新型MIMO系统中的资源分配
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摘要
多输入多输出(Multiple-Input Multiple-Output,MIMO)技术作为提高无线通信系统频谱效率的一种重要手段,在过去十余年间得到了飞速的发展。近年来,为了应对当今无线网络特别是移动通信网络拓扑日益复杂、需求日益多样的发展趋势,在传统点对点MIMO无线通信系统的基础上,一些新的MIMO技术被提出,比如多用户MIMO技术、认知MIMO技术以及绿色MIMO技术等。由于这些新出现的MIMO传输技术相比传统的点对点MIMO传输技术,可以显著提升特定网络拓扑和网络需求下的MIMO无线通信系统的性能,适应未来无线通信系统发展的需求,因此近年来上述新型MIMO通信技术受到了研究者的格外关注
本论文主要针对多用户MIMO系统的调度技术,认知MIMO系统中的有限反馈传输技术以及绿色认知MIMO系统的功率控制和预编码技术展开研究,其主要贡献在于针对这些新型MIMO系统的实际需求,合理利用MIMO系统中天线映射、功率控制和用户调度等无线资源分配手段,提出更加简单高效的传输方案,并能够对方案的性能进行理论分析。
第一,论文针对多用户MIMO调度复杂度过高的问题,提出了种低复杂度的多用户MIMO调度算法。该算法以著名的半正交多用户MIMO调度算法为基础,根据运用矩阵论等数学方法推导出的用户调度参考变量的迭代关系化简得到。论文从理论上证明所提算法其性能与半正交的多用户MIMO调度算法一致,计算复杂度阶数降低一阶。
第二,论文针对信道状态信息误差对多用户MIMO调度性能影响严重的问题,提出了一种能够对信道状态信息误差鲁棒的多用户MIMO调度算法。该算法通过计算信道状态信息误差下的系统遍历容量,从而提高多用户MIMO调度算法的性能。基于推导得到的系统遍历容量下界,论文又进一步提出了一种信道修正因子,用于修正待调度的用户信道,从而使得传统的基于理想信道状态信息的多用户MIMO调度算法能够对信道状态信息误差鲁棒。仿真结果表明,所提信道修正因子能够有效提升信道状态信息误差下的多用户MIMO调度性能,其性能非常接近基于所提的基于系统遍历容量的调度算法。
第三,论文针对认知MIMO系统有限反馈传输的问题,提出了一种统计信道信息反馈下的认知MIMO系统传输方法,并对其性能进行了分析。该方法基于MIMO信道的衰落特性,在统计信道信息反馈的条件下通过最大化系统的遍历容量来设计预编码和功率分配策略。仿真结果表明所提传输方法可以接近理想信道状态信息反馈条件下的最优传输性能。
第四,论文针对绿色MIMO通信的高能效需求,提出了一种适用于绿色认知多用户MIMO系统的能效最优的功率分配算法。绿色认知MIMO系统的能效优化问题是一个非凸的多维优化问题,难于直接求解。论文将其转化为一个等效的一维优化问题,并证明其拟凹特性,从而构造出求解算法对其进行求解,并从理论上说明了所提算法的收敛性和最优性。仿真结果表明所提算法相比传统的认知多用户MIMO传输方法,能够显著提升系统的能量效率,适应绿色通信的需求。
As a key role of improving the spectrum efficiency of wireless communication systems, the multiple-input multiple-output (MIMO) technique was developed quickly during the last decade. In partciluar, since nowdays the topology and the requirement of celluar networks and other wireless networks become more and more diverse, based on the researches on traditional point-to-point MIMO systems, some advanced MIMO techniques have been proposed recently to deal with these new characteristics of wireless systems, such as multi-user MIMO techniques, cognitive MIMO techniques and green MIMO techniques. Compared with the traditional point-to-point MIMO techniques, these emerging MIMO techniques can significantly improve the performance of the MIMO systems under some special topologies and meets the requirments of future wireless systems. Therefore, the aforementioned advanced MIMO techniques have drawn wide attention in recent years.
This thesis focuses on the scheduling techniques of muti-user MIMO systems, the limited-feedback transmission schemes of cognitive MIMO systems and the power allocation and precoding techniques of green MIMO systems. The main contribution of our works is proposing some simple and efficient resource allocation schemes on antenna mapping, power allocation and user scheduling according to the requirements of these advanced MIMO systems, and also providing some theoretical results on the system performance.
Firstly, to reduce the computation complexity during the muti-user MIMO scheduing, a low complexity mutli-user MIMO scheduling algorithm is proposed. Based on the well known semi-orthogonal user selection algorithm, the proposed algorithm is obtained via the iteration relationship of the parameters between each user selection step according to the matrix theory. It can be proved that the proposed algorithm can achieve the same throughput as the semi-orthogonal user selection algorithm while the complexity order is reduced by one.
Secondly, to relieve the performance decrement during multi-user MIMO scheduling caused by imperfect channel state information (CSI), a robust multi-user MIMO scheduling scheme is proposed. The proposed algorithm can improve the system througput via mesuring the ergodic capacity under CSI errors. Based on the lower bound of measured ergodic capacity, a CSI modification factor is also proposed to modify the scheduling user CSI and make the tradional multi-user MIMO scheduling algorithm based on perfect CSI become robust under imperfect CSI scenarios. Simulation results show that the poposed CSI modification factor can improve the scheduling performance of the mutli-user MIMO systems with imperfect CSI significantly, and achieve the performance of the proposed ergodic capacity based scheduling algorithm.
Thirdly, to deal with the limited-feedback transmission problem of cognitive MIMO systems, a cognitve MIMO transmission scheme based on the statistical CSI feedback is proposed, and the corresponding system performance analysis is also given. The proposed scheme gives the power allocation and the precoding algorithms to maximize the ergodic capacity based on the statistical CSI feedback and the MIMO channel fading characteristic. Simulation results show that the proposed scheme can approach the optimal system performance with perfect CSI.
Finally, according to the energy efficiency requriment of green MIMO systems, an energy efficiency optimization power allocation algorithm for green cognitive multi-user MIMO systems is proposed. Since the energy efficiency optimization problem of green cognitive multi-user MIMO systems is non-convex and hard to solve directly, the proposed algorithm transforms it to an equivalent quasi-concave one-dimension problem to solve it. The convergence and the optimiality of the proposed algorithm are shown in theory. Similuation results show that compared with the traditional transmission scheme, the proposed scheme can improve the system energy efficiency significantly and meets the requirments of green communications.
本论文主要针对多用户MIMO系统的调度技术,认知MIMO系统中的有限反馈传输技术以及绿色认知MIMO系统的功率控制和预编码技术展开研究,其主要贡献在于针对这些新型MIMO系统的实际需求,合理利用MIMO系统中天线映射、功率控制和用户调度等无线资源分配手段,提出更加简单高效的传输方案,并能够对方案的性能进行理论分析。
第一,论文针对多用户MIMO调度复杂度过高的问题,提出了种低复杂度的多用户MIMO调度算法。该算法以著名的半正交多用户MIMO调度算法为基础,根据运用矩阵论等数学方法推导出的用户调度参考变量的迭代关系化简得到。论文从理论上证明所提算法其性能与半正交的多用户MIMO调度算法一致,计算复杂度阶数降低一阶。
第二,论文针对信道状态信息误差对多用户MIMO调度性能影响严重的问题,提出了一种能够对信道状态信息误差鲁棒的多用户MIMO调度算法。该算法通过计算信道状态信息误差下的系统遍历容量,从而提高多用户MIMO调度算法的性能。基于推导得到的系统遍历容量下界,论文又进一步提出了一种信道修正因子,用于修正待调度的用户信道,从而使得传统的基于理想信道状态信息的多用户MIMO调度算法能够对信道状态信息误差鲁棒。仿真结果表明,所提信道修正因子能够有效提升信道状态信息误差下的多用户MIMO调度性能,其性能非常接近基于所提的基于系统遍历容量的调度算法。
第三,论文针对认知MIMO系统有限反馈传输的问题,提出了一种统计信道信息反馈下的认知MIMO系统传输方法,并对其性能进行了分析。该方法基于MIMO信道的衰落特性,在统计信道信息反馈的条件下通过最大化系统的遍历容量来设计预编码和功率分配策略。仿真结果表明所提传输方法可以接近理想信道状态信息反馈条件下的最优传输性能。
第四,论文针对绿色MIMO通信的高能效需求,提出了一种适用于绿色认知多用户MIMO系统的能效最优的功率分配算法。绿色认知MIMO系统的能效优化问题是一个非凸的多维优化问题,难于直接求解。论文将其转化为一个等效的一维优化问题,并证明其拟凹特性,从而构造出求解算法对其进行求解,并从理论上说明了所提算法的收敛性和最优性。仿真结果表明所提算法相比传统的认知多用户MIMO传输方法,能够显著提升系统的能量效率,适应绿色通信的需求。
As a key role of improving the spectrum efficiency of wireless communication systems, the multiple-input multiple-output (MIMO) technique was developed quickly during the last decade. In partciluar, since nowdays the topology and the requirement of celluar networks and other wireless networks become more and more diverse, based on the researches on traditional point-to-point MIMO systems, some advanced MIMO techniques have been proposed recently to deal with these new characteristics of wireless systems, such as multi-user MIMO techniques, cognitive MIMO techniques and green MIMO techniques. Compared with the traditional point-to-point MIMO techniques, these emerging MIMO techniques can significantly improve the performance of the MIMO systems under some special topologies and meets the requirments of future wireless systems. Therefore, the aforementioned advanced MIMO techniques have drawn wide attention in recent years.
This thesis focuses on the scheduling techniques of muti-user MIMO systems, the limited-feedback transmission schemes of cognitive MIMO systems and the power allocation and precoding techniques of green MIMO systems. The main contribution of our works is proposing some simple and efficient resource allocation schemes on antenna mapping, power allocation and user scheduling according to the requirements of these advanced MIMO systems, and also providing some theoretical results on the system performance.
Firstly, to reduce the computation complexity during the muti-user MIMO scheduing, a low complexity mutli-user MIMO scheduling algorithm is proposed. Based on the well known semi-orthogonal user selection algorithm, the proposed algorithm is obtained via the iteration relationship of the parameters between each user selection step according to the matrix theory. It can be proved that the proposed algorithm can achieve the same throughput as the semi-orthogonal user selection algorithm while the complexity order is reduced by one.
Secondly, to relieve the performance decrement during multi-user MIMO scheduling caused by imperfect channel state information (CSI), a robust multi-user MIMO scheduling scheme is proposed. The proposed algorithm can improve the system througput via mesuring the ergodic capacity under CSI errors. Based on the lower bound of measured ergodic capacity, a CSI modification factor is also proposed to modify the scheduling user CSI and make the tradional multi-user MIMO scheduling algorithm based on perfect CSI become robust under imperfect CSI scenarios. Simulation results show that the poposed CSI modification factor can improve the scheduling performance of the mutli-user MIMO systems with imperfect CSI significantly, and achieve the performance of the proposed ergodic capacity based scheduling algorithm.
Thirdly, to deal with the limited-feedback transmission problem of cognitive MIMO systems, a cognitve MIMO transmission scheme based on the statistical CSI feedback is proposed, and the corresponding system performance analysis is also given. The proposed scheme gives the power allocation and the precoding algorithms to maximize the ergodic capacity based on the statistical CSI feedback and the MIMO channel fading characteristic. Simulation results show that the proposed scheme can approach the optimal system performance with perfect CSI.
Finally, according to the energy efficiency requriment of green MIMO systems, an energy efficiency optimization power allocation algorithm for green cognitive multi-user MIMO systems is proposed. Since the energy efficiency optimization problem of green cognitive multi-user MIMO systems is non-convex and hard to solve directly, the proposed algorithm transforms it to an equivalent quasi-concave one-dimension problem to solve it. The convergence and the optimiality of the proposed algorithm are shown in theory. Similuation results show that compared with the traditional transmission scheme, the proposed scheme can improve the system energy efficiency significantly and meets the requirments of green communications.
引文
[1]Cisco, "Cisco Visual Network Index:Global Mobile Data Traffic Forecast Update 2012-2017," Cisco White Paper, Feb.2013.
[2]E. Telatar, "Capacity of multi-antenna Gaussian channels," AT&T-Bell Labs Internal Tech. Memo., June 1995.
[3]G. J. Foschini and M. J. Gans, "On limits of wireless communication in a fading environment when using multiple antennas," Wireless Personal Commun., vol.6, no.3, pp.311-335, Mar.1998.
[4]3GPP TR 25.912:"Feasibility study for evolved Universal Terrestrial Radio Access (UTRA) and Universal Terrestrial Radio Access Network (UTRAN) (Release 8)," V8.0.0, Dec.2008.
[5]Q. H. Spencer, C. B. Peel, L. Swindlehurst, et al, "An introduction to the multi-user MIMO downlink," IEEE Commun. Mag., vol.42, no.10, pp.60-67, Oct.2004.
[6]D. Gesbert, M. Kountouris, R.W. Heath Jr., et al, "From single user to multiuser communications:Shifting the MIMO paradigm," IEEE Signal Process. Mag., vol. 24, no.5, pp.36-46, Sept.2007.
[7]J. Mitola and G. Q. Maguire, "Cognitive radio:Making software radios more personal," IEEE Pers. Commun., vol.6, no.6, pp.13-18, Aug.1999.
[8]S. Haykin, "Cognitive radio:Brain-empowered wireless communications," IEEE J. Sel. Areas Commun., vol.23, no.2, pp.201-220, Feb.2005.
[9]Federal Communication Commission, "Spectrum Policy Task Force," Rep. ET Docket, no.02-135, Nov 2002.
[10]"IEEE 802.22.1-2010 standard," [Online], available:http://standards.ieee.org/ getieee802/download/802.22.1-2010.pdf.
[11]"IEEE 802.11h-2003 Standard," [Online], available:http://standards.ieee.org/ getieee802/download/802.11h-2003.pdf.
[12]"IEEE 802.11y-2003 Standard," [Online], available:http://standards.ieee.org/ getieee802/download/802.11y-2008.pdf.
[13]R. Zhang and Y.-C. Liang, "Exploiting multi-antennas for opportunistic spectrum sharing in cognitive radio networks," IEEE J. Sel. Topics Signal Process., vol.2, no.1, pp.88-102, Feb.2008.
[14]"Improving energy efficiency, Lower CO2 emission and TCO," Whitepaper, Huawei energy effi ciency solution, Huawei Technologies,2010.
[15]Daquan Feng, Chenzi Jiang, Gubong Lim, et al, "A survey of energy-efficient wireless communications," IEEE Communications Surveys & Tutorials, vol.15, no.1, pp.167-178, Feb.2013.
[16]Li, G.Y., Zhikun Xu, Cong Xiong, et al, "Energy-efficient wireless communications:tutorial, survey, and open issues," IEEE Wireless Communications, vol.18, no.6, pp.28-35, December 2011.
[17]Neri F, "TREND:towords real energy-efficient network design," Network of excellence proposal, FP7-1CT-2009-5, April,2010.
[18]Andrea Goldsmith, Wireless Communications, Cambridge University Press, 2005.
[19]C. Windpassinger, R. F. H. Fischer, T. Vencel, et al, "Precoding in multiantenna and multiuser communications,"'IEEE Trans. Wireless Commun., vol.3, no.4, pp. 1305-1336, July 2004.
[20]M. Costa, "Writing on dirty paper," IEEE Trans. Inform. Theory, vol.29, no.3, pp.439-441, May 1983.
[21]S. Vishwanath, N. Jindal, and A. Goldsmith, "Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels," IEEE Trans.on Inform. Theory, vol.49, no.10, pp.2658-2668, Oct.2003.
[22]G. Caire and S. Shamai, "On the achievable throughput of a multiantenna Gaussian broadcast channel," IEEE Trans. Inform. Theory, vol.49, no.7, pp. 1691-1706, July 2003.
[23]C. B. Peel, B. M. Hochwald, and A. L. Swindelhurst, "A vector-perturbation technique for near-capacity multiantenna multiuser communication-part 1: channel inversion and regularization," IEEE Trans. Commun., vol.53, pp. 195-202, Jan.2005.
[24]J. Liu and W. A. Krzymien, "Improved Tomlinson-Harashima precoding for the downlink of multiple antenna multi-user systems,'" in Proc. IEEE WCNC 2005, pp.466-472. Mar.2005.
[25]C. H. F. Fung, W. Yu, A. D. Dabbagh, et al, "Precoding for multiple antenna Gaussian broadcast channels with successive zeroforcing," IEEE Trans. Signal Process., vol.55, no.7, pp.3837-3850, July 2007.
[26]T. Yoo and A. Goldsmith, "On the optimality of multi-antenna broadcast scheduling using zero-forcing beamforming," IEEE J. Sel. Areas Commun., vol. 24, pp.528-542, Mar.2006.
[27]H. Sung, S. R. Lee, and I. Lee, "Generalized channel inversion methods for multiuser MIMO systems," IEEE Trans. Commun., vol.57, no.11, pp.3489-3499, Nov.2009.
[28]Q. H. Spencer, A. L. Swindlehurst, and M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels," IEEE Trans. Signal Process., vol.52, no.2, pp.461-471, Feb.2004.
[29]T. Haustein, C. von Helmolt, E. Jorswieck, et al, "Performance of MIMO systems with channel inversion," in Proc. IEEE VTC 2002, vol.1, pp.35-39, May 2002.
[30]R. Chen, Z. Shen, J. G. Andrews, et al, "Multimode transmission for multiuser MIMO systems with block diagonalization," IEEE Trans. Signal Process., vol.56, no.7, pp.3294-3302, July 2008.
[31]S. Kaviani and W. A. Krzymien, "On the optimality of multiuser zero-forcing precoding in MIMO broadcast channels," in Proc. IEEE VTC 2009, pp.1-5, April 2009.
[32]S. Shi and M. Schubert, "MMSE transmit optimization for multi-user multi-antenna systems," in Proc. IEEE ICASSP 2005, pp.409-412, Mar.2005.
[33]J. Zhang, Y. Wu, S. Zhou, et al, "Joint linear transmitter and receiver design for the downlink of multiuser MIMO systems," IEEE Commun. Letters, vol.9, no.11, pp.991-993, Nov.2005.
[34]J. Joung, Y. H. Lee, "Regularized channel diagonalization for multiuser MIMO downlink using a modified MMSE criterion," IEEE Trans. Signal Process., vol. 55, no.7, pp.1573-1579, Apr.2007.
[35]Vucic N., Boche H. and Shuying Shi "Robust transceiver optimization in downlink multiuser MIMO systems," IEEE Trans. Signal Process., vol.57, no.9, pp.3576-3587, Sept.2009.
[36]Shuying Shi, Schubert M. and Boche H., "Downlink MMSE transceiver optimization for multiuser MIMO systems:MMSE balancing," IEEE Trans. Signal Process., vol.56, no.8, pp.3702-3712, Aug.2008.
[37]Shuying Shi, Schubert M. and Boche H., "Downlink MMSE transceiver optimization for multiuser MIMO systems:duality and sum-MSE minimization," IEEE Trans. Signal Process., vol.55, no.11, pp.5436-5446, Nov.2007.
[38]M. Sadek, A. Tarighat, and A. H. Sayed, "A leakage-based precoding scheme for downlink multi-user MIMO channels," IEEE Transactions on Wireless Communications, vol.6, no.5, pp.1711-1721, May 2007.
[39]Peng Cheng, Meixia Tao and Wenjun Zhang, "A new SLNR-based linear precoding for downlink multi-user multi-stream MIMO systems," IEEE Communications Letters, vol.14, no.11, pp.1008-1020, Nov.2010.
[40]Wei Fang, Huan Sun and Lin Yang, "Power allocation for maximizing sum capacity of multiuser MIMO downlink with transmit precoding based on SLNR," in Proc. IEEE VTC Spring 2011, pp.15-18, May 2011.
[41]M. Sharif and B. Hassibi, "On the capacity of MIMO broadcast channels with partial side information," IEEE Trans. Inform. Theory, vol.51, no.2, pp.506-522, Feb.2005.
[42]Park, David J. Love and Sung Jin Kim, "Improved multiuser MIMO unitary precoding using partial channel state information and insights from the riemannian manifold," IEEE Trans. Wireless Commun., vol.8, no.8, pp. 4011-4023, Aug.2009.
[43]Sung-Jin Kim, Ki-Ho Kim, Chang-Soon Park,.et al, "Mobile communication apparatus and method including base station and mobile station having multi-antenna," U.S. Patent 7,324,480, Jan.29.2008.
[44]Motorola, "DL MU-MIMO summary," 3GPP technical document, Rl-072693, June 22-June 25,2007.
[45]Samsung Electronics and Samsung Advanced Institute of Technology, "Downlink MIMO schemes for IEEE 802.16m," IEEE C802.16m-08/285, May 2008.
[46]H.Weingarten, Y. Steinberg, and S. Shamai, "The capacity region of the Gaussian multiple-input multiple-output broadcast channel," IEEE Trans. Inform. Theory, vol.52, no.9, pp.3936-3964, Sept.2006.
[47]J. Wang, D. J. Love, and M. D. Zoltowski, "User selection with zeroforcing beamforming achieves the asymptotically optimal sum rate," IEEE Trans. Signal Process., vol.56, no.8, pp.3713-3726, Aug.2008.
[48]Z. Shen. R. Chen, J. G. Andrews.et al, "Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization" IEEE Trans. Signal Process., vol.54, no.9, pp.3658-3663, Sept.2006.
[49]R. Chen. J. G. Andrews. R. W. Heath,et al, "'Low-complexity user and antenna selection for multiuser MIMO systems with block diagonalization," in Proc. IEEE ICASSP 2007, vol.3, pp.613-616, April 2007.
[50]Z. Shi, C. Zhao, and Z. Ding, "Low complexity eigenmode selection for MIMO broadcast systems with block diagonalization," in Proc. IEEE ICC 2008, pp. 3976-3981, May 2008.
[51]Zhang X. J., Lee J. W., "Low complexity MIMO scheduling with channel decomposition using capacity upperbound," IEEE Trans. Commun., vol.56, no.6, pp.871-876, June 2008.
[52]Sigdel S., Krzymien W. A., "Simplified fair scheduling and antenna selection algorithms for multiuser MIMO orthogonal space-division multiplexing downlink," IEEE Trans Veh Technol, vol.58, no.3, pp.1329-1343, March 2009.
[53]A. Goldsmith, S. A. Jafar and S. Srinivasay, "Breaking spectrum gridlock with cognitive radios:An information theoretic perspective," Proc. IEEE, vol.97, no. 5, pp.894-914, May 2009.
[54]R. Zhang, Y.-C. Liang, and S. Cui, "Dynamic resource allocation in cognitive radio networks:A convex optimization perspective," IEEE Signal Process. Mag., vol.27, no.3, pp.102-114, May 2010.
[55]R. Zhang, F. Gao, and Y.-C. Liang, "Cognitive beamforming made practical: Effective interference channel and learning-throughput tradeoff," IEEE Trans.Commun., vol.58, no.2, pp.706-718, Feb.2010.
[56]Feifei Gao, Rui Zhang and Ying-Chang Liang, "Design of Learning-Based MIMO Cognitive Radio Systems," IEEE Trans Veh Technol, vol.59, no.4, pp.1707-1720, May 2010.
[57]L. Zhang, Y.-C. Liang and Y. Xin, "Robust cognitive beamforming with partial channel state information," IEEE Trans. Wireless Commun., vol.8, no.8, pp. 4143-4153, Aug.2009.
[58]G. Zheng, K.-K.Wong and B. Ottersten, "Robust cognitive beamforming with bounded channel uncertainties," IEEE Trans. Signal Process., vol.57, no.12, pp. 4871-4881, Dec.2009.
[59]Scutari G., Palomar D.P. and Barbarossa S., "Cognitive MIMO radio," IEEE Signal Process. Mag., vol.25, no.6, pp.46-59, Nov.2008.
[60]G. Scutari and D. P. Palomar. "MIMO cognitive radio:A game theoretical approach," IEEE Trans. Signal Process., vol.58, no.2, pp.761-780, Feb.2010.
[61]J.Wang, G. Scutari and D. P. Palomar, "Robust MIMO cognitive radio via game theory.'" IEEE Trans. Signal Process., vol.59, no.3, pp.1183-1201, Mar.2011.
[62]G. Scutari, D. P. Palomar and F. Facchinei,"Convex optimization, game theory, and variational inequality theory in multiuser communication systems," IEEE Signal Process. Mag., vol.27, no.3, pp.35-49, May 2010.
[63]S.-J. Kim and G. B. Giannakis, "Optimal resource allocation for MIMO ad hoc cognitive radio networks," in Proc.46th Annu. Allerton Conf., pp.39-45, Sep. 2008.
[64]L. Zhang, R. Zhang and Y.-C. Liang, "On Gaussian MIMO BC-MAC duality with multiple transmit covariance constraints," IEEE Trans. Inf. Theory, vol.58, no.4, pp.2064-2078, Apr.2012.
[65]L. Zhang, Y. Xin, and Y.-C. Liang, "Weighted sum rate optimization for cognitive radio MIMO broadcast channels," IEEE Trans. Wireless Commun., vol.8, no.6, pp.2950-2959, June 2009.
[66]Hamdi, K.; Wei Zhang; Letaief, K., "Opportunistic spectrum sharing in cognitive MIMO wireless networks," IEEE Trans. Wireless Commun., vol.8, no.8, pp.4098-4109, Aug.2009.
[67]Kyoung-Jae Lee and Inkyu Lee, "MMSE Based Block Diagonalization for Cognitive Radio MIMO Broadcast Channels," IEEE Trans. Wireless Commun., vol.10, no.10, pp.3139-3144, Oct.2011.
[68]L. Zhang, Y.-C. Liang and Y. Xin, "Joint beamforming and power control for multiple access channels in cognitive radio networks," IEEE J. Select. Areas Commun.,vol.26, no.1, pp.38-51, Jan.2008.
[69]R. Zhang, S. Cui and Y.-C. Liang, "On ergodic sum capacity of fading cognitive multiple-access and broadcast channels," IEEE Trans. Inform. Theory, vol.55, no. 11, pp.5161-5178, Nov.2009.
[70]R. Kumar and L. Mieritz, "Conceptualizing "green" IT and data center power and cooling issues," Gartner, Research Paper G00150322, Sep.2007.
[71]T. Edler and S. Lundberg, "Energy efficiency enhancements in radio access networks," in Erricsson Review,2004.
[72]K. Pentikousis,"in search of energy-efficient mobile networking," IEEE Commun. Mag., vol.48, no.1, pp.95-103, Jan.2010.
[73]F. Meshkati, H. V. Poor, and S. C. Schwartz. "Energy-efficient resource allocation in wireless networks," IEEE Signal Process. Mag., vol.24, no.3, pp. 58-68, May 2007.
[74]G. Miao, N. Himayat. Y. Li. and A. Swami, "Cross-layer optimization for energy-effi cient wireless communications:a survey," Wireless Communications and Mobile Computing, vol.9, no.4, pp.529-542, Apr.2009.
[75]Y. Chen, S. Zhang, S. Xu, and G. Y. Li, "Fundamental trade-offs on green wireless networks," IEEE Commun. Mag., vol.49, no.6, pp.30-37, June 2011.
[76]F. Meshkati, H. Poor, S. Schwartz, and R. Balan, "Energy-efficient resource allocation in wireless networks with quality-of-service constraints," IEEE Trans. Commun., vol.57, no.11, pp.3406-3414,2009.
[77]Lei Deng, Yun Rui, Peng Cheng, et al "A unified energy efficiency and spectral efficiency tradeoff metric in wireless networks," IEEE Communications Letters, vol.17, no.1, pp.55-58, Jan.2013.
[78]G. Miao, N. Himayat, Y. Li, et al, "Energy efficient design in wireless OFDM systems," in Proc. IEEE ICC 2008, pp.3307-3312,2008.
[79]G. Miao, N. Himayat, and G. Li, "Energy-efficient link adaptation in frequency-selective channels," IEEE Trans. Commun., vol.58, no.2, pp.545-554, Feb.2010.
[80]G. Miao, N. Himayat, G. Li, et al, "Low complexity energy efficient OFDM systems," in Proc. IEEE ICC 2009, pp.1-5,2009.
[81]R. S. Prabhu and B. Daneshrad, "An energy-efficient water-filling algorithm for OFDM systems," in Proc. IEEE ICC 2010, pp.1-5,2010.
[82]Eickhoff R., Kraemer R. and Santamaria I., "Developing energy-efficient MIMO radios,", IEEE Vehicular Technology Magazine, vol.4, no.1, pp.34-41, March 2009.
[83]E. Belmega and S. Lasaulce, "Energy-efficient precoding for multiple-antenna terminals," IEEE Trans. Signal Process., vol.59, no.1, pp.329-340, Jan.2011.
[84]Z. Chong and E. Jorswieck, "Energy-efficient power control for MIMO time-varying channels," in Proc.2011 IEEE Online Green Communica-tions Conference, pp.92-97,2011.
[85]X. Ge, C. Cao, M. Jo, et ai, "Energy efficiency modelling and analyzing based on multi-cell and multi-antenna cellular networks," KSII Transactions on Internet and Information Systems, vol.4, no.4, pp.560-574,2010.
[86]Jie Xu and Ling Qiu, "Energy Efficiency Optimization for MIMO Broadcast Channels," IEEE Trans. Wireless Commun., vol.12, no.2, pp.690-701, Feb. 2013.
[87]Nicolaou Marios, Han Congzheng, Beh, Kian Chung, et al, "MIMO techniques for green radio guaranteeing QoS," Journal of Communications and Networks, vol.12, no.2, pp.130-139, April 2010.
[88]Z. Pan, K. K. Wong, and T. S. Ng, "Generalized multiuser orthogonal space-division multiplexing," IEEE Trans. Wireless Commun., vol.3, no.6, pp. 1969-1973, Nov.2004.
[89]T. Yoo and A. Goldsmith, "Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search," in Proc. IEEE Global Telecommun. Conf., pp.5-10,2005.
[90]R. A. Horn and C. R. Johnson, Matrix analysis, Cambridge University Press, 1985.
[91]Jakes W C, Microwave Mobile Communication, New York:Wiley,1974.
[92]S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press,2004.
[93]A. W. Marshall and I. Olkin, Inequalities:Theory of Majorization and Its Applications. New York:Academic,1979.
[94]A. Hjorungnes and D. Gesbert, "Complex-valued matrix differentiation: Techniques and key results," IEEE Trans. Signal Process., vol.55, no.6, pp. 2740-2746, June 2007.
[95]S. Boyd, "Stochastic programming," [Online]. Available:http://www. stanford.edu/class/ee364a/lectures/stochprog.pdf.
[96]D. P. Bertsekas, Nonlinear Programming, Athena Scientific,1995.
[97]S. Boyd, L. Xiao, and A. Mutapcic, "Subgradient methods," [Online]. Available: http://www.stanford.edu/class/ee392o/subgrad_method.pdf
[98]C.Isheden,Z. Chong, E. Jorswieck, et al, "Framework for link-level energy efficiency optimization with informed transmitter," IEEE Trans. Wireless Commun., vol.11, no.8, pp.2946-2957, Aug.2012.
[99]J. Rodriguez. "C2Power:cognitive radio and cooperative strategies for power saving in multi-standard wireless devices." FP7 ICT Objective 1.1, The Network of the Future. January,2010.
[100]Yan Wang, Wenjun Xu, Kewen Yang, et al, "Optimal energy-efficient power allocation for OFDM-based cognitive radio networks," IEEE Communications Letters, vol.16, no.9, pp.1420-1423, Sep.2012.
[101]Pirmoradian M., Adigun O. and Politis C., "Adaptive power control scheme for energy efficient cognitive radio networks," in Proc. IEEE ICC 2012, pp. 6988-6992,2012.
[102]R. G. Bland, D. Goldfarb, and M. J. Todd,"The ellipsoid method:A survey," Oper. Res., vol.29, no.6, pp.1039-1091, Nov.1981.
[103]T. Yoo, N. Jindal, and A. Goldsmith, "Multi-antenna downlink channels with limited feedback and user selection," IEEE J. Sel. Areas Commun., vol.25, no.7, pp.1478-1491, Sept.2007.
[104]K. Huang, J. G. Andrews, and R. W. Heath, "Performance of orthogonal beamforming for SDMA with limited feedback," IEEE Trans. Veh. Technol., vol. 58, no.1, pp.152-164, Jan.2009.
[105]Gradshteyn I S and Ryzhik I M, Table of Integrals, Series, and Products, New York:Academic Press,2007
[2]E. Telatar, "Capacity of multi-antenna Gaussian channels," AT&T-Bell Labs Internal Tech. Memo., June 1995.
[3]G. J. Foschini and M. J. Gans, "On limits of wireless communication in a fading environment when using multiple antennas," Wireless Personal Commun., vol.6, no.3, pp.311-335, Mar.1998.
[4]3GPP TR 25.912:"Feasibility study for evolved Universal Terrestrial Radio Access (UTRA) and Universal Terrestrial Radio Access Network (UTRAN) (Release 8)," V8.0.0, Dec.2008.
[5]Q. H. Spencer, C. B. Peel, L. Swindlehurst, et al, "An introduction to the multi-user MIMO downlink," IEEE Commun. Mag., vol.42, no.10, pp.60-67, Oct.2004.
[6]D. Gesbert, M. Kountouris, R.W. Heath Jr., et al, "From single user to multiuser communications:Shifting the MIMO paradigm," IEEE Signal Process. Mag., vol. 24, no.5, pp.36-46, Sept.2007.
[7]J. Mitola and G. Q. Maguire, "Cognitive radio:Making software radios more personal," IEEE Pers. Commun., vol.6, no.6, pp.13-18, Aug.1999.
[8]S. Haykin, "Cognitive radio:Brain-empowered wireless communications," IEEE J. Sel. Areas Commun., vol.23, no.2, pp.201-220, Feb.2005.
[9]Federal Communication Commission, "Spectrum Policy Task Force," Rep. ET Docket, no.02-135, Nov 2002.
[10]"IEEE 802.22.1-2010 standard," [Online], available:http://standards.ieee.org/ getieee802/download/802.22.1-2010.pdf.
[11]"IEEE 802.11h-2003 Standard," [Online], available:http://standards.ieee.org/ getieee802/download/802.11h-2003.pdf.
[12]"IEEE 802.11y-2003 Standard," [Online], available:http://standards.ieee.org/ getieee802/download/802.11y-2008.pdf.
[13]R. Zhang and Y.-C. Liang, "Exploiting multi-antennas for opportunistic spectrum sharing in cognitive radio networks," IEEE J. Sel. Topics Signal Process., vol.2, no.1, pp.88-102, Feb.2008.
[14]"Improving energy efficiency, Lower CO2 emission and TCO," Whitepaper, Huawei energy effi ciency solution, Huawei Technologies,2010.
[15]Daquan Feng, Chenzi Jiang, Gubong Lim, et al, "A survey of energy-efficient wireless communications," IEEE Communications Surveys & Tutorials, vol.15, no.1, pp.167-178, Feb.2013.
[16]Li, G.Y., Zhikun Xu, Cong Xiong, et al, "Energy-efficient wireless communications:tutorial, survey, and open issues," IEEE Wireless Communications, vol.18, no.6, pp.28-35, December 2011.
[17]Neri F, "TREND:towords real energy-efficient network design," Network of excellence proposal, FP7-1CT-2009-5, April,2010.
[18]Andrea Goldsmith, Wireless Communications, Cambridge University Press, 2005.
[19]C. Windpassinger, R. F. H. Fischer, T. Vencel, et al, "Precoding in multiantenna and multiuser communications,"'IEEE Trans. Wireless Commun., vol.3, no.4, pp. 1305-1336, July 2004.
[20]M. Costa, "Writing on dirty paper," IEEE Trans. Inform. Theory, vol.29, no.3, pp.439-441, May 1983.
[21]S. Vishwanath, N. Jindal, and A. Goldsmith, "Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels," IEEE Trans.on Inform. Theory, vol.49, no.10, pp.2658-2668, Oct.2003.
[22]G. Caire and S. Shamai, "On the achievable throughput of a multiantenna Gaussian broadcast channel," IEEE Trans. Inform. Theory, vol.49, no.7, pp. 1691-1706, July 2003.
[23]C. B. Peel, B. M. Hochwald, and A. L. Swindelhurst, "A vector-perturbation technique for near-capacity multiantenna multiuser communication-part 1: channel inversion and regularization," IEEE Trans. Commun., vol.53, pp. 195-202, Jan.2005.
[24]J. Liu and W. A. Krzymien, "Improved Tomlinson-Harashima precoding for the downlink of multiple antenna multi-user systems,'" in Proc. IEEE WCNC 2005, pp.466-472. Mar.2005.
[25]C. H. F. Fung, W. Yu, A. D. Dabbagh, et al, "Precoding for multiple antenna Gaussian broadcast channels with successive zeroforcing," IEEE Trans. Signal Process., vol.55, no.7, pp.3837-3850, July 2007.
[26]T. Yoo and A. Goldsmith, "On the optimality of multi-antenna broadcast scheduling using zero-forcing beamforming," IEEE J. Sel. Areas Commun., vol. 24, pp.528-542, Mar.2006.
[27]H. Sung, S. R. Lee, and I. Lee, "Generalized channel inversion methods for multiuser MIMO systems," IEEE Trans. Commun., vol.57, no.11, pp.3489-3499, Nov.2009.
[28]Q. H. Spencer, A. L. Swindlehurst, and M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels," IEEE Trans. Signal Process., vol.52, no.2, pp.461-471, Feb.2004.
[29]T. Haustein, C. von Helmolt, E. Jorswieck, et al, "Performance of MIMO systems with channel inversion," in Proc. IEEE VTC 2002, vol.1, pp.35-39, May 2002.
[30]R. Chen, Z. Shen, J. G. Andrews, et al, "Multimode transmission for multiuser MIMO systems with block diagonalization," IEEE Trans. Signal Process., vol.56, no.7, pp.3294-3302, July 2008.
[31]S. Kaviani and W. A. Krzymien, "On the optimality of multiuser zero-forcing precoding in MIMO broadcast channels," in Proc. IEEE VTC 2009, pp.1-5, April 2009.
[32]S. Shi and M. Schubert, "MMSE transmit optimization for multi-user multi-antenna systems," in Proc. IEEE ICASSP 2005, pp.409-412, Mar.2005.
[33]J. Zhang, Y. Wu, S. Zhou, et al, "Joint linear transmitter and receiver design for the downlink of multiuser MIMO systems," IEEE Commun. Letters, vol.9, no.11, pp.991-993, Nov.2005.
[34]J. Joung, Y. H. Lee, "Regularized channel diagonalization for multiuser MIMO downlink using a modified MMSE criterion," IEEE Trans. Signal Process., vol. 55, no.7, pp.1573-1579, Apr.2007.
[35]Vucic N., Boche H. and Shuying Shi "Robust transceiver optimization in downlink multiuser MIMO systems," IEEE Trans. Signal Process., vol.57, no.9, pp.3576-3587, Sept.2009.
[36]Shuying Shi, Schubert M. and Boche H., "Downlink MMSE transceiver optimization for multiuser MIMO systems:MMSE balancing," IEEE Trans. Signal Process., vol.56, no.8, pp.3702-3712, Aug.2008.
[37]Shuying Shi, Schubert M. and Boche H., "Downlink MMSE transceiver optimization for multiuser MIMO systems:duality and sum-MSE minimization," IEEE Trans. Signal Process., vol.55, no.11, pp.5436-5446, Nov.2007.
[38]M. Sadek, A. Tarighat, and A. H. Sayed, "A leakage-based precoding scheme for downlink multi-user MIMO channels," IEEE Transactions on Wireless Communications, vol.6, no.5, pp.1711-1721, May 2007.
[39]Peng Cheng, Meixia Tao and Wenjun Zhang, "A new SLNR-based linear precoding for downlink multi-user multi-stream MIMO systems," IEEE Communications Letters, vol.14, no.11, pp.1008-1020, Nov.2010.
[40]Wei Fang, Huan Sun and Lin Yang, "Power allocation for maximizing sum capacity of multiuser MIMO downlink with transmit precoding based on SLNR," in Proc. IEEE VTC Spring 2011, pp.15-18, May 2011.
[41]M. Sharif and B. Hassibi, "On the capacity of MIMO broadcast channels with partial side information," IEEE Trans. Inform. Theory, vol.51, no.2, pp.506-522, Feb.2005.
[42]Park, David J. Love and Sung Jin Kim, "Improved multiuser MIMO unitary precoding using partial channel state information and insights from the riemannian manifold," IEEE Trans. Wireless Commun., vol.8, no.8, pp. 4011-4023, Aug.2009.
[43]Sung-Jin Kim, Ki-Ho Kim, Chang-Soon Park,.et al, "Mobile communication apparatus and method including base station and mobile station having multi-antenna," U.S. Patent 7,324,480, Jan.29.2008.
[44]Motorola, "DL MU-MIMO summary," 3GPP technical document, Rl-072693, June 22-June 25,2007.
[45]Samsung Electronics and Samsung Advanced Institute of Technology, "Downlink MIMO schemes for IEEE 802.16m," IEEE C802.16m-08/285, May 2008.
[46]H.Weingarten, Y. Steinberg, and S. Shamai, "The capacity region of the Gaussian multiple-input multiple-output broadcast channel," IEEE Trans. Inform. Theory, vol.52, no.9, pp.3936-3964, Sept.2006.
[47]J. Wang, D. J. Love, and M. D. Zoltowski, "User selection with zeroforcing beamforming achieves the asymptotically optimal sum rate," IEEE Trans. Signal Process., vol.56, no.8, pp.3713-3726, Aug.2008.
[48]Z. Shen. R. Chen, J. G. Andrews.et al, "Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization" IEEE Trans. Signal Process., vol.54, no.9, pp.3658-3663, Sept.2006.
[49]R. Chen. J. G. Andrews. R. W. Heath,et al, "'Low-complexity user and antenna selection for multiuser MIMO systems with block diagonalization," in Proc. IEEE ICASSP 2007, vol.3, pp.613-616, April 2007.
[50]Z. Shi, C. Zhao, and Z. Ding, "Low complexity eigenmode selection for MIMO broadcast systems with block diagonalization," in Proc. IEEE ICC 2008, pp. 3976-3981, May 2008.
[51]Zhang X. J., Lee J. W., "Low complexity MIMO scheduling with channel decomposition using capacity upperbound," IEEE Trans. Commun., vol.56, no.6, pp.871-876, June 2008.
[52]Sigdel S., Krzymien W. A., "Simplified fair scheduling and antenna selection algorithms for multiuser MIMO orthogonal space-division multiplexing downlink," IEEE Trans Veh Technol, vol.58, no.3, pp.1329-1343, March 2009.
[53]A. Goldsmith, S. A. Jafar and S. Srinivasay, "Breaking spectrum gridlock with cognitive radios:An information theoretic perspective," Proc. IEEE, vol.97, no. 5, pp.894-914, May 2009.
[54]R. Zhang, Y.-C. Liang, and S. Cui, "Dynamic resource allocation in cognitive radio networks:A convex optimization perspective," IEEE Signal Process. Mag., vol.27, no.3, pp.102-114, May 2010.
[55]R. Zhang, F. Gao, and Y.-C. Liang, "Cognitive beamforming made practical: Effective interference channel and learning-throughput tradeoff," IEEE Trans.Commun., vol.58, no.2, pp.706-718, Feb.2010.
[56]Feifei Gao, Rui Zhang and Ying-Chang Liang, "Design of Learning-Based MIMO Cognitive Radio Systems," IEEE Trans Veh Technol, vol.59, no.4, pp.1707-1720, May 2010.
[57]L. Zhang, Y.-C. Liang and Y. Xin, "Robust cognitive beamforming with partial channel state information," IEEE Trans. Wireless Commun., vol.8, no.8, pp. 4143-4153, Aug.2009.
[58]G. Zheng, K.-K.Wong and B. Ottersten, "Robust cognitive beamforming with bounded channel uncertainties," IEEE Trans. Signal Process., vol.57, no.12, pp. 4871-4881, Dec.2009.
[59]Scutari G., Palomar D.P. and Barbarossa S., "Cognitive MIMO radio," IEEE Signal Process. Mag., vol.25, no.6, pp.46-59, Nov.2008.
[60]G. Scutari and D. P. Palomar. "MIMO cognitive radio:A game theoretical approach," IEEE Trans. Signal Process., vol.58, no.2, pp.761-780, Feb.2010.
[61]J.Wang, G. Scutari and D. P. Palomar, "Robust MIMO cognitive radio via game theory.'" IEEE Trans. Signal Process., vol.59, no.3, pp.1183-1201, Mar.2011.
[62]G. Scutari, D. P. Palomar and F. Facchinei,"Convex optimization, game theory, and variational inequality theory in multiuser communication systems," IEEE Signal Process. Mag., vol.27, no.3, pp.35-49, May 2010.
[63]S.-J. Kim and G. B. Giannakis, "Optimal resource allocation for MIMO ad hoc cognitive radio networks," in Proc.46th Annu. Allerton Conf., pp.39-45, Sep. 2008.
[64]L. Zhang, R. Zhang and Y.-C. Liang, "On Gaussian MIMO BC-MAC duality with multiple transmit covariance constraints," IEEE Trans. Inf. Theory, vol.58, no.4, pp.2064-2078, Apr.2012.
[65]L. Zhang, Y. Xin, and Y.-C. Liang, "Weighted sum rate optimization for cognitive radio MIMO broadcast channels," IEEE Trans. Wireless Commun., vol.8, no.6, pp.2950-2959, June 2009.
[66]Hamdi, K.; Wei Zhang; Letaief, K., "Opportunistic spectrum sharing in cognitive MIMO wireless networks," IEEE Trans. Wireless Commun., vol.8, no.8, pp.4098-4109, Aug.2009.
[67]Kyoung-Jae Lee and Inkyu Lee, "MMSE Based Block Diagonalization for Cognitive Radio MIMO Broadcast Channels," IEEE Trans. Wireless Commun., vol.10, no.10, pp.3139-3144, Oct.2011.
[68]L. Zhang, Y.-C. Liang and Y. Xin, "Joint beamforming and power control for multiple access channels in cognitive radio networks," IEEE J. Select. Areas Commun.,vol.26, no.1, pp.38-51, Jan.2008.
[69]R. Zhang, S. Cui and Y.-C. Liang, "On ergodic sum capacity of fading cognitive multiple-access and broadcast channels," IEEE Trans. Inform. Theory, vol.55, no. 11, pp.5161-5178, Nov.2009.
[70]R. Kumar and L. Mieritz, "Conceptualizing "green" IT and data center power and cooling issues," Gartner, Research Paper G00150322, Sep.2007.
[71]T. Edler and S. Lundberg, "Energy efficiency enhancements in radio access networks," in Erricsson Review,2004.
[72]K. Pentikousis,"in search of energy-efficient mobile networking," IEEE Commun. Mag., vol.48, no.1, pp.95-103, Jan.2010.
[73]F. Meshkati, H. V. Poor, and S. C. Schwartz. "Energy-efficient resource allocation in wireless networks," IEEE Signal Process. Mag., vol.24, no.3, pp. 58-68, May 2007.
[74]G. Miao, N. Himayat. Y. Li. and A. Swami, "Cross-layer optimization for energy-effi cient wireless communications:a survey," Wireless Communications and Mobile Computing, vol.9, no.4, pp.529-542, Apr.2009.
[75]Y. Chen, S. Zhang, S. Xu, and G. Y. Li, "Fundamental trade-offs on green wireless networks," IEEE Commun. Mag., vol.49, no.6, pp.30-37, June 2011.
[76]F. Meshkati, H. Poor, S. Schwartz, and R. Balan, "Energy-efficient resource allocation in wireless networks with quality-of-service constraints," IEEE Trans. Commun., vol.57, no.11, pp.3406-3414,2009.
[77]Lei Deng, Yun Rui, Peng Cheng, et al "A unified energy efficiency and spectral efficiency tradeoff metric in wireless networks," IEEE Communications Letters, vol.17, no.1, pp.55-58, Jan.2013.
[78]G. Miao, N. Himayat, Y. Li, et al, "Energy efficient design in wireless OFDM systems," in Proc. IEEE ICC 2008, pp.3307-3312,2008.
[79]G. Miao, N. Himayat, and G. Li, "Energy-efficient link adaptation in frequency-selective channels," IEEE Trans. Commun., vol.58, no.2, pp.545-554, Feb.2010.
[80]G. Miao, N. Himayat, G. Li, et al, "Low complexity energy efficient OFDM systems," in Proc. IEEE ICC 2009, pp.1-5,2009.
[81]R. S. Prabhu and B. Daneshrad, "An energy-efficient water-filling algorithm for OFDM systems," in Proc. IEEE ICC 2010, pp.1-5,2010.
[82]Eickhoff R., Kraemer R. and Santamaria I., "Developing energy-efficient MIMO radios,", IEEE Vehicular Technology Magazine, vol.4, no.1, pp.34-41, March 2009.
[83]E. Belmega and S. Lasaulce, "Energy-efficient precoding for multiple-antenna terminals," IEEE Trans. Signal Process., vol.59, no.1, pp.329-340, Jan.2011.
[84]Z. Chong and E. Jorswieck, "Energy-efficient power control for MIMO time-varying channels," in Proc.2011 IEEE Online Green Communica-tions Conference, pp.92-97,2011.
[85]X. Ge, C. Cao, M. Jo, et ai, "Energy efficiency modelling and analyzing based on multi-cell and multi-antenna cellular networks," KSII Transactions on Internet and Information Systems, vol.4, no.4, pp.560-574,2010.
[86]Jie Xu and Ling Qiu, "Energy Efficiency Optimization for MIMO Broadcast Channels," IEEE Trans. Wireless Commun., vol.12, no.2, pp.690-701, Feb. 2013.
[87]Nicolaou Marios, Han Congzheng, Beh, Kian Chung, et al, "MIMO techniques for green radio guaranteeing QoS," Journal of Communications and Networks, vol.12, no.2, pp.130-139, April 2010.
[88]Z. Pan, K. K. Wong, and T. S. Ng, "Generalized multiuser orthogonal space-division multiplexing," IEEE Trans. Wireless Commun., vol.3, no.6, pp. 1969-1973, Nov.2004.
[89]T. Yoo and A. Goldsmith, "Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search," in Proc. IEEE Global Telecommun. Conf., pp.5-10,2005.
[90]R. A. Horn and C. R. Johnson, Matrix analysis, Cambridge University Press, 1985.
[91]Jakes W C, Microwave Mobile Communication, New York:Wiley,1974.
[92]S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press,2004.
[93]A. W. Marshall and I. Olkin, Inequalities:Theory of Majorization and Its Applications. New York:Academic,1979.
[94]A. Hjorungnes and D. Gesbert, "Complex-valued matrix differentiation: Techniques and key results," IEEE Trans. Signal Process., vol.55, no.6, pp. 2740-2746, June 2007.
[95]S. Boyd, "Stochastic programming," [Online]. Available:http://www. stanford.edu/class/ee364a/lectures/stochprog.pdf.
[96]D. P. Bertsekas, Nonlinear Programming, Athena Scientific,1995.
[97]S. Boyd, L. Xiao, and A. Mutapcic, "Subgradient methods," [Online]. Available: http://www.stanford.edu/class/ee392o/subgrad_method.pdf
[98]C.Isheden,Z. Chong, E. Jorswieck, et al, "Framework for link-level energy efficiency optimization with informed transmitter," IEEE Trans. Wireless Commun., vol.11, no.8, pp.2946-2957, Aug.2012.
[99]J. Rodriguez. "C2Power:cognitive radio and cooperative strategies for power saving in multi-standard wireless devices." FP7 ICT Objective 1.1, The Network of the Future. January,2010.
[100]Yan Wang, Wenjun Xu, Kewen Yang, et al, "Optimal energy-efficient power allocation for OFDM-based cognitive radio networks," IEEE Communications Letters, vol.16, no.9, pp.1420-1423, Sep.2012.
[101]Pirmoradian M., Adigun O. and Politis C., "Adaptive power control scheme for energy efficient cognitive radio networks," in Proc. IEEE ICC 2012, pp. 6988-6992,2012.
[102]R. G. Bland, D. Goldfarb, and M. J. Todd,"The ellipsoid method:A survey," Oper. Res., vol.29, no.6, pp.1039-1091, Nov.1981.
[103]T. Yoo, N. Jindal, and A. Goldsmith, "Multi-antenna downlink channels with limited feedback and user selection," IEEE J. Sel. Areas Commun., vol.25, no.7, pp.1478-1491, Sept.2007.
[104]K. Huang, J. G. Andrews, and R. W. Heath, "Performance of orthogonal beamforming for SDMA with limited feedback," IEEE Trans. Veh. Technol., vol. 58, no.1, pp.152-164, Jan.2009.
[105]Gradshteyn I S and Ryzhik I M, Table of Integrals, Series, and Products, New York:Academic Press,2007