energy and spectral efficiency of secure massive MIMO downlink systems[J]. IET Communications, 2019, 13(10): 1364-1372.

[3]Ge X, Yang J, Gharavi H, et al. Energy efficiency challenges of 5G small cell networks[J]. IEEE Communications Magazine, 2017, 55(5): 184-191.

[4]Zhao H, Liu Z, Sun Y. Energy efficiency optimization for SWIPT in K-user MIMO interference channels[J]. Physical Communication, 2018, 27: 197-202.

[5]Saatlou O, Ahmad M O, Swamy M N S. Spectral efficiency maximization of multiuser massive MIMO systems with finite-dimensional channel via control of users’ power[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2017, 65(7): 883-887.

[6]Pan S, Chen J, Chen Y, et al. An energy efficiency maximization scheme for the wireless information and power transfer system with MU-MIMO uplink access[J]. IEEE Access, 2018, 6: 58754-58763.

[7]Mohamed K S, Alias M Y, Roslee M, et al. Towards green communication in 5G systems: Survey on beamforming concept[J]. IET Communications, 2021, 15(1): 142-154.

[8]Chen S, Zhang J, Jin Y, et al. Wireless powered IoE for 6G: massive access meets scalable cell-free massive MIMO[J]. China Communications, 2020, 17(12): 92-109.

[9]Panwar N, Sharma S, Singh A K. A survey on 5G: The next generation of mobile communication[J]. Physical Communication, 2016, 18: 64-84.

[10]Lin Y, Yang Z, Guo H. Proportional fairness-based energy-efficient power allocation in downlink MIMO-NOMA systems with statistical CSI[J]. China Communications, 2019, 16(12): 47-55.

[11]Purushothaman K E, Nagarajan V. Evolutionary multi-Objective optimization algorithm for resource allocation using deep neural network in 5G multi-User massive MIMO[J]. International Journal of Electronics, 2020: 1-20.

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

[13]Marzetta T L, Ngo H Q. Fundamentals of massive MIMO[M]. Cambridge University Press, 2016.

[14]王正强,杨晓娜,万晓榆,等.大规模MIMO系统能效优化算法研究综述[J].重庆邮电大学学报,2019,31(6):743-752.

[15]Nguyen B C, Tran X N. Transmit antenna selection for full-duplex spatial modulation multiple-input multiple-output system[J]. IEEE Systems Journal, 2020, 14(4): 4777-4785.

[16]Ubiali G A, Abrão T. XL-MIMO energy-efficient antenna selection under non-stationary channels[J]. Physical Communication, 2020, 43: 1-25.

[17]Le N P, Safaei F. Antenna selection strategies for MIMO-OFDM wireless systems: An energy efficiency perspective[J]. IEEE Transactions on Vehicular Technology, 2015, 65(4): 2048-2062.

[18]Kuai Z, Wang S. Thompson sampling-based antenna selection with partial CSI for TDD massive MIMO systems[J]. IEEE Transactions on Communications, 2020, 68(12): 7533-7546.

[19]Qian K, Wang W Q. Energy-efficient antenna selection in green MIMO relaying communication systems[J]. Journal of Communications and Networks, 2016, 18(3): 320-326.

[20]Khalid S, Mehmood R, Abbas W B, et al. Joint transmit antenna selection and precoding for millimeter wave massive MIMO systems[J]. Physical Communication, 2020, 42: 101137.

[21]Li J, Li S, Mu X, et al. Energy efficiency of very large multiuser MIMO systems with transmit antenna selection[J]. International Journal of Multimedia and Ubiquitous Engineering, 2015, 10(6): 243-252.

[22]Li H, Guo J, Wang Y, et al. Energy efficient antenna selection scheme for downlink massive MIMO systems[C]//2018 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2018: 1-4.

[23]Mahajan M, Yoon W. Energy-efficient resource allocation in multicell large-scale distributed antenna system with imperfect CSI[J]. IETE Journal of Research, 2020, 66(6): 772-780.

[24]Marinello J C, Abrão T, Amiri A, et al. Antenna selection for improving energy efficiency in XL-MIMO systems[J]. IEEE Transactions on Vehicular Technology, 2020, 69(11): 13305-13318.

[25]Xue Y, Zhang J, Gao X. Resource allocation for pilot-assisted massive MIMO transmission[J]. Science China Information Sciences, 2017, 60(4): 1-13.

[26]Zhou Z, Yu H, Mumtaz S, et al. Power control optimization for large-scale multi-antenna systems[J]. IEEE Transactions on Wireless Communications, 2020, 19(11): 7339-7352.

[27]Raafat A, Agustin A, Vidal J. Downlink multi-user massive MIMO transmission using receive spatial modulation[J]. IEEE Transactions on Wireless Communications, 2020, 19(10): 6871-6883.

[28]Liu Z, Li J, Sun D. Circuit power consumption-unaware energy efficiency optimization for massive MIMO systems[J]. IEEE Wireless Communications Letters, 2017, 6(3): 370-373.

[29]Honggui D, Jinli Y, Gang L. Enhanced Energy Efficient Power Allocation Algorithm for Massive MIMO Systems[C] //2019 IEEE 11th International Conference on Communication Software and Networks (ICCSN). IEEE, 2019: 280-285.

[30]Sobhi-Givi S, Shayesteh M G, Kalbkhani H. Energy-efficient power allocation and user selection for mmWave-NOMA transmission in M2M communications underlaying cellular heterogeneous networks[J]. IEEE Transactions on Vehicular Technology, 2020, 69(9): 9866-9881.

[31]Bonsu K A, Zhou W, Pan S, et al. Optimal power allocation with limited feedback of channel state information in multi-user MIMO systems[J]. China Communications, 2020, 17(2): 163-175.

[32]Liu G, Deng H, Qian X, et al. Joint pilot allocation and power control to enhance max-min spectral efficiency in TDD massive MIMO systems[J]. IEEE Access, 2019, 7: 149191-149201.

[33]Yang R, Lin B, Yu F R, et al. A dynamic pilot and data power allocation for TDD massive MIMO systems[C]//2018 IEEE Global Communications Conference (GLOBECOM). IEEE, 2018: 1-6.

[34]You L, Xiong J, Yi X, et al. Energy efficiency optimization for downlink massive MIMO with statistical CSIT[J]. IEEE Transactions on Wireless Communications, 2020, 19(4): 2684-2698.

[35]Zhang T, Mao S. Energy-efficient power control in wireless networks with spatial deep neural networks[J]. IEEE Transactions on Cognitive Communications and Networking, 2019, 6(1): 111-124.

[36]Souto V D P, Souza R D, Uchôa-Filho B F, et al. Beamforming optimization for intelligent reflecting surfaces without CSI[J]. IEEE Wireless Communications Letters, 2020, 9(9): 1476-1480.

[37]Kim K, Lee J, Choi J. Deep learning based pilot allocation scheme (DL-PAS) for 5G massive MIMO system[J]. IEEE Communications Letters, 2018, 22(4): 828-831.

[38]Amin O, Bedeer E, Ahmed M H, et al. Energy efficiency–spectral efficiency tradeoff: A multi-objective optimization approach[J]. IEEE Transactions on Vehicular Technology, 2015, 65(4): 1975-1981.

[39]H. Q. Ngo, E. G. Larsson and T. L. Marzetta. Energy and spectral efficiency of very large multiuser MIMO systems[J]. IEEE Transactions on Communications, 2013.61(4): 1436-1449.

[40]Tan W, Jin S, Yuan J. Spectral and energy efficiency of downlink MU-MIMO systems with MRT[J]. China Communications, 2017, 14(5): 105-111.

[41]Chen J, Chen H, Zhang H, et al. Spectral-energy efficiency tradeoff in relay-aided massive MIMO cellular networks with pilot contamination[J]. IEEE Access, 2016, 4: 5234-5242.

[42]Li Y, Fan P, Leukhin A, et al. On the spectral and energy efficiency of full-duplex small-cell wireless systems with massive MIMO[J]. IEEE Transactions on Vehicular Technology, 2016, 66(3): 2339-2353.

[43]Li H, Cheng J, Wang Z, et al. Joint antenna selection and power allocation for an energy-efficient massive MIMO system[J]. IEEE Wireless Communications Letters, 2018, 8(1): 257-260.

[44]Gao H, Su Y, Zhang S, et al. Antenna selection and power allocation design for 5G massive MIMO uplink networks[J]. China Communications, 2019, 16(4): 1-15.

[45]赵迎芝, 唐宏, 叶宗刚, 等.多用户大规模MIMO系统中能效的研究[J].重庆邮电大学学报（自然科学版）,2016,28(5):737-742.

[46]Salh A, Shah N S M, Audah L, et al. Energy-efficient power allocation and joint user association in multiuser-downlink massive MIMO system[J]. IEEE Access, 2019, 8: 1314-1326.

[47]R. Hamdi, E. Driouch and W. Ajib.Resource allocation in downlink large-scale MIMO systems[J].IEEE Access, 2016,4: 8303-8316.

[48]赵迎芝, 唐宏, 叶宗刚, 等.多用户大规模MIMO系统中能效的研究[J].重庆邮电大学学报（自然科学版）,2016,28(5):737-742

[49]李梦珠,傅友华.无小区大规模MIMO系统中结合贪婪导频分配的导频功率控制的算法[J].信号处理,2021,37(01):133-140..

[50]Wang Y,Ma P, Zhao R.et al. Near-Optimal pilot signal design for FDD massive MIMO system:an energy-efficient perspective[J]. IEEE Access,2018,6:13275-13288.

[51]王毅,马鹏阁,黄开支,等.导频序列长度对多用户大规模MIMO FDD 系统速率的性能影响及优化[J].通信学报,2018,39(7):92-102.

[52]Gu Y, Zhang Y D. Information-theoretic pilot design for downlink channel estimation in FDD massive MIMO systems[J]. IEEE Transactions on Signal Processing, 2019, 67(9): 2334-2346.

[53]Saatlou O, Ahmad M O, Swamy M N S. Spectral efficiency maximization of single cell massive multiuser MIMO systems via optimal power control with ZF receiver[C]//2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC). IEEE, 2017: 1-5.

[54]Saatlou O ,Ahmad M O ,Swamy M N S .Spectral efficiency maximization of a single cell massive MU-MIMO down-link TDD system by appropriate resource allocation [J].IEEE Access,2019,7: 182758-182771

[55]Saatlou O, Ahmad M O, Swamy M N S. Joint data and pilot power allocation for massive MU-MIMO downlink TDD systems[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2018, 66(3): 512-516.

[56]刘紫燕,刘世美,唐虎,等.多用户Massive MIMO系统能效资源分配方案[J].中国科技论文,2018,13(14):1658-1663.

[57]Huang K, Wang Z, Wan X, et al. Max-min energy efficiency optimization algorithm for wireless power transfer enabled massive MIMO systems[C]//2019 IEEE 5th International Conference on Computer and Communications (ICCC). IEEE, 2019: 2029-2033.

[58]Yan L, Bai B, Chen W. Energy efficiency maximization in downlink multiuser MIMO systems: an asymptotic analysis approach[C] //2014 IEEE Global Communications Conference. IEEE, 2014: 3916-3921.

[59]Shen K, Yu W. Fractional programming for communication systems—Part I: Power control and beamforming[J]. IEEE Transactions on Signal Processing, 2018, 66(10): 2616-2630.

[60]Corless R M, Gonnet G H, Hare D E G, et al. On the lambert W function[J]. Advances in Computational mathematics, 1996, 5(1): 329-359.

[61]刘世美. Massive MIMO 系统能效资源分配研究[D]. 贵州大学, 2018.

[62]Eskandari M,Doost Hoseini A M, Fzael M S. An energy-efficient joint antenna selection and power allocation for MIMO system under limited feedback[J].Signal Processing,2019,163:66-74

[63]智应娟,曹海燕,马智尧,等.基于用户选择的大规模MIMO能效联合优化算法[J].杭州电子科技大学学报(自然科学版),2020,40(05):7-12.

[64]苗盼盼. Massive MIMO 系统能效优化关键技术研究[D]. 郑州大学, 2017

[65]Dao H T, Kim S. Power allocation for multiple user-type massive MIMO systems[J]. IEEE Transactions on Vehicular Technology, 2020, 69(10): 10965-10974.

[66]Taneja A, Saluja N. A Transmit antenna selection based energy-harvesting MIMO cooperative communication system[J]. IETE Journal of Research, 2020: 1-10.

[67]万晓榆,魏霄,王正强,等.基于能量采集的大规模MIMO系统能效优化[J].计算机应用研究,2019,36(04):1193-1196.

[68]范建存,宁悦,邓建国,等.多小区MIMO系统中基于能效最大的天线数和用户数联合优化方案[J].中国科学:信息科学,2016,46(02):281-290.

[69]Hoang T M, Duong T Q, Tuan H D, et al. Secure massive MIMO relaying systems in a Poisson field of eavesdroppers[J]. IEEE Transactions on Communications, 2017, 65(11): 4857-4870.