无线通信MIMO中的频率同步技术研究
|
摘要
作为能有效提高无线通信频谱利用率和系统容量的重要技术手段，多入多出(MIMO)技术特别是采用分布式天线的分布式MIMO技术，近年来得到了人们的广泛关注。正交频分复用(OFDM)技术能够有效的对抗无线信道的频率选择性衰落，成为无线通信领域的另一个研究热点。因此，MIMO技术与OFDM技术的结合将是新一代无线通信发展的趋势和潮流。
与单天线系统中类似，由于振荡器的不稳定性以及发射机与接收机之间的相对运动，MIMO系统中不可避免的会存在载波频偏(CFO)，而频偏的存在会严重降低系统的信号检测性能。特别是在MIMO-OFDM系统中，频偏的存在会使子载波间的正交性遭到破坏，产生载波间干扰(ICI)，因而其性能对频偏非常敏感。由此可见，在检测之前对频偏进行准确的估计和有效的补偿是非常重要的，这便是频率同步所要完成的任务。由于分布式MIMO系统中可能存在多个频偏，使得其频偏估计和补偿问题变得更为复杂。
本文研究MIMO中的频率同步问题，具体研究内容包括空间相关MIMO信道下的最大似然(ML)频偏估计、分布式MIMO中的频偏估计以及分布式空间复用MIMO-OFDM中的频偏补偿三个方面。
首先，在考虑MIMO信道各收发支路之间的空间相关性的情况下，提出了一种基于平均似然函数的数据辅助(DA)最大似然频偏估计器，它能够利用MIMO信道提供的空间分集以及信道空间相关性这一统计信息。同时推导了空间相关MIMO信道下的频偏估计问题的克拉美-罗界(CRB)。
接下来，考虑各发射天线与接收机之间的时延和频偏均可能不同这一普遍情况，给出了分布式MIMO系统中频偏估计问题的一般系统模型。并通过适当选择训练序列，提出了一种基于最大似然的次优频偏估计器，它能对各个发射天线的频偏分别进行估计并能利用空间分集。
最后，研究了分布式空间复用MIMO-OFDM系统中的频偏补偿问题。首先在考虑大尺度衰落和多径瑞利衰落的条件下，推导出了使平均信干噪比(SINR)最大的最优初始频偏校正值；然后利用迫零(ZF)检测的固有特性，提出了一种适用于低时延扩展多径信道的无需矩阵求逆运算的频偏补偿方法，它能在迫零检测之后对每个空间复用子流分别进行频偏补偿；最后针对两者各自的不足，将其结合起来，提出了一种采用两次频偏校正的信号检测方法。
本文的研究内容丰富了现有的传统MIMO中的频率同步技术研究，并对分布式MIMO中的频率同步技术进行了探索性的研究，所得到的研究成果具有一定的理论价值和应用价值。
As an important approach to increasing the spectral efficiency and the system capacity of wireless communications, multiple input multiple output (MIMO), with emphasis on distributed MIMO deploying distributed antennas, has been attracting much research interest. Orthogonal frequency division multiplexing (OFDM) can effectively combat the multipath fading of wireless channels and has become another hot point in the area of wireless communications. Hence the combination of MIMO and OFDM is a promising technique for the new generation of wireless communications.
Like that of single antenna systems, the performance of MIMO systems may seriously degrade with the presence of the carrier frequency offset (CFO) that is unavoidably present due to the possible oscillator mismatch as well as the relative motion between the transmitter and the receiver. In particular, MIMO-OFDM systems are very sensitive to the CFO. Any CFO causes a loss in the orthogonality of the subcarriers which results in inter-carrier interference (ICI) and hence performance degradation. Therefore, it is of primary importance to accurately estimate this frequency offset and compensate for it prior to performing detection. This is the task of frequency synchronization. Since there may exist multiple CFOs in distributed MIMO systems, the CFO estimation and compensation become more difficult for this case.
This thesis focuses on the problem of frequency synchronization for MIMO systems. More specificly, it consists of the following three aspects: maximum likelihood (ML) CFO estimation in spatially correlated MIMO channels, CFO estimation for distributed MIMO, and CFO compensation for distributed spatial multiplexing MIMO-OFDM.
Firstly, taking the spatial correlation among channels corresponding to different pairs of transmit and receive antennas into account, a data aided (DA) ML CFO estimator based on the marginal likelihood function is proposed. It can exploit spatial diversity and make use of the knowledge of spatial correlation. The Cramer-Rao bound (CRB) for the problem is also derived as a benchmark.
Secondly, considering the general case where both the time delays and the CFOs are possibly different between the receiver and each transmit antenna, a general model for CFO estimation in distributed MIMO systems is presented. Then a suboptimal CFO estimator based on ML is proposed by making a suitable choice of the training sequences, which can estimate the CFO for each transmit antenna respectively and can exploit spatial diversity.
Finally, the proplem of CFO compensation in distributed spatial multiplexing MIMO-OFDM systems is addressed. Firstly, considering macroscopic fading and multipath Rayleigh fading, the optimal initial CFO correction value is derived by maximizing the average signal to interference and noise ratio (SINR). Secondly, by exploiting the underlying characteristics of the zero forcing (ZF) detection and assuming low delay spread of the multipath channel, a CFO compensation method without need for computationally complex matrix inversions is proposed, which can compensate for the CFO for each spatially multiplexed substream respectively. Finally, a detection method involving two CFO correction processes is presented by combining the initial CFO correction method and the CFO compensation method presented above.
The research in this thesis extends the existing researches on frequency synchronization for traditional MIMO systems, and explores the problem of frequency synchronization in distributed MIMO systems. The results have some theoretical and practical values.
与单天线系统中类似，由于振荡器的不稳定性以及发射机与接收机之间的相对运动，MIMO系统中不可避免的会存在载波频偏(CFO)，而频偏的存在会严重降低系统的信号检测性能。特别是在MIMO-OFDM系统中，频偏的存在会使子载波间的正交性遭到破坏，产生载波间干扰(ICI)，因而其性能对频偏非常敏感。由此可见，在检测之前对频偏进行准确的估计和有效的补偿是非常重要的，这便是频率同步所要完成的任务。由于分布式MIMO系统中可能存在多个频偏，使得其频偏估计和补偿问题变得更为复杂。
本文研究MIMO中的频率同步问题，具体研究内容包括空间相关MIMO信道下的最大似然(ML)频偏估计、分布式MIMO中的频偏估计以及分布式空间复用MIMO-OFDM中的频偏补偿三个方面。
首先，在考虑MIMO信道各收发支路之间的空间相关性的情况下，提出了一种基于平均似然函数的数据辅助(DA)最大似然频偏估计器，它能够利用MIMO信道提供的空间分集以及信道空间相关性这一统计信息。同时推导了空间相关MIMO信道下的频偏估计问题的克拉美-罗界(CRB)。
接下来，考虑各发射天线与接收机之间的时延和频偏均可能不同这一普遍情况，给出了分布式MIMO系统中频偏估计问题的一般系统模型。并通过适当选择训练序列，提出了一种基于最大似然的次优频偏估计器，它能对各个发射天线的频偏分别进行估计并能利用空间分集。
最后，研究了分布式空间复用MIMO-OFDM系统中的频偏补偿问题。首先在考虑大尺度衰落和多径瑞利衰落的条件下，推导出了使平均信干噪比(SINR)最大的最优初始频偏校正值；然后利用迫零(ZF)检测的固有特性，提出了一种适用于低时延扩展多径信道的无需矩阵求逆运算的频偏补偿方法，它能在迫零检测之后对每个空间复用子流分别进行频偏补偿；最后针对两者各自的不足，将其结合起来，提出了一种采用两次频偏校正的信号检测方法。
本文的研究内容丰富了现有的传统MIMO中的频率同步技术研究，并对分布式MIMO中的频率同步技术进行了探索性的研究，所得到的研究成果具有一定的理论价值和应用价值。
As an important approach to increasing the spectral efficiency and the system capacity of wireless communications, multiple input multiple output (MIMO), with emphasis on distributed MIMO deploying distributed antennas, has been attracting much research interest. Orthogonal frequency division multiplexing (OFDM) can effectively combat the multipath fading of wireless channels and has become another hot point in the area of wireless communications. Hence the combination of MIMO and OFDM is a promising technique for the new generation of wireless communications.
Like that of single antenna systems, the performance of MIMO systems may seriously degrade with the presence of the carrier frequency offset (CFO) that is unavoidably present due to the possible oscillator mismatch as well as the relative motion between the transmitter and the receiver. In particular, MIMO-OFDM systems are very sensitive to the CFO. Any CFO causes a loss in the orthogonality of the subcarriers which results in inter-carrier interference (ICI) and hence performance degradation. Therefore, it is of primary importance to accurately estimate this frequency offset and compensate for it prior to performing detection. This is the task of frequency synchronization. Since there may exist multiple CFOs in distributed MIMO systems, the CFO estimation and compensation become more difficult for this case.
This thesis focuses on the problem of frequency synchronization for MIMO systems. More specificly, it consists of the following three aspects: maximum likelihood (ML) CFO estimation in spatially correlated MIMO channels, CFO estimation for distributed MIMO, and CFO compensation for distributed spatial multiplexing MIMO-OFDM.
Firstly, taking the spatial correlation among channels corresponding to different pairs of transmit and receive antennas into account, a data aided (DA) ML CFO estimator based on the marginal likelihood function is proposed. It can exploit spatial diversity and make use of the knowledge of spatial correlation. The Cramer-Rao bound (CRB) for the problem is also derived as a benchmark.
Secondly, considering the general case where both the time delays and the CFOs are possibly different between the receiver and each transmit antenna, a general model for CFO estimation in distributed MIMO systems is presented. Then a suboptimal CFO estimator based on ML is proposed by making a suitable choice of the training sequences, which can estimate the CFO for each transmit antenna respectively and can exploit spatial diversity.
Finally, the proplem of CFO compensation in distributed spatial multiplexing MIMO-OFDM systems is addressed. Firstly, considering macroscopic fading and multipath Rayleigh fading, the optimal initial CFO correction value is derived by maximizing the average signal to interference and noise ratio (SINR). Secondly, by exploiting the underlying characteristics of the zero forcing (ZF) detection and assuming low delay spread of the multipath channel, a CFO compensation method without need for computationally complex matrix inversions is proposed, which can compensate for the CFO for each spatially multiplexed substream respectively. Finally, a detection method involving two CFO correction processes is presented by combining the initial CFO correction method and the CFO compensation method presented above.
The research in this thesis extends the existing researches on frequency synchronization for traditional MIMO systems, and explores the problem of frequency synchronization in distributed MIMO systems. The results have some theoretical and practical values.
引文
[1]W.W.Lu.4G mobile research in Asia.IEEE Commun.Mag.,2003,41(3):104-106.
[2]曹淑敏．第三代移动通信的发展现状与趋势．当代通信，2004，(10)：31-33．
[3]尤肖虎．未来移动通信技术发展趋势与展望．电信技术，2003，(6)：14-17．
[4]T.S.Rappaport.Wireless Communications:Principles and Practice,2nd ed.New York: Addison Wesley/Pearson,2004.
[5]王京，姚彦，赵明，等．分布式无线通信系统的概念平台．电子学报，2002，30(7)：937-940．
[6]M.Rahnema.Overview of the GSM system and protocol architecture.IEEE Commun.Mag., 1993,31(4):92-100.
[7]E.Dahlman,B.Gudmundson,M.Nilsson,et al.UMTS/IMT-2000 based on wideband CDMA.IEEE Commun.Mag.,1998,36(9):70-80.
[8]A.Bria,F.Gessler,O.Queseth,et al.4th-generation wireless infrastructures:scenarios and research challenges.IEEE Personal Commun.,2001,8(6):25-31.
[9]尤肖虎，曹淑敏，傅学群．我国未来移动通信研究开发展望，电信科学，2002，(8)：26-29．
[10]D.Gesbert,M.Shafi,S.Da-shan,et al.From theory to practice:An overview of MIMO space-time coded wireless systems.IEEE J.Select.Areas Commun.,2003,21(3):281-302.
[11]A.Naguib,N.Seshadri,A.Calderbank.Increasing data rate over wireless channels.IEEE Signal Processing Mag.,2000,17(3):76-92.
[12]G.J.Foschini,M.J.Gans.On limits of wireless communications in a fading environment when using multiple antennas.Wireless Personal Commun.,1998,6(3):311-335.
[13]A.Paulraj,R.Nabar,D.Gore.Introduction to Space-Time Wireless Communications.Cambridge,U.K.:Cambridge Univ.Press,2003.
[14]A.Saleh,A.Rustako,R.Roman.Distributed antennas for indoor radio communications.IEEE Trans.Commun.,1987,35(12):1245-1251.
[15]K.J.Kerpez.A radio access system with distributed antennas.IEEE Trans.Veh.Technol., 1996,45(2):265-275.
[16]M.V.Clark,T.M.Willis Ⅲ,L.J.Greenstein,et al.Distributed versus centralized antenna arrays in broadband wireless networks.IEEE VTC-Spring,Rhodes,Greece,2001,33-37.
[33]S.M.Alamouti.A simple transmitter diversity scheme for wireless communications.IEEE J.Select.Areas Commun.,1998,16(8):1451-1458.
[34]G.J.Foschini.Layered space-time architecture for wireless communication in a fading environment when using multielement antennas.Bell Lab.Tech.J.,1996,1(2):41-59.
[35]G.D.Golden,G.J.Foschini,R.A.Valenzuela,et al.Detection algorithm and initial laboratory results using the V-BLAST space-time communication architecture.Electron.Lett.,1999,35(1):14-16.
[36]A.J.Grant.Performance analysis of transmit beamforming.IEEE Trans.Commun.,2005, 53(4):738-744.
[37]H.Sampath,P.Stoica,A.Paulraj.Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion.IEEE Trans.Commun.,2001,49(12): 2198-2206.
[38]M.Z.Win,J.H.Winters.Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading.IEEE Trans.Commun.,2001,49(11): 1926-1934.
[39]G.L.St(?)ber.Principles of Mobile Communications.New York:Kluwer,2002.
[40]D.Chizhik,F.Rashid-Farrokhi,J.Ling,et al.Effect of antenna separation on the capacity of BLAST in correlated channels.IEEE Commun.Lett.,2000,4(11):337-339.
[41]O.Damen,A.Chkeif,J.C.Belfiore.Lattice code decoder for fading channels.IEEE Commun.Lett.,2000,4(5):161-163.
[42]M.Pohst.On the computation of lattice vectors of minimal length,successive minima and reduced basis with applications.ACM SIGSAM,1981,15:37-44.
[43]U.Fincke,M.Pohst.Improved methods for calculating vectors of short length in a lattice, including a complexity analysis.Math.Computation,1985,44(4):463-471.
[44]E.Viterbo,J.Bouros.A universal lattice code decoder for fading channels.IEEE Trans.Inform.Theory,1999,45(5):1693-1642.
[45]D．G.Luenberger．最优化的矢量空间方法(蒋正新，郑梅春，译)．北京：国防工业出版社， 1987．
[46]J.Yang,S.Roy.On joint transmitter and receiver optimization for multiple-input multiple-output(MIMO)transmission systems.IEEE Trans.Commun.,1994,42(12): 3221-3231.
[47]X.Tao,L.Ni,Z.Dai,et al.Intelligent group handover mode in multicell infrastructure.IEEE PIMRC,Beijing,China,2003,351-354.
[48] Y. G. Li, J. H. Winters, N. R. Sollenberger. MIMO-OFDM for wireless communications: signal detection with enhanced channel estimation. IEEE Trans. Commun., 2002, 50(9): 1471-1477.
[49] M. Shin, H. Lee, C. Lee. Enhanced channel-estimation technique for MIMO-OFDM systems. IEEE Trans. Veh. Technol, 2004, 53(1): 261-265.
[50] P. Tarasak, M. Hlaing, V. K. Bhargava. Improved approximate maximum-likelihood receiver for differential space-time block codes over Rayleigh-fading channels. IEEE Trans. Veh. Technol., 2004, 53(2): 461-468.
[51] C.-S. Hwang, S. H. Nam, J. Chung, et al. Differential space time block codes using nonconstant modulus constellations. IEEE Trans. Signal Processing, 2003, 51(11): 2955-2964.
[52] B. Hassibi, B. M. Hochwald. Cayley differential unitary space-time codes. IEEE Trans. Inform. Theory, 2002,48(6): 1485-1503.
[53] B. L. Hughes. Differential space-time modulation. IEEE Trans. Inform. Theory, 2000, 46(7): 2567-2578.
[54] D. Guo, X. Wang. Blind detection in MIMO systems via sequential Monte Carlo. IEEE J. Select. Areas Commun., 2003, 21(3): 464-473.
[55] J. G. Proakis. Digital Communications, 4th ed. New York: McGraw-Hill, 2001.
[56] F. Simoens, M. Moeneclaey. Reduced complexity data-aided and code-aided frequency offset estimation for flat-fading MIMO channels. IEEE Trans. Wireless Commun., 2006, 5(6): 1558-1567.
[57] S. Kay. A fast and accurate single frequency estimator. IEEE Trans. Acoust, Speech, Signal Processing, 1989,37(12): 1987-1990.
[58] D. C. Rife, R. R. Boorstyn. Single-tone parameter estimation from discrete-time observations. IEEE Trans. Inform Theory, 1974, 20(5): 591-598.
[59] M. Luise, R. Reggiannini. Carrier frequency recovery in all-digital modems for burst-mode transmissions. IEEE Trans. Commun., 1995, 43(2/3/4): 1169-1178.
[60] W. Y. Kuo, M. P. Fitz. Frequency offset compensation of pilot symbol assisted modulation in frequency flat fading. IEEE Trans. Commun., 1997, 45(11): 1412-1416.
[61] M. Morelli, U. Mengali. Carrier-frequency estimation for transmissions over selective channels. IEEE Trans. Commun., 2000,48(9): 1580-1589.
[62] Z. Liu, G. Giannakis, B. Hughes. Double-differential space-time block coding for time-selective fading channels. IEEE Trans. Commun., 2001,49(9): 1529-1539.
[63] H. L. Van Trees. Detection, Estimation, and Modulation: Part Ⅰ. New York: Wiley, 1968.
[94] M. Sandell, D. McNamara, S. Parker. Analysis of frequency-offset tracking in MIMO OFDM systems. IEEE Trans. Commun., 2006, 54(8): 1481-1489.
[95] T.-H. Pham, A. Nallanathan, Y.-C. Liang. Joint channel and frequency offset estimation in distributed MIMO flat-fading channels. IEEE Trans. Wireless Commun., 2008, 7(2): 648-656.
[96] O. Besson, P. Stoica. On parameter estimation of MIMO flat-fading channels with frequency offsets. IEEE Trans. Signal Processing, 2003, 51(3): 602-613.
[97] O. Besson, P. Stoica. Channel and frequency offsets estimation in MIMO time-selective channels. IEEE SAM, Washington D.C., 2002, 135-139.
[98] Y. Yao, T.-S. Ng. Correlation-based frequency offset estimation in MIMO system. IEEE VTC-Fall, Orlando, FL, 2003,438-442.
[99] S. Ahmed, S. Lambotharan, A. Jakobsson, et al. MIMO frequency-selective channels with multiple-frequency offsets: estimation and detection techniques. IEE Proc.-Commun., 2005, 152(4): 489-494.
[100] T. Pollet, M. V. Bladel, M. Moeneclaey. BER sensitivity of OFDM systems to carrier frequency offset and Weiner phase noise. IEEE Trans. Commun., 1995,43(2/3/4): 191-193.
[101] Z. Li, D. Qu, G. Zhu. An equalization technique for distributed STBC-OFDM system with multiple carrier frequency offsets. IEEE WCNC, Las Vegas, NV, 2006, 839-843.
[102] W. Zhang, D. Qu, G. Zhu. Performance investigation of distributed STBC-OFDM system with multiple carrier frequency offsets. IEEE PIMRC, Helsinki, Finland, 2006, 1-5.
[103] G. Barriac, U. Madhow. Space-time communication for OFDM with implicit channel feedback. IEEE Trans. Inform. Theory, 2004, 50(12): 3111-3129.
[104] J.-M. Chaufray, P. Loubaton, P. Chevalier. Consistent estimation of Rayleigh fading channel second-order statistics in the context of the wideband CDMA mode of the UMTS. IEEE Trans. Signal Processing, 2001,49(12): 3055-3064.
[105] Y. Liu, T. F. Wong, A. Pandharipande. Timing estimation in multiple-antenna systems over Rayleigh flat-fading channels. IEEE Trans. Signal Processing, 2005, 53(6): 2074-2088.
[106] R. J. Muirhead. Aspects of multivariate statistical theory. New York: Wiley, 1982.
[107] H. Cramer. Mathematical Methods of Statistics. Princeton, NJ: Princeton Univ. Press, 1946.
[108] M. K. Simon, M.-S. Alouini. Digital communication over fading channels: a unified approach to performance analysis. New York: Wiley, 2000.
[109] S. Shao, Y. Tang, T. Kong, et al. Performance analysis of a modified V-BLAST system with delay offsets using zero-forcing detection. IEEE Trans. Veh. Technol., 2007, 56(6): 3827-3837.
[110] D. Sun, Y. Tang, S. Shao. A differential modulation scheme for MIMO links with distributed transmit antennas. IEEE Commun. Lett., 2007, 11(11): 892-894.
[111] Y. Shen, Y. Tang, T. Kong, S. Shao. Optimal antenna location for STBC-OFDM downlink with distributed transmit antennas in linear cells. IEEE Commun. Lett., 2007, 11(5): 387-389.
[112] D. N. Dao, C. Tellambura. Intercarrier interference self-cancellation space-frequency codes for MIMO-OFDM. IEEE Trans. Veh. Technol., 2005, 54(5): 1729-1738.
[113] Y. H. Kim, I. Song, S. Yoon, et al. An efficient frequency offset estimator for OFDM systems and its performance characteristics. IEEE Trans. Veh. Technol., 2001, 50(5): 1307-1312.
[114] P. H. Moose. A technique for orthogonal frequency division multiplexing frequency offset correction. IEEE Trans. Commun., 1994,42(10): 2908-2914.
[115] ITU. ITU-R M.1225-1997. Guidelines for Evaluation of Radio Transmission Technologies for IMT-2000. 1997.
[2]曹淑敏．第三代移动通信的发展现状与趋势．当代通信，2004，(10)：31-33．
[3]尤肖虎．未来移动通信技术发展趋势与展望．电信技术，2003，(6)：14-17．
[4]T.S.Rappaport.Wireless Communications:Principles and Practice,2nd ed.New York: Addison Wesley/Pearson,2004.
[5]王京，姚彦，赵明，等．分布式无线通信系统的概念平台．电子学报，2002，30(7)：937-940．
[6]M.Rahnema.Overview of the GSM system and protocol architecture.IEEE Commun.Mag., 1993,31(4):92-100.
[7]E.Dahlman,B.Gudmundson,M.Nilsson,et al.UMTS/IMT-2000 based on wideband CDMA.IEEE Commun.Mag.,1998,36(9):70-80.
[8]A.Bria,F.Gessler,O.Queseth,et al.4th-generation wireless infrastructures:scenarios and research challenges.IEEE Personal Commun.,2001,8(6):25-31.
[9]尤肖虎，曹淑敏，傅学群．我国未来移动通信研究开发展望，电信科学，2002，(8)：26-29．
[10]D.Gesbert,M.Shafi,S.Da-shan,et al.From theory to practice:An overview of MIMO space-time coded wireless systems.IEEE J.Select.Areas Commun.,2003,21(3):281-302.
[11]A.Naguib,N.Seshadri,A.Calderbank.Increasing data rate over wireless channels.IEEE Signal Processing Mag.,2000,17(3):76-92.
[12]G.J.Foschini,M.J.Gans.On limits of wireless communications in a fading environment when using multiple antennas.Wireless Personal Commun.,1998,6(3):311-335.
[13]A.Paulraj,R.Nabar,D.Gore.Introduction to Space-Time Wireless Communications.Cambridge,U.K.:Cambridge Univ.Press,2003.
[14]A.Saleh,A.Rustako,R.Roman.Distributed antennas for indoor radio communications.IEEE Trans.Commun.,1987,35(12):1245-1251.
[15]K.J.Kerpez.A radio access system with distributed antennas.IEEE Trans.Veh.Technol., 1996,45(2):265-275.
[16]M.V.Clark,T.M.Willis Ⅲ,L.J.Greenstein,et al.Distributed versus centralized antenna arrays in broadband wireless networks.IEEE VTC-Spring,Rhodes,Greece,2001,33-37.
[33]S.M.Alamouti.A simple transmitter diversity scheme for wireless communications.IEEE J.Select.Areas Commun.,1998,16(8):1451-1458.
[34]G.J.Foschini.Layered space-time architecture for wireless communication in a fading environment when using multielement antennas.Bell Lab.Tech.J.,1996,1(2):41-59.
[35]G.D.Golden,G.J.Foschini,R.A.Valenzuela,et al.Detection algorithm and initial laboratory results using the V-BLAST space-time communication architecture.Electron.Lett.,1999,35(1):14-16.
[36]A.J.Grant.Performance analysis of transmit beamforming.IEEE Trans.Commun.,2005, 53(4):738-744.
[37]H.Sampath,P.Stoica,A.Paulraj.Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion.IEEE Trans.Commun.,2001,49(12): 2198-2206.
[38]M.Z.Win,J.H.Winters.Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading.IEEE Trans.Commun.,2001,49(11): 1926-1934.
[39]G.L.St(?)ber.Principles of Mobile Communications.New York:Kluwer,2002.
[40]D.Chizhik,F.Rashid-Farrokhi,J.Ling,et al.Effect of antenna separation on the capacity of BLAST in correlated channels.IEEE Commun.Lett.,2000,4(11):337-339.
[41]O.Damen,A.Chkeif,J.C.Belfiore.Lattice code decoder for fading channels.IEEE Commun.Lett.,2000,4(5):161-163.
[42]M.Pohst.On the computation of lattice vectors of minimal length,successive minima and reduced basis with applications.ACM SIGSAM,1981,15:37-44.
[43]U.Fincke,M.Pohst.Improved methods for calculating vectors of short length in a lattice, including a complexity analysis.Math.Computation,1985,44(4):463-471.
[44]E.Viterbo,J.Bouros.A universal lattice code decoder for fading channels.IEEE Trans.Inform.Theory,1999,45(5):1693-1642.
[45]D．G.Luenberger．最优化的矢量空间方法(蒋正新，郑梅春，译)．北京：国防工业出版社， 1987．
[46]J.Yang,S.Roy.On joint transmitter and receiver optimization for multiple-input multiple-output(MIMO)transmission systems.IEEE Trans.Commun.,1994,42(12): 3221-3231.
[47]X.Tao,L.Ni,Z.Dai,et al.Intelligent group handover mode in multicell infrastructure.IEEE PIMRC,Beijing,China,2003,351-354.
[48] Y. G. Li, J. H. Winters, N. R. Sollenberger. MIMO-OFDM for wireless communications: signal detection with enhanced channel estimation. IEEE Trans. Commun., 2002, 50(9): 1471-1477.
[49] M. Shin, H. Lee, C. Lee. Enhanced channel-estimation technique for MIMO-OFDM systems. IEEE Trans. Veh. Technol, 2004, 53(1): 261-265.
[50] P. Tarasak, M. Hlaing, V. K. Bhargava. Improved approximate maximum-likelihood receiver for differential space-time block codes over Rayleigh-fading channels. IEEE Trans. Veh. Technol., 2004, 53(2): 461-468.
[51] C.-S. Hwang, S. H. Nam, J. Chung, et al. Differential space time block codes using nonconstant modulus constellations. IEEE Trans. Signal Processing, 2003, 51(11): 2955-2964.
[52] B. Hassibi, B. M. Hochwald. Cayley differential unitary space-time codes. IEEE Trans. Inform. Theory, 2002,48(6): 1485-1503.
[53] B. L. Hughes. Differential space-time modulation. IEEE Trans. Inform. Theory, 2000, 46(7): 2567-2578.
[54] D. Guo, X. Wang. Blind detection in MIMO systems via sequential Monte Carlo. IEEE J. Select. Areas Commun., 2003, 21(3): 464-473.
[55] J. G. Proakis. Digital Communications, 4th ed. New York: McGraw-Hill, 2001.
[56] F. Simoens, M. Moeneclaey. Reduced complexity data-aided and code-aided frequency offset estimation for flat-fading MIMO channels. IEEE Trans. Wireless Commun., 2006, 5(6): 1558-1567.
[57] S. Kay. A fast and accurate single frequency estimator. IEEE Trans. Acoust, Speech, Signal Processing, 1989,37(12): 1987-1990.
[58] D. C. Rife, R. R. Boorstyn. Single-tone parameter estimation from discrete-time observations. IEEE Trans. Inform Theory, 1974, 20(5): 591-598.
[59] M. Luise, R. Reggiannini. Carrier frequency recovery in all-digital modems for burst-mode transmissions. IEEE Trans. Commun., 1995, 43(2/3/4): 1169-1178.
[60] W. Y. Kuo, M. P. Fitz. Frequency offset compensation of pilot symbol assisted modulation in frequency flat fading. IEEE Trans. Commun., 1997, 45(11): 1412-1416.
[61] M. Morelli, U. Mengali. Carrier-frequency estimation for transmissions over selective channels. IEEE Trans. Commun., 2000,48(9): 1580-1589.
[62] Z. Liu, G. Giannakis, B. Hughes. Double-differential space-time block coding for time-selective fading channels. IEEE Trans. Commun., 2001,49(9): 1529-1539.
[63] H. L. Van Trees. Detection, Estimation, and Modulation: Part Ⅰ. New York: Wiley, 1968.
[94] M. Sandell, D. McNamara, S. Parker. Analysis of frequency-offset tracking in MIMO OFDM systems. IEEE Trans. Commun., 2006, 54(8): 1481-1489.
[95] T.-H. Pham, A. Nallanathan, Y.-C. Liang. Joint channel and frequency offset estimation in distributed MIMO flat-fading channels. IEEE Trans. Wireless Commun., 2008, 7(2): 648-656.
[96] O. Besson, P. Stoica. On parameter estimation of MIMO flat-fading channels with frequency offsets. IEEE Trans. Signal Processing, 2003, 51(3): 602-613.
[97] O. Besson, P. Stoica. Channel and frequency offsets estimation in MIMO time-selective channels. IEEE SAM, Washington D.C., 2002, 135-139.
[98] Y. Yao, T.-S. Ng. Correlation-based frequency offset estimation in MIMO system. IEEE VTC-Fall, Orlando, FL, 2003,438-442.
[99] S. Ahmed, S. Lambotharan, A. Jakobsson, et al. MIMO frequency-selective channels with multiple-frequency offsets: estimation and detection techniques. IEE Proc.-Commun., 2005, 152(4): 489-494.
[100] T. Pollet, M. V. Bladel, M. Moeneclaey. BER sensitivity of OFDM systems to carrier frequency offset and Weiner phase noise. IEEE Trans. Commun., 1995,43(2/3/4): 191-193.
[101] Z. Li, D. Qu, G. Zhu. An equalization technique for distributed STBC-OFDM system with multiple carrier frequency offsets. IEEE WCNC, Las Vegas, NV, 2006, 839-843.
[102] W. Zhang, D. Qu, G. Zhu. Performance investigation of distributed STBC-OFDM system with multiple carrier frequency offsets. IEEE PIMRC, Helsinki, Finland, 2006, 1-5.
[103] G. Barriac, U. Madhow. Space-time communication for OFDM with implicit channel feedback. IEEE Trans. Inform. Theory, 2004, 50(12): 3111-3129.
[104] J.-M. Chaufray, P. Loubaton, P. Chevalier. Consistent estimation of Rayleigh fading channel second-order statistics in the context of the wideband CDMA mode of the UMTS. IEEE Trans. Signal Processing, 2001,49(12): 3055-3064.
[105] Y. Liu, T. F. Wong, A. Pandharipande. Timing estimation in multiple-antenna systems over Rayleigh flat-fading channels. IEEE Trans. Signal Processing, 2005, 53(6): 2074-2088.
[106] R. J. Muirhead. Aspects of multivariate statistical theory. New York: Wiley, 1982.
[107] H. Cramer. Mathematical Methods of Statistics. Princeton, NJ: Princeton Univ. Press, 1946.
[108] M. K. Simon, M.-S. Alouini. Digital communication over fading channels: a unified approach to performance analysis. New York: Wiley, 2000.
[109] S. Shao, Y. Tang, T. Kong, et al. Performance analysis of a modified V-BLAST system with delay offsets using zero-forcing detection. IEEE Trans. Veh. Technol., 2007, 56(6): 3827-3837.
[110] D. Sun, Y. Tang, S. Shao. A differential modulation scheme for MIMO links with distributed transmit antennas. IEEE Commun. Lett., 2007, 11(11): 892-894.
[111] Y. Shen, Y. Tang, T. Kong, S. Shao. Optimal antenna location for STBC-OFDM downlink with distributed transmit antennas in linear cells. IEEE Commun. Lett., 2007, 11(5): 387-389.
[112] D. N. Dao, C. Tellambura. Intercarrier interference self-cancellation space-frequency codes for MIMO-OFDM. IEEE Trans. Veh. Technol., 2005, 54(5): 1729-1738.
[113] Y. H. Kim, I. Song, S. Yoon, et al. An efficient frequency offset estimator for OFDM systems and its performance characteristics. IEEE Trans. Veh. Technol., 2001, 50(5): 1307-1312.
[114] P. H. Moose. A technique for orthogonal frequency division multiplexing frequency offset correction. IEEE Trans. Commun., 1994,42(10): 2908-2914.
[115] ITU. ITU-R M.1225-1997. Guidelines for Evaluation of Radio Transmission Technologies for IMT-2000. 1997.