MU-MIMO系统下行链路的低复杂度算法
|
摘要
多输入多输出(MIMO, Multiple-Input Multiple-Output)系统是近几年飞速发展的无线通信系统核心技术之一,不仅可以用来提高信道容量,还可以提高信号的信噪比(SNR, Signal And Noise Ratio)。在IEEE802.11n (Wi-Fi),3GPP LTE, WiMAX, HSPA+等技术标准中已经融合了MIMO系统。MIMO系统主要有三种技术,分别是预编码技术,空间复用技术和分集编码技术。其中预编码技术可以自适应的调整用户的预编码矩阵,进而抑制信道衰落、降低系统误码率、扩大系统容量。
相比传统的单用户MIMO预编码技术,多用户MIMO预编码技术需要处理多个并行的数据流,并且还要确保能够消除共信道干扰(CCI,Co-Channel Interference)。多用户MIMO预编码技术可以分为基于信道分解的预编码和最优化预编码。
本论文主要对下行链路最优化预编码以及其相关技术进行了研究。下行链路最优化预编码模型是一个带一个二次不等式约束的分式优化问题。目前通常的办法是直接将分子看做目标函数(忽视分母)进行求解,毫无疑问,这样计算出来的结果误差很大。本文通过把分母从分式中分离出来作为约束条件,获得了与原问题等价的带两个约束的二次优化问题,接着使用半正定松弛方法和矩阵秩一分解技术对该等价问题精确求解。仿真结果表明本文所求结果的误差远远小于目前使用方法造成的误差,初步显示本文所提预编码技术效果显著。
Multiple-Input Multiple-Output (MIMO) system is one of the important technologies in wireless communication system. It will not only improve the channel capacity, but also rise the Ratio of Signal and Noise (SNR). The IEEE802.11n(Wi-Fi),3GPP LTE, WiMAX and HSPA+have contained MIMO system. In general, MIMO system has three technologies, that is Pre-coding technology, Spatial multiplexing technology and Diversity coding technology. Pre-coding technology can adjust pre-coding matrices of users adaptively to suppress channel fading, to reduce system's Bit Error Ratio (BER) and to improve system capacity.
Different from the traditional one-single-user MIMO pre-coding technology, Multi-User MIMO (MU-MIMO) pre-coding technology has to process multiple parallel data stream, and to ensure removement of Co-Channel Interference (CCI). MU-MIMO pre-coding technology could be divided into pre-coding based on channel decomposition and optimal pre-coding.
In this paper, we have discussed downlink optimal pre-coding technology. Downlink optimal pre-coding model is a fractional optimization problem with one quadratic inequality constraint. As we know, the current popular approach for solving the downlink optimal pre-coding model is to optimize only the numerator of the fractional objective function (that is, ignore its denominator), which, of course, causes great errors. In this paper, we manage to transform the original problem into a quadratic optimization problem with two constraints equivalently, by moving the denominator to a constraint. Then we solve the new problem accurately by semi-definite programming relaxation method and rank-one matrix-decomposition technique. Simulation results show that the errors caused by our algorithm are far less than those of the current approach, that is the new approach is effective.
相比传统的单用户MIMO预编码技术,多用户MIMO预编码技术需要处理多个并行的数据流,并且还要确保能够消除共信道干扰(CCI,Co-Channel Interference)。多用户MIMO预编码技术可以分为基于信道分解的预编码和最优化预编码。
本论文主要对下行链路最优化预编码以及其相关技术进行了研究。下行链路最优化预编码模型是一个带一个二次不等式约束的分式优化问题。目前通常的办法是直接将分子看做目标函数(忽视分母)进行求解,毫无疑问,这样计算出来的结果误差很大。本文通过把分母从分式中分离出来作为约束条件,获得了与原问题等价的带两个约束的二次优化问题,接着使用半正定松弛方法和矩阵秩一分解技术对该等价问题精确求解。仿真结果表明本文所求结果的误差远远小于目前使用方法造成的误差,初步显示本文所提预编码技术效果显著。
Multiple-Input Multiple-Output (MIMO) system is one of the important technologies in wireless communication system. It will not only improve the channel capacity, but also rise the Ratio of Signal and Noise (SNR). The IEEE802.11n(Wi-Fi),3GPP LTE, WiMAX and HSPA+have contained MIMO system. In general, MIMO system has three technologies, that is Pre-coding technology, Spatial multiplexing technology and Diversity coding technology. Pre-coding technology can adjust pre-coding matrices of users adaptively to suppress channel fading, to reduce system's Bit Error Ratio (BER) and to improve system capacity.
Different from the traditional one-single-user MIMO pre-coding technology, Multi-User MIMO (MU-MIMO) pre-coding technology has to process multiple parallel data stream, and to ensure removement of Co-Channel Interference (CCI). MU-MIMO pre-coding technology could be divided into pre-coding based on channel decomposition and optimal pre-coding.
In this paper, we have discussed downlink optimal pre-coding technology. Downlink optimal pre-coding model is a fractional optimization problem with one quadratic inequality constraint. As we know, the current popular approach for solving the downlink optimal pre-coding model is to optimize only the numerator of the fractional objective function (that is, ignore its denominator), which, of course, causes great errors. In this paper, we manage to transform the original problem into a quadratic optimization problem with two constraints equivalently, by moving the denominator to a constraint. Then we solve the new problem accurately by semi-definite programming relaxation method and rank-one matrix-decomposition technique. Simulation results show that the errors caused by our algorithm are far less than those of the current approach, that is the new approach is effective.
引文
[1]邬正义,徐惠钢《现代无线通信技术》高等教育出版社2008年参考页码110-165；
[2]谢益溪《无线电波传播：原理与应用》人民邮电出版社2010年参考页码54-60；
[3]Agilent 《MIMO Channel Modeling and Emulation Test Challenges)) 2011;
[4]刘化君《物联网技术》电子工业出版社2010年参考页码115-154；
[5]D. Tse, P. Viswanath 《Fundamentals of Wireless Communication》 Cambridge University Press,2005;
[6]林云,何丰《MIMO技术原理及应用》人民邮电出版社2010年参考页码62-78；
[7]祁玉生,邵世祥《现代移动通信系统》人民邮电出版社1999年参考页码130-169；
[8]Wiesel A. Eldar Y. C. Shamai (Shitz)S. " Linear Precoding via Conic Optimization for Fixed MIMO Receivers," IEEE Trans. Signal Process., vol.54 January 2006 pp.161-176;
[9]陈学平,左晓萍《局域网组件、管理与维护》化学工业出版社2011年参考页码128-138；
[10]S.Coleri, M.Ergen, A.Puri,and so on "Channel estimation techniques based on pilot arrangement in OFDM systems" IEEE Transactions on Broadcasting, September 2002.pp.745-788;
[11]D. Love, R. Heath, V. Lau, and so on "An overview of limited feedback in wireless communication systems" IEEE Journal on Selected Areas Communication vol.26 2008 pp.1341-1365;
[12]Chee Wei Tan Mung Chiang R.Srikant "Maximizing Sum Rate and Minimizing MSE on Multiuser Downlink:Optimality Fast Algorithms and Equivalence via Max-min SINR "IEEE Transanction Signal Process vol.59 December 2011 no.12 pp.6127-6139;
[13]Sung H. Lee S.R. and Lee I. "Generalized Channel Inversion Methods for Multiuser MIMO systems, "IEEE Trans.Communications November vol.57 no.11 2009 pp.3489-3499;
[14]Peel C. B. Hochwald B. M. A. L. Swindlehurst, "A Vector-Perturbation Technique for Near-Capacity Multiantenna Multiuser Communication-Part I: Channel Inversion and Regularization," IEEE Trans.Commun., January 2005 vol.53,, pp.195-202,;
[15]Spencer Q. H. Swindelhurst A. L. Haardt M. "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels "IEEE Trans. Signal Processing February 2004 vol.52 pp.461-471;
[16]M. Schubert and H. Boche "Solution of the multiuser downlink beamforming problem with individual SINR constraints " IEEE Trans, on Vehicular Technology January.2004 vol.53 no.1 pp.18-28;
[17]A. Beck and M. Teboulle, "A convex optimization approach for minimizing the ratio of indefinite quadratic functions over an ellipsoid," Math. Program., Ser. A., pp.13-35,2009;
[18]Ai Weibao and Zhang Shuzhong, "Strong Duality for the CDT subproblem:A Necessary and sufficient condition[J]." SIAM Journal on Optimization, pp.1735-1756,2008;
[19]A. Beck, and Y. C. Eldary,"Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints," September,2005;
[20]A. Beck, A. BEN-TAL and M. Teboulle, "Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares[J]." SIAM J. Matrix Anal. APPL.,vol.28, pp. 425-445,2006;
[21]Y. Y. Ye, "Linear Conic Programming",December 2004;
[22]N. Jindal, W. Rhee, S. Vishwanath, S. Jafar, and A. Goldsmith, "Sum power iterative water-filling for multi-antenna Gaussian broadcast channels," IEEE Trans. Inf. Theory, vol.50, pp.1570-1580, April 2005;
[23]G.J. Foschini and M.J. Gans, On limits of wireless communications in a fading environment when using multiple antennas, Wireless Personal Communications, vol.6, no.3, pp.311-335,1998;
[24]D. Gesbert, M. Kountouris, R.W. Heath Jr., C.-B. Chae, and T. Salzer, Shifting the MIMO Paradigm, IEEE Signal Processing Magazine, vol.24, no.5, pp.36-46,2007;
[25]E. Telatar, Capacity of multiantenna Gaussian channels, European Transactions on Telecommunications, vol.10, no.6, pp.585-595,1999;
[26]H. Weingarten, Y. Steinberg, and S. Shamai, The capacity region of the Gaussian multiple-input multiple-output broadcast channel, IEEE Transactions on Information Theory, vol.52, no.9, pp.3936-3964,2006;
[27]M. Sharif and B. Hassibi, On the Capacity of MIMO Broadcast Channels With Partial Side Information, IEEE Transactions on Information Theory, vol.51, no.2, pp.506-522,2005;
[28]E. Bjornson, R. Zakhour, D. Gesbert, B. Ottersten, Cooperative Multicell Precoding:Rate Region Characterization and Distributed Strategies with Instantaneous and Statistical CSI, IEEE Transactions on Signal Processing, vol. 58, no.8, pp.4298-4310,2010;
[29]T. Lo, Maximum ratio transmission, IEEE Transactions on Communications, vol.47, no.10 1999 pp.1458-1461,;
[30]a b N. Jindal, MIMO Broadcast Channels with Finite Rate Feedback, IEEE Transactions on Information Theory, vol.52, no.11, pp.5045-5059,2006;
[31]D.J. Love, R.W. Heath, and T. Strohmer, Grassmannian Beamforming for Multiple-Input Multiple-Output Wireless Systems, IEEE Transactions on Information Theory, vol.49, no.10, pp.2735-2747,2003;
[32]P. Viswanath, D. N. C. Tse, Member, and R. Laroia, Opportunistic Beamforming Using Dumb Antennas, IEEE Transactions on Information Theory, vol.48, no.6, pp.1277-1294,2002;
[33]D. Hammarwall, M. Bengtsson, and B. Ottersten, Utilizing the spatial information provided by channel norm feedback in SDMA systems, IEEE Transactions on Signal Processing, vol.56, no.7, pp.3278-3293,2008;
[34]E. Bjomson, D. Hammarwall, B. Ottersten, Exploiting Quantized Channel Norm Feedback through Conditional Statistics in Arbitrarily Correlated MIMO Systems, IEEE Transactions on Signal Processing, vol.57, no.10, pp.4027-4041, 2009;
[35]M. Costa, Writing on dirty paper, IEEE Transactions on Information Theory, vol.29, no.3, pp.439-441,1983;
[36]M. Tomlinson, New automatic equalizer employing modulo arithmetic, Electronics Letters, vol.7, no.5, pp.138-139,1971;
[37]H. Harashima and H. Miyakawa, Matched-transmission technique for channels with intersymbol interference, IEEE Transactions on Communications, vol.20, no.4, pp.774-780,1972;
[38]B. M. Hochwald, C. B. Peel, and A. L. Swindlehurst, A vector-perturbation technique for near-capacity multiantenna multi-user communication-Part II: Perturbation, IEEE Transactions on Communications, vol.53 no.l 2005 pp.537-544;
[2]谢益溪《无线电波传播：原理与应用》人民邮电出版社2010年参考页码54-60；
[3]Agilent 《MIMO Channel Modeling and Emulation Test Challenges)) 2011;
[4]刘化君《物联网技术》电子工业出版社2010年参考页码115-154；
[5]D. Tse, P. Viswanath 《Fundamentals of Wireless Communication》 Cambridge University Press,2005;
[6]林云,何丰《MIMO技术原理及应用》人民邮电出版社2010年参考页码62-78；
[7]祁玉生,邵世祥《现代移动通信系统》人民邮电出版社1999年参考页码130-169；
[8]Wiesel A. Eldar Y. C. Shamai (Shitz)S. " Linear Precoding via Conic Optimization for Fixed MIMO Receivers," IEEE Trans. Signal Process., vol.54 January 2006 pp.161-176;
[9]陈学平,左晓萍《局域网组件、管理与维护》化学工业出版社2011年参考页码128-138；
[10]S.Coleri, M.Ergen, A.Puri,and so on "Channel estimation techniques based on pilot arrangement in OFDM systems" IEEE Transactions on Broadcasting, September 2002.pp.745-788;
[11]D. Love, R. Heath, V. Lau, and so on "An overview of limited feedback in wireless communication systems" IEEE Journal on Selected Areas Communication vol.26 2008 pp.1341-1365;
[12]Chee Wei Tan Mung Chiang R.Srikant "Maximizing Sum Rate and Minimizing MSE on Multiuser Downlink:Optimality Fast Algorithms and Equivalence via Max-min SINR "IEEE Transanction Signal Process vol.59 December 2011 no.12 pp.6127-6139;
[13]Sung H. Lee S.R. and Lee I. "Generalized Channel Inversion Methods for Multiuser MIMO systems, "IEEE Trans.Communications November vol.57 no.11 2009 pp.3489-3499;
[14]Peel C. B. Hochwald B. M. A. L. Swindlehurst, "A Vector-Perturbation Technique for Near-Capacity Multiantenna Multiuser Communication-Part I: Channel Inversion and Regularization," IEEE Trans.Commun., January 2005 vol.53,, pp.195-202,;
[15]Spencer Q. H. Swindelhurst A. L. Haardt M. "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels "IEEE Trans. Signal Processing February 2004 vol.52 pp.461-471;
[16]M. Schubert and H. Boche "Solution of the multiuser downlink beamforming problem with individual SINR constraints " IEEE Trans, on Vehicular Technology January.2004 vol.53 no.1 pp.18-28;
[17]A. Beck and M. Teboulle, "A convex optimization approach for minimizing the ratio of indefinite quadratic functions over an ellipsoid," Math. Program., Ser. A., pp.13-35,2009;
[18]Ai Weibao and Zhang Shuzhong, "Strong Duality for the CDT subproblem:A Necessary and sufficient condition[J]." SIAM Journal on Optimization, pp.1735-1756,2008;
[19]A. Beck, and Y. C. Eldary,"Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints," September,2005;
[20]A. Beck, A. BEN-TAL and M. Teboulle, "Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares[J]." SIAM J. Matrix Anal. APPL.,vol.28, pp. 425-445,2006;
[21]Y. Y. Ye, "Linear Conic Programming",December 2004;
[22]N. Jindal, W. Rhee, S. Vishwanath, S. Jafar, and A. Goldsmith, "Sum power iterative water-filling for multi-antenna Gaussian broadcast channels," IEEE Trans. Inf. Theory, vol.50, pp.1570-1580, April 2005;
[23]G.J. Foschini and M.J. Gans, On limits of wireless communications in a fading environment when using multiple antennas, Wireless Personal Communications, vol.6, no.3, pp.311-335,1998;
[24]D. Gesbert, M. Kountouris, R.W. Heath Jr., C.-B. Chae, and T. Salzer, Shifting the MIMO Paradigm, IEEE Signal Processing Magazine, vol.24, no.5, pp.36-46,2007;
[25]E. Telatar, Capacity of multiantenna Gaussian channels, European Transactions on Telecommunications, vol.10, no.6, pp.585-595,1999;
[26]H. Weingarten, Y. Steinberg, and S. Shamai, The capacity region of the Gaussian multiple-input multiple-output broadcast channel, IEEE Transactions on Information Theory, vol.52, no.9, pp.3936-3964,2006;
[27]M. Sharif and B. Hassibi, On the Capacity of MIMO Broadcast Channels With Partial Side Information, IEEE Transactions on Information Theory, vol.51, no.2, pp.506-522,2005;
[28]E. Bjornson, R. Zakhour, D. Gesbert, B. Ottersten, Cooperative Multicell Precoding:Rate Region Characterization and Distributed Strategies with Instantaneous and Statistical CSI, IEEE Transactions on Signal Processing, vol. 58, no.8, pp.4298-4310,2010;
[29]T. Lo, Maximum ratio transmission, IEEE Transactions on Communications, vol.47, no.10 1999 pp.1458-1461,;
[30]a b N. Jindal, MIMO Broadcast Channels with Finite Rate Feedback, IEEE Transactions on Information Theory, vol.52, no.11, pp.5045-5059,2006;
[31]D.J. Love, R.W. Heath, and T. Strohmer, Grassmannian Beamforming for Multiple-Input Multiple-Output Wireless Systems, IEEE Transactions on Information Theory, vol.49, no.10, pp.2735-2747,2003;
[32]P. Viswanath, D. N. C. Tse, Member, and R. Laroia, Opportunistic Beamforming Using Dumb Antennas, IEEE Transactions on Information Theory, vol.48, no.6, pp.1277-1294,2002;
[33]D. Hammarwall, M. Bengtsson, and B. Ottersten, Utilizing the spatial information provided by channel norm feedback in SDMA systems, IEEE Transactions on Signal Processing, vol.56, no.7, pp.3278-3293,2008;
[34]E. Bjomson, D. Hammarwall, B. Ottersten, Exploiting Quantized Channel Norm Feedback through Conditional Statistics in Arbitrarily Correlated MIMO Systems, IEEE Transactions on Signal Processing, vol.57, no.10, pp.4027-4041, 2009;
[35]M. Costa, Writing on dirty paper, IEEE Transactions on Information Theory, vol.29, no.3, pp.439-441,1983;
[36]M. Tomlinson, New automatic equalizer employing modulo arithmetic, Electronics Letters, vol.7, no.5, pp.138-139,1971;
[37]H. Harashima and H. Miyakawa, Matched-transmission technique for channels with intersymbol interference, IEEE Transactions on Communications, vol.20, no.4, pp.774-780,1972;
[38]B. M. Hochwald, C. B. Peel, and A. L. Swindlehurst, A vector-perturbation technique for near-capacity multiantenna multi-user communication-Part II: Perturbation, IEEE Transactions on Communications, vol.53 no.l 2005 pp.537-544;