基于信道统计信息的MIMO系统发射端最优设计
|
摘要
现代无线通信面临着频谱资源有限,传输环境复杂等诸多困难。随着对更高的数据传输率、更好的服务质量、更大的网络容量和覆盖等需求的增大,许多能够提高频谱效率和传输可靠性的新技术和新方案应运而生。在无线通信系统的发射机和接收机处使用多元天线阵,即无线MIMO技术,就是其中之一。MIMO系统用于分集传输,能更有效的克服各种信道衰落和干扰,提高信号的传输性能。随着对MIMO技术研究的深入,它所能提供的性能增益也越来越引人注目,并且被认为是实现未来高速宽带无线Internet接入网的关键技术之一,在第三代(3G)乃至三代以后(B3G)的移动通信系统中有着广阔的应用前景。目前,MIMO技术已被引入到诸如UMTS和CDMA 2000标准中。在固定无线接入和WLAN应用中,MIMO技术也被IEEE 802.16和802.11标准制订者作为一种重要实现方案进行研究。
MIMO系统用于空间多路复用,可以在不增加发射功率和占用带宽的条件下极大地提高数据传输速率。目前已经证明在发射端和接收端都已知信道信息的理想情况下,MIMO系统的容量与发射端和接收端最小天线数目成正比。但是当发射端不能获得信道的准确信息时,系统的容量性能会受很大的影响。在实际的传输系统中,由于信道的快速变化、传输时延或信道估计误差等多种因素的制约,在发射端不可能获得准确的信道信息,而信道的统计信息(如:均值、协方差信息)在一段时间内可以看作是不变的,因此对于快速变化的信道,不需要频繁的将信道信息反馈到发射端,只有当信道的统计信息发生变化时再反馈即可,并且已经证明利用发射端的信道统计信息可以提高MIMO系统的容量,本文主要讨论利用反馈到发射端的信道统计信息对发射端进行最优化设计,主要研究成果如下:
分别采用遍历容量、中断概率和误码率作为性能指标来分析发射端获得信道的统计信息时,发射信号的最优化设计问题。首先以遍历容量作为性能准则,在分别介绍了发射端获得信道均值信息或者协方差信息时,最优发射信号形式的基础上,着重介绍了当信道的均值和协方差信息同时反馈到发射端时,系统的最优信号发射形式,推导了信号的最优发射方向,并且给出了功率优化分配的算法。接着以最小化系统的中断概率为性能指标,针对发射端和接收端都存在空间相关性的MIMO系统,讨论了协方差反馈时发射信号的最优发射形式。最后以误码率为性能准则,讨论协方差反馈时系统的最优预编码矩阵设计,推导了一个误码率的上界,给出了最优预编码矩阵的特征向量方向以及功率分配方案,最后通过仿真分析了各种信道因素对系统性能的影响。
提出了一种适用于非正交空时分组码的预编码设计方案。空时编码技术将多天线技术和编码技术相结合,可以在不牺牲带宽的条件下起到发射分集和功率增益的作用,是MIMO系统中一项十分重要的信号处理技术,将空时编码技术和预编码技术相结合是MIMO系统研究的一个重要领域。本文在正交空时分组码的基础上进行推广,提出了一种适用于其他非正交结构空时分组码的预编码设计方案,推导出最优预编码矩阵的特征向量与发射相关矩阵的特征向量和空时分组码的结构有关,并且给出了最优预编码矩阵功率分配的公式。
分析了接收端的信道估计误差对于系统性能的影响。针对SISO系统,文章以中断容量为性能准则,讨论了Nakagami-m和Rice信道中由于信道估计误差的存在导致系统中断容量的不确定,推导了中断容量的上界和下界。对于MIMO系统,分析了信道估计误差对于系统信道容量的影响,给出了信道容量的边界,着重分析了在接收端存在信道估计误差,发射端具有不同的信道状态信息时,系统发射信号的最优传输策略,并且通过仿真分析了信道估计误差对于MIMO系统性能的影响,同时比较了发射端具有不同的信道信息时,系统的信道容量性能。
文章最后对本文的内容进行了总结,展望未来的研究方向。
Modern wireless communications must cope with critical performance limiting challenges that include limited availability of radio frequency spectrum and a complex time-varying wireless environment (fading and multipath). Meeting the increasing demand for higher data rates, better quality of service, higher network capacity and user coverage calls for innovative techniques that improve spectral efficiency and link reliability. The use of multiple antennas at receiver and transmitter in a wireless system, popularly known as MIMO wireless is an emerging cost-effective technology that promises significant improvement in these measures. It is believed that the wireless MIMO technology will be one of the key ones that realize the high-speed broadband wireless Internet access networks in the future and has wide application prospect in the third generation (3G) or beyond third generation (B3G) mobile communications. A growing acknowledgment of the performance gains from MIMO technology has spurred the insertion of this technology into wireless standards, notably the mobile standards such as UMTS and CDMA 2000. MIMO techniques are also under study in IEEE 802.16 and 802.11 standards for fixed and WLAN applications respectively.
MIMO technology can increase data rate without increasing transmission power and bandwidth. It has been proved that the capacity of MIMO system increases as the minimum number of transmit and receive antennas when the channel state information (CSI) is perfectly known at transmitter and receiver. The capacity will degrade greatly when the CSI is not known at transmitter. But in real transmission environment, the perfect CSI can not be obtained at transmitter because of fast change of fading channel, transmission delay and channel estimation error. The channel statistical information can be taken as stationary in a long time. The channel statistical information need to be fed back to the transmitter only when it is changed. It has been proved that the channel statistical information is beneficial to capacity. The optimal design of transmitter with channel statistical information is analyzed in this paper. The main contribution of this paper is listed as follows.
Shannon capacity, outage probability and system error probability are taken as performance criterion separately to study the optimal transmitter design when the channel statistical information is fed back to transmitter. When Shannon capacity is taken as the performance criterion, the optimal transmitter design with channel mean information or channel covariance information is introduced firstly. Then the optimal design is studied in detail when both of these two statistical information can be obtained simultaneously. The optimal transmission direction is derived and the optimal power allocation algorithm is given. When outage probability is taken as the performance criterion, the optimal transmitter design of MIMO system with spatial correlation at both transmitter and receiver is discussed. Finally, an upper bound of SEP is derived and the optimal precoder design is analyzed when the system error probability is taken as the performance criterion.
A new precoder structure which suits to non-orthogonal STBC with covariance feedback to the transmitter is presented. STBC is often designed for i.i.d. Rayleigh fading channels, assuming no CSI at transmitter. A linear precoder functions as a multi-mode beamformer matching the channel, based on the CSI at transmitter. The precoder and STBC combination, therefore, can exploit the available CSI and is robust to channel fading at the same time. Based on the OSTBC, a new precoder design method which suits to non-orthogonal STBC with covariance information at the transmitter is presented. The optimal eigen-vectors of this precoder are proved to be related to the transmit correlation matrix and STBC, and the optimal power allocation method is also given.
The effect of channel estimation error on the system performance is analyzed. For SISO system, the effects of channel estimation error on the outage capacity in Nakagami-m and Rice fading channels are discussed. The upper and lower bounds on outage capacity are derived. For MIMO system, the channel capacity is taken as the performance and the effect of channel estimation error is analyzed. The optimal transmission strategy is studied when there is channel estimation error at receiver and different channel state information can be obtained at transmitter. The effect of channel estimation error on the channel capacity is analyzed by simulation and the system performance with different transmission strategies is compared.
At the last part of this dissertation, the whole work of the dissertation is outlined and the future research issues are discussed.
MIMO系统用于空间多路复用,可以在不增加发射功率和占用带宽的条件下极大地提高数据传输速率。目前已经证明在发射端和接收端都已知信道信息的理想情况下,MIMO系统的容量与发射端和接收端最小天线数目成正比。但是当发射端不能获得信道的准确信息时,系统的容量性能会受很大的影响。在实际的传输系统中,由于信道的快速变化、传输时延或信道估计误差等多种因素的制约,在发射端不可能获得准确的信道信息,而信道的统计信息(如:均值、协方差信息)在一段时间内可以看作是不变的,因此对于快速变化的信道,不需要频繁的将信道信息反馈到发射端,只有当信道的统计信息发生变化时再反馈即可,并且已经证明利用发射端的信道统计信息可以提高MIMO系统的容量,本文主要讨论利用反馈到发射端的信道统计信息对发射端进行最优化设计,主要研究成果如下:
分别采用遍历容量、中断概率和误码率作为性能指标来分析发射端获得信道的统计信息时,发射信号的最优化设计问题。首先以遍历容量作为性能准则,在分别介绍了发射端获得信道均值信息或者协方差信息时,最优发射信号形式的基础上,着重介绍了当信道的均值和协方差信息同时反馈到发射端时,系统的最优信号发射形式,推导了信号的最优发射方向,并且给出了功率优化分配的算法。接着以最小化系统的中断概率为性能指标,针对发射端和接收端都存在空间相关性的MIMO系统,讨论了协方差反馈时发射信号的最优发射形式。最后以误码率为性能准则,讨论协方差反馈时系统的最优预编码矩阵设计,推导了一个误码率的上界,给出了最优预编码矩阵的特征向量方向以及功率分配方案,最后通过仿真分析了各种信道因素对系统性能的影响。
提出了一种适用于非正交空时分组码的预编码设计方案。空时编码技术将多天线技术和编码技术相结合,可以在不牺牲带宽的条件下起到发射分集和功率增益的作用,是MIMO系统中一项十分重要的信号处理技术,将空时编码技术和预编码技术相结合是MIMO系统研究的一个重要领域。本文在正交空时分组码的基础上进行推广,提出了一种适用于其他非正交结构空时分组码的预编码设计方案,推导出最优预编码矩阵的特征向量与发射相关矩阵的特征向量和空时分组码的结构有关,并且给出了最优预编码矩阵功率分配的公式。
分析了接收端的信道估计误差对于系统性能的影响。针对SISO系统,文章以中断容量为性能准则,讨论了Nakagami-m和Rice信道中由于信道估计误差的存在导致系统中断容量的不确定,推导了中断容量的上界和下界。对于MIMO系统,分析了信道估计误差对于系统信道容量的影响,给出了信道容量的边界,着重分析了在接收端存在信道估计误差,发射端具有不同的信道状态信息时,系统发射信号的最优传输策略,并且通过仿真分析了信道估计误差对于MIMO系统性能的影响,同时比较了发射端具有不同的信道信息时,系统的信道容量性能。
文章最后对本文的内容进行了总结,展望未来的研究方向。
Modern wireless communications must cope with critical performance limiting challenges that include limited availability of radio frequency spectrum and a complex time-varying wireless environment (fading and multipath). Meeting the increasing demand for higher data rates, better quality of service, higher network capacity and user coverage calls for innovative techniques that improve spectral efficiency and link reliability. The use of multiple antennas at receiver and transmitter in a wireless system, popularly known as MIMO wireless is an emerging cost-effective technology that promises significant improvement in these measures. It is believed that the wireless MIMO technology will be one of the key ones that realize the high-speed broadband wireless Internet access networks in the future and has wide application prospect in the third generation (3G) or beyond third generation (B3G) mobile communications. A growing acknowledgment of the performance gains from MIMO technology has spurred the insertion of this technology into wireless standards, notably the mobile standards such as UMTS and CDMA 2000. MIMO techniques are also under study in IEEE 802.16 and 802.11 standards for fixed and WLAN applications respectively.
MIMO technology can increase data rate without increasing transmission power and bandwidth. It has been proved that the capacity of MIMO system increases as the minimum number of transmit and receive antennas when the channel state information (CSI) is perfectly known at transmitter and receiver. The capacity will degrade greatly when the CSI is not known at transmitter. But in real transmission environment, the perfect CSI can not be obtained at transmitter because of fast change of fading channel, transmission delay and channel estimation error. The channel statistical information can be taken as stationary in a long time. The channel statistical information need to be fed back to the transmitter only when it is changed. It has been proved that the channel statistical information is beneficial to capacity. The optimal design of transmitter with channel statistical information is analyzed in this paper. The main contribution of this paper is listed as follows.
Shannon capacity, outage probability and system error probability are taken as performance criterion separately to study the optimal transmitter design when the channel statistical information is fed back to transmitter. When Shannon capacity is taken as the performance criterion, the optimal transmitter design with channel mean information or channel covariance information is introduced firstly. Then the optimal design is studied in detail when both of these two statistical information can be obtained simultaneously. The optimal transmission direction is derived and the optimal power allocation algorithm is given. When outage probability is taken as the performance criterion, the optimal transmitter design of MIMO system with spatial correlation at both transmitter and receiver is discussed. Finally, an upper bound of SEP is derived and the optimal precoder design is analyzed when the system error probability is taken as the performance criterion.
A new precoder structure which suits to non-orthogonal STBC with covariance feedback to the transmitter is presented. STBC is often designed for i.i.d. Rayleigh fading channels, assuming no CSI at transmitter. A linear precoder functions as a multi-mode beamformer matching the channel, based on the CSI at transmitter. The precoder and STBC combination, therefore, can exploit the available CSI and is robust to channel fading at the same time. Based on the OSTBC, a new precoder design method which suits to non-orthogonal STBC with covariance information at the transmitter is presented. The optimal eigen-vectors of this precoder are proved to be related to the transmit correlation matrix and STBC, and the optimal power allocation method is also given.
The effect of channel estimation error on the system performance is analyzed. For SISO system, the effects of channel estimation error on the outage capacity in Nakagami-m and Rice fading channels are discussed. The upper and lower bounds on outage capacity are derived. For MIMO system, the channel capacity is taken as the performance and the effect of channel estimation error is analyzed. The optimal transmission strategy is studied when there is channel estimation error at receiver and different channel state information can be obtained at transmitter. The effect of channel estimation error on the channel capacity is analyzed by simulation and the system performance with different transmission strategies is compared.
At the last part of this dissertation, the whole work of the dissertation is outlined and the future research issues are discussed.
引文
[1] 吴伟陵 牛凯 移动通信原理 电子工业出版社 2005
[2] 邬正义 范瑜 徐惠钢 现代无线通信技术 高等教育出版社 2006.
[3] 黄韬 袁超伟 杨睿哲等 MIMO 相关技术与应用 机械工业出版社 2007
[4] Telatar I.E. Capacity of Multi-antenna Gaussian Channels. AT&T-Bell Labs Technical Report. June 1995.
[5] Foschini G.J. Layered Space-Time Architecture for Wireless Communication in a Fading Environment When Using Multiple Antennas. Bell Labs Tech. J. , 1996, pp. 41-59
[6] Foschini G.J. Gans M.J. On Limits of Wireless Communications in a Fading Environment When Using Multiple Antennas. Wireless Personal Communications , 1998, vol.6, pp.311-335
[7] Alamouti S.M. A simple transmit diversity technique for wireless communications. IEEE Jounal on Select Areas in Communications, 1998, 16(8), pp. 1451-1458
[8] Tarokh V , Seshadri N , Calderbank A R. Space-Time Block Codes from Orthogonal Designs. IEEE Trans. On Inform. Theory, Jul. 1999, 45(5), pp. 1456-1467.
[9] Tarokh V., Naguib A., Seshadri N.etc. Space–Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction. IEEE Trans. On Inform. Theory, Mar. 1998, 44(2), pp. 744-765
[10] Wolniansky P.W., Foschini, G.J., Golden, G.D., etc. V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel. International Symposium on Signal, Systems, and Electronics. 1998, pp. 295-300
[11] Simon M.K. Alouini M.S Digital Communication over Fading Channels: A Unified Approach to Performance Analysis. John Wiley&Sons, 2000
[12] Rappaport T.S. Wireless Communication: Principle and Practice, Prentice Hall, 1996
[13] Jankiraman M. Space-time codes and MIMO systems Artech House. 2004
[14] Vucetic B. Yuan J.H, Space-Time Coding. Chichester U.K.: John Wiley & Sons. 2004
[15] Naguib A. Tarokh V. Seshadri N. etc. A space-time coding modem for high-data-rate wireless communications. IEEE Journal Select. Areas Commun. Oct. 1998, 16(10), pp. 1459-1478
[16] Baro S. Bauch G. Hansmann A. Improved codes for space-time trellis coded modulation. IEEE Comm. Lett. Jan 2000, 4(1), pp. 20-22
[17] Tarokh V., Naguib A., Seshadri N.etc. Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths. IEEE Trans. On Inform. Theory, Feb. 1999, 47(2), pp. 199-207.
[18] Tarokh V., Jafarkhani H. Calderbank A.R. Space–Time Block Coding for Wireless Communications: Performance Results Mar. 1999, IEEE Jounal on Selected Areas in Comm. 17(3), pp. 451-460
[19] Tse D. Viswanath P. Fundamentals of Wireless Communication. Cambridge University Press, 2004
[20] Goldsmith A. Wireless Communication. Cambridge University Press, 2005
[21] Cover T.M. Thomas J.A. Elements of Information Theory. John Wiley & Sons, 1991
[22] Jafar S.A. Fundamental Capacity Limits of Multiple Antenna Wireless Systems. PHD dissertation. 2003
[23] Chizhik D. Rashid-Farrokhi F. Ling J. etc. Effect of antenna sepapation on the capacity of BLAST in correlated channels. IEEE Commun. Letters, Nov. 2000, 4(11), pp. 337-339
[24] Chizhik D. Foschini G. Gans M. etc. Keyholes, correlations and capacities of multielement transmit and receive antennas. IEEE Trans. On Wireless Commun. Apr.2002, 1(2), pp. 361-368
[25] Shiu D.S. Goschini G. Gans M. etc. Fading correlation and its effect on the capacity of multielement antenna systems. IEEE Trans. On Commun. Mar.2000, 48(3), pp. 502-512
[26] Uysal M. Georghiades C.N. Effect of spatial fading correlation on performance of space-time codes. IEEE Electronics Letters. Feb.2001, 37(3), pp. 181-183
[27] Chuah C.N. Tse D.N.C. Kahn J.M. etc. Capacity scaling in MIMO wireless systems under correlated fading. IEEE Trans. On Inform. Theory. Mar.2002, 48(3), pp. 637-650
[28] Viswanathan H. Capacity of Markov channels with receiver CSI and delayed feedback. IEEE Trans. On Inform. Theory. Mar. 1999, 45, pp. 744-765.
[29] Caire G. Shamai S. On the capacity of some channels with channel state information. IEEE Trans. On Inform. Theory. Sep. 1999, 45, pp. 2007-2019
[30] Goldsmith A. Varaiya P. Capacity of fading channels with channel side information. IEEE Trans. On Inform. Theory. Nov. 1997, 43, pp. 1986-1992
[31] Venkatesan S. Simon S.H. Valenzuela A. Capacity of a Gaussian MIMO channel with nonzero mean. Proc. IEEE Vehicular. Tech. Conf. Oct. 2003, 3, pp. 1767–1771
[32] Hoesli D. Kim Y.H. Lapidoth A. Monotonicity Results for Coherent MIMO Rician Channels. IEEE Trans. On Inform. Theory. Dec. 2005, 51(12), pp. 4334-4339
[33] Visotsky E. Madhow U. Space-time Transmit Precoding with Imperfect Feedback. IEEE Trans. On Inform. Theory. Sep. 2001, 47(6), pp. 2632-2639
[34] Moustakas A.L. Simon S.H. Optimizing Multiple-Input Single-Output(MISO) Communicationsystems with general Gaussian channels: Nontrival covariance and NonzeroMean. Oct 2003. IEEE Trans. On Information Theory. 49(10): 2770-2780.
[35] Jafar S.A. Goldsmith A. Transmitter Optimization and Optimality of Beamforming for multiple antenna systems. IEEE Trans. on Wireless Comm., July 2004, 3(4), pp. 1165–. 1175
[36] Simon S.H. Moustakas A.L. Optimizing MIMO antenna systems with channel covariance feedback. Apr. 2003, IEEE Journal on Selected Areas in Comm. 21(3), pp. 406-417
[37] Jafar S.A. Goldsmith A. On optimality of beamforming for multiple antenna systems with imperfect feedback. Proc. IEEE Int. Symp.Information Theory, 2001, pp.321-321.
[38] Jafar S.A. Vishwanath S. Goldsmith A. Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback. Proc. IEEE. Int. Conf. Comm. 2001, pp. 2266-2270
[39] Jafar S.A. Goldsmith A. Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information. IEEE Trans. Wireless. Comm., May. 2005 4(3), pp.990–997,
[40] Goldsmith A. Jafar S.A. Jindal N. etc. Capacity Limits of MIMO Channels. IEEE Journal on Selected Areas in Communications. Jul 2003, 21(5), pp. 684-702
[41] Jorswieck E.A. Boche H. Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information. IEEE Trans. On Signal Processing. Dec 2004, 52(12), pp. 3440-3453
[42] Boche H. Jorswieck E.A. On the ergodic capacity as a function of the correlation properties in systems with multiple transmit antennas without CSI at the transmitter. IEEE Trans. On Communication. Oct 2004, 52(10), pp. 1654-1657
[43] Jorswieck E.A. Boche H. Channel capacity and capacity-range of beamforming in MIMO wireless systems under correlated fading with covariance feedback. IEEE Trans. On Wireless Comm. Sep 2004, 3(5), pp. 1543-1553
[44] Jorswieck E.A. Oechtering T.J. Boche H. Performance analysis of combining techniques with correlated diversity. Proc. IEEE Wireless Communication and Networking Conference. 2005, pp. 849-854.
[45] Jorswieck E.A. Boche H. On transmit diversity with imperfect channel state information. ICASSP’02, 2002, pp. 2181-2184
[46] Uthansakul P. Bialkowski M.E. Investigations into an Optimal Transmission Scheme for a MIMO System Operating in a Rician Fading Environment. in Proc. IEEE APCC2005, Oct 2005, pp. 339-343
[47] Ming K. Alouini M.S. Water-filling capacity and beamforming performance of MIMO systems with covariance feedback. In Proc. SPAWC2003, Jun 2003, pp. 556-560
[48] Li Y.P. Ye Z.F. Characterization of optimal power allocation at the transmit antennas in MIMOsystem with covariance feedback. In Proc. ECSP’04, Sep 2004, pp. 1910-1913
[49] Liang Y B. Veeravalli V.V. Correlated MIMO Rayleigh fading channels: capacity and optimal signaling. In Proc. of Asilomar Conference on Signals, Systems and Computers, Nov. 2003, pp. 1166-1170
[50] Mckay M.R. Collings I.B. General Capacity Bounds for Spatially Correlated Rician MIMO Channels. IEEE Trans. On Inform. Theory. Sep 2005, 51(9), pp. 3121-2145
[51] Gupta A.K., Nagar D. K., Matrix Variate Distributions. 2000. New York: Chapman & Hall/CRC
[52] Bolcskei H., Borgmann M., Paulraj A.J. Impact of the propagation environment on the performance of space-frequency coded MIMO-OFDM. IEEE J. Select. Areas Commun, 2003, 21(3), pp. 427-439
[53] Roh J.C. Rao B.D. An Improved Transmission Strategy for Multiple Antenna Channels with Partial Feedback. 2002. Asilomar Conference on Signals, Systems and Computer.
[54] Salo J. Mikas F. and Vainikainen P. An upper bound on the ergodic mutual information in Rician fading MIMO channels. Jun 2006. IEEE Trans. On Wireless Communications. 5(6): 1415-1421
[55] Prasad N. Varanasi M.K. Analysis of decision feedback detection for MIMO Rayleigh-fading channels and the optimization of power and rate allocations. Jun 2004. IEEE Trans. On Information Theory. 50(6): 1009-1025
[56] Zheng J and Rao B.D. Capacity analysis of MIMO systems with unknown channel state information. 2004. in IEEE information Theory Workshop. pp. 413-417
[57] Nguyen H.T. Andersen J.B. and Pedersen G.F. Capacity and performance of MIMO systems under the impact of feedback delay. 2004. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications. Pp. 53-57
[58] Kang M. Alouini M. Capacity of correlated MIMO Rayleigh channels. Jan 2006. IEEE Trans. On Wireless Communications. 5(1): 143-155.
[59] Kang M. Alouini M. Capacity of MIMO rician channels. Jan 2006. IEEE Trans. On Wireless Communications. 5(1): 112-122.
[60] Viswanathan H. Capacity of Markov channels with receiver CSI and delayed feedback. Mar 1999. IEEE Trans. On Information Theory. 45(2): 761-771
[61] Jayaweera S.K. Poor H.V. Capacity of multiple-antenna systems with both receiver and transmitter channel state information. Oct 2003. IEEE Trans. On Information Theory. 49(10): 2697-2709
[62] Tulino A.M. Lozano A. and Verdu S. Capacity-achieving input covariance for single-user multi-antenna channels. Mar 2006. IEEE Trans. On Wireless Communications. 5(3): 662-671
[63] Ivanis P. Drajic D. Combined optimal power allocation and adaptive modulation for MIMO systems with imperfect CSI. 2003. IEEE International Conference on Telecommunications in ModernSatellite, Cable and Broadcasting Services. Pp. 167-170.
[64] Liu J. Chen J. Host-Madsen A. and Fossorier M.P.C. Correlated MIMO Rayleigh fading systems with transmit channel state information. IEEE Vehicular Technology Conference. Pp. 26-29.
[65] Kiessling M. Speidel J. and Reinhardt M. Ergodic capacity of MIMO channels with statistical channel state information at the transmitter. 2004. ITG Workshop on Smart Antennas. Pp. 79-86.
[66] Jafar S.A. Fundamental Capacity Limits of Multiple Antenna Wireless Systems. 2003. Ph.d dissertation.
[67] Jorswieck E.A. Unified approach for optimization of single-user and multi-user multiple-input multiple-output wireless systems. 2004. Ph.d dissertation.
[68] Jayaweera S.K. Poor H.V. MIMO capacity results for Rician fading channels. 2003. IEEE Globecom. Pp. 1806-1810.
[69] Lebrun G. Faulkner M. Shafi M. and Smith P.J. MIMO Ricean channel capacity: an asymptotic analysis. Jun 2006. IEEE Trans. On Wireless Communications. 5(6): 1343-1350
[70] Kiessling M. Speidel J. Mutual Information of MIMO Channels in Correlated Rayleigh Fading Environments – a General Solution. 2004. ICC. pp. 814-818.
[71] Sagias N.C. Tombras G.S. and Karagiannidis G.K. New results for the Shannon channel capacity in generalized fading channels. 2005. IEEE Communications Letters. 9(2): 97-99
[72] Khan E. Heneghan C. Nonzero Mean Gaussian Mimo Channel Capacity. 2005. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications. pp. 146-150.
[73] Rosenzweig A. Steinberg Y. and Shamai S. On channels with partial channel state information at the transmitter. May 2005. IEEE Trans. On Information Theory. 51(5): 1817-1830.
[74] Li Y.P. Ye Z.F. On optimum transmission power strategy in MIMO systems with covariance feedback. May 2005. IEEE Communications Letters. 9(5): 444-446.
[75] Skoglund M. Jongren G. On the capacity of a multiple-antenna communication link with channel side information. Apr 2003. IEEE Journal on Selected Areas in Communications. 21(3): 395-405.
[76] Shin H. Win M.Z. Lee J.H. and Chiani M. On the capacity of doubly correlated MIMO channels. Aug 2006. IEEE Trans. On Wireless Communications. 5(8): 2253-2265
[77] Jayaweera S.K. Poor H.V. On the capacity of multi-antenna systems in the presence of Rician fading. 2002. in Proc. Of IEEE Vehicular Technology Conference. Pp. 1963-1967.
[78] Jayaweera S.K. Poor H.V. On the capacity of multiple-antenna systems in Rician fading. May 2005. IEEE Trans. On Wireless Communications. 4(3): 1102-1111.
[79] Jorswieck E.A. Sezgin A. Boche H. and Costa E. Optimal transmit strategies in MIMO Ricean channels with MMSE receiver. 2004. in Proc. of IEEE VTC. Pp. 3787-3791
[80] Moustakas A.L.Simon S.H. Optimizing multiple-input single-output (MISO) communication systems with general Gaussian channels: nontrivial covariance and nonzero mean. Oct 2003. IEEE Trans. On Information Theory. 49(10): 2770-2780.
[81] Luo J.H. Blum R.S. Cimini L. Greenstein L. and Haimovich A. Power allocation in a transmit diversity system with mean channel gain information. Jul 2005. IEEE Communications Letters. 9(7): 616-618.
[82] Kotecha J.H. Sayeed A.M. Transmit signal design for optimal estimation of correlated MIMO channels. Feb 2004. IEEE Trans. On Signal Processing. 52(2): 546-557.
[83] Caire G. Taricco G. and Biglieri E. Optimal power control over fading channels. Jul 1999. IEEE Trans. On Inform. Theory. 45: 1468-1489.
[84] Biglieri E. Caire G. and Taricco G. Limiting performance of block fading channels with multiple antennas. May 2001. IEEE Trans. On Inform. Theory. 47(4): 1273-1289.
[85] Jorswieck E.A. and Boche H. Behavior of outage probability in MISO systems with no Channel State Information at the transmitter. 2003. Proc. Inform. Theory Workshop. pp: 353-356.
[86] Boche H. and Jorswieck E.A. Outage probability of multiple antenna systems: optimal transmission and impact of correlation. 2004. International Zurich Seminar on Communications. pp: 116-119.
[87] Xie Y.Z. Georghiades C.N. and Araposathis A. Outage probability for MISO fading channels with imperfect feedback. 2003. IEEE Global Telecommunications Conference, pp. 1674-1678
[88] Xie Y.Z. Georghiades C.N. and Araposathis A. Minimum outage probability transmission with imperfect feedback for MISO fading channels. May 2005. IEEE Trans. On Wireless Communications. 4(3): 1084-1091
[89] Srinivasan R. Tiba G. Fast estimation of outage probabilities in MIMO channels. May 2004. IEEE Trans. On Communications. 52(5): 711-715.
[90] Wang Z.D. Biannakis G. Outage mutual information of space-time MIMO channels. Apr 2004. IEEE Trans. On Information Theory. 50(4): 657-662.
[91] Kandukuri S. Boyd S. Optimal power control in interference-limited fading wireless channels with outage-probability specifications. Jan 2002. IEEE Trans. On Wireless Communications. 1(1): 46-55.
[92] Laneman J.N. Limiting analysis of outage probabilities for diversity schemes in fading channels. 2003. in Proc. IEEE Global Comm. Conf. (GLOBECOM). Pp. 1242-1246.
[93] Ko Y. Alouini M. and Simon M.K. Outage probability of diversity systems over generalized fading channels. Nov 2000. IEEE Trans. On Communications. 48(11): 1783-1787.
[94] Mondal B. Jr R.W. A lower bound on outage probability of limited feedback MIMO beamforming systems. 2004. In Proc. Of IEEE Asilomar Conf. on Signals, Systems and Computers. Pp. 876-880
[95] Zhang Q.T. Cui X.W. Outage probability for optimum combining of arbitrarily faded signals in the presence of correlated Rayleigh interferers. Jul 2004. IEEE Trans. On Vehicular Technology. 53(4): 1043-1051.
[96] Perez J. Ibanez J. Vielva L. and Santamaria I. Closed-form approximation for the outage capacity of orthogonal STBC. Nov 2005. IEEE Communications Letters. 9(11): 961-963.
[97] Varadarajan B. Barry J.R. The Outage Capacity of Linear Space–Time Codes. Nov 2005. IEEE Trans. On Wireless Communications. 14(6):2642-2648.
[98] Sezgin A. Oechtering T.J. On the outage probability of quasi-orthogonal space-time codes. 2004. in Proc. IEEE Information Theory Workshop. pp. 381-386.
[99] Rajan D. Sabharwal A. and Aazhang B. Outage behavior with delay and CSIT. 2004. IEEE International Conference on Communications. pp. 578-582.
[100] Nabar R.U. Bolcskei H. and Paulraj A.J. Outage properties of space-time block codes in correlated Rayleigh or Rician fading environments. 2002. International Conference on Acoustics, Speech and Signal Processing. Pp. 2381-2384.
[101] Kamath K.M. Goeckel D.L. Adaptive modulation schemes for minimum outage probability in wireless systems
[102] Yang H. Alouini M. Closed-form formulas for the outage probability of wireless communication systems with a minimum signal power constraint. Nov 2002. IEEE Trans. On Vehicular Technology. 51(6): 1689-1698.
[103] Hjorungnes A. Gesbert D. Precoding of Orthogonal Space-Time Block Codes in Arbitrarily Correlated MIMO Channels: Iterative and Closed-Form Solutions. http://www.unik.no/personer/arehj/publications/i3etwcsep2005.pdf
[104] Hjorungnes A. Gesbert D. Akhtar J. Precoding of space-time block coded signals for joint transmit-receive correlated MIMO channels. IEEE Trans. On Wireless Comm. Mar 2006, 5(3), pp. 492-497
[105] Hjorungnes A. Gesbert D. Precoding of Orthogonal Space-Time Block Codes over Correlated Ricean MIMO Channels. IEEE Vehicular Technology Conference. 2005. pp. 3024-3028.
[106] Liu H.P. Song Y.Z. Qiu R.C. The impact of fading correlation on the error performance of MIMO systems over Rayleigh fading channels. IEEE Trans. On Wireless Comm. Sep. 2005, 4(5), pp.2014-2019
[107] Annamalai A. Tellambura C. Bhagava V.K. A General Method for Calculating Error Probabilities Over Fading Channels. IEEE Trans. On Comm. May 2005, 53(5), pp. 841-852.
[108] Zhang H. Gulliver T.A. Capacity and Error Probability Analysis for Orthogonal Space-Time BlockCodes Over Fading Channels. IEEE Trans. On Wireless Comm. Mar 2005, 4(2), pp. 808-819
[109] Xian L. Liu H.P. An adaptive power allocation scheme for space-time block coded MIMO systems. Proc. Of IEEE WCNC’05, Mar 2005, pp. 504-508
[110] Hedayat A. Shah H. Nosratinia A. Analysis of space-time coding in correlated fading channels. IEEE Trans. On Wireless Comm. Nov 2005, 4(6), pp. 2882-2891
[111] Zhou S.L. Giannakis G.B. Optimal transmitter eigen-beamforming and space-time block coding based on channel mean feedback. IEEE Trans. On Signal Precessing. Oct 2002, 50(10), pp. 2599-2613.
[112] Zhou S.L. Giannakis G.B. Optimal transmitter eigen-beamforming and space-time block coding based on channel correlations. IEEE Trans. On Inform. Theory. Jul 2003, 49(7), pp. 1673-1690
[113] Zerlin B. Joham M. Utschick W. and Nossek J.A. Covariance-Based linear precoding. Jan 2006. IEEE Journal on Selected Areas in Communications. 24(1): 190-199.
[114] Love D.J. Jr R.W. Limited feedback unitary precoding for orthogonal space-time block codes. Jan 2005. IEEE Trans. On Signal Processing. 53(1): 64-73.
[115] Akhtar J. Gesbert D. Spatial multiplexing over correlated MIMO channels with a closed-form precoder. Sep 2005. 4(5): 2400-2409
[116] Bahrami H.R. Le-Ngoc T. Nasrabadi A.M.N. Jamali S.H. Precoder design based on correlation matrices for MIMO systems. 2005. IEEE International Conference on Communications. pp. 2001-2005.
[117] Kim J.S. Nam H. and Kim H. Performance of adaptive precoding for wireless MIMO broadcast channels with limited feedback. 2005. Vehicular Technology Conference. Pp. 487-491.
[118] Wang J.Q. Zoltowski M.D. Capacity Analysis and Precoding for MIMO Channels with Covariance Feedback. 2005. Proceedings Asilomar Conference on Signals, Systems and Computer. Pp. 393-397.
[119] Huang K. Andrews J.G. Unified linear precoding for minimum SER. 2005. GLOBECOM. Pp. 1495-1499
[120] Zhao Y. Adve R. and Lim T.J. Precoding of orthogonal STBC with channel covariance feedback for minimum error probability. 2004. IEEE International Symposium on Personal Indoor and Mobile Radio Communications. pp. 503-507.
[121] Vu M. Paulraj A. and Evans R. Linear space-time precoding for Rician fading MISO channels. 2004. in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing. Pp. 461-464.
[122] Vu M. Paulraj A. Linear precoding for MIMO channels with non-zero mean and transmit correlation in orthogonal space-time coded systems. 2004. Vehicular Technology Conference. Pp. 2503-2507.
[123] Simon M.K. Alouini M.S. A unified approach to the performance analysis of digital communicationover generalized fading channels. Proc. IEEE, Sep 1998, pp.1860-1877
[124] Simon M.K. Alouini M.S. Digital Communication over Generalized Fading Channels: A unified Approach to the Performance Analysis. New York: Wiely, 2000
[125] Skoglund M. Jongren G. On the capapcity of a multiple-antenna communication link with channel side information. IEEE J. on Selected Area in Comm. Apr 2003, 21(3), pp. 395-405
[126] Jongren G. Sglund M. Ottersten B. Combining Beamforming and Orthogonal Space-Time Block Coding. IEEE Trans. On Inof. Theory. Mar 2002, 48, pp. 611-627
[127] Sampath H. Paulraj A. Linear precoding for space-time coded systems with known fading correlations. IEEE Comm. Lett., Jun 2002, 6, pp. 239-241
[128] Francisco R. Slock D. Linear precoding for MIMO transmission with partial CSIT. IEEE 6th workshop on signal Processing advances in wireless communications. 2005, pp. 660-664
[129] Love D.J. Heath R.W. Multimode precoding for MIMO wireless systems. IEEE Trans. On Signal Processiong. Oct 2005, 53(10), pp. 3674-3773
[130] Love D.J. Heath R.W. Diversity performance of precoded orthogonal space-time block codes using limited feedback. IEEE Comm. Letters. May 2004, 8(5), pp. 305-307
[131] Bahrami H.R. Le-Ngoc T. Nasrabadi A. etc. Precoder design based on correlation matrices for MIMO systems. IEEE International Conference on Communications. 2005, pp. 2001-2005.
[132] Sanayei S. Love D.J. Nosratinia A. On the design of linear precoders for orthogonal space-time block codes with limited feedback. IEEE Wireless Comm. and Networking Conference, 2005, pp. 489-493
[133] Huang K. Andrews J.G. Unified linear precoding for minimum SER. IEEE Globlecom 2005, pp. 1495-1499
[134] Zhao Y. Adve R. Lim T.J. Precoding of orthogonal STBC with channel covariance feedback for minimum error probability. IEEE International Symposium on Personal, indoor and Mobile Radio Communications. 2004, pp. 503-507
[135] Zhao Y., Adve R. and Lim T.J., Optimal STBC precoding with channel covariance feedback for minimum error probability. Eurasip Journal on Applied Signal Processing. 2004, 9, pp. 1257-1265
[136] Liu L. Jafarkhani H. Application of Quasi-Orthogonal Space-Time Block Codes in Beamforming. IEEE Trans. On Signal Processing, Jan 2005, 53(1), pp. 54-63
[137] Liu L. Jafarkhani H. Combining beamforming and quasi-orthogonal space-time block coding using channel mean feedback. IEEE Globecom 2003, pp. 1925-1930
[138] Graham A. Kronecker Products and Matrix Calculus with Applications. Ellis Horwood Ltd. 1981
[139] Marshall A.M. Olkin I. Inequalitilies: Theory of Majorization and Its Applications. Academic Press,1979.
[140] Medard M. The effect upon Channel Capacity in Wireless Communications of Perfect and Imperfect Knowledge of the Channel. IEEE Trans. Inform. Theory. May 2000. 46: 933-946.
[141] Klein T.E. Gallager R.G.. Power control for the additive white Gaussian noise channel under channel estimation errors. IEEE International Symposium on Information Theory. 2001, pp. 304.
[142] Lapidoth A. Shamai S. Fading Channels: How Perfect Need “Perfect Side Information” Be?. IEEE Trans. Inform. Theory. May 2002. 48: 1118-1134.
[143] Diaz J. Latinovic Z. and Bar-Ness Y. Impact of imperfect channel state information upon the outage capacity of Rayleigh fading channels. Global Telecommunications Conference, 2004. GLOBECOM '04. IEEE. 2004. 2: 887-892.
[144] Proakis J. Digital Communications. Third Edition. New York: McGraw-Hill, 1995.
[145] Hassibi B. Hochwald B. How much training is needed in multiple-antenna wireless links?. IEEE Trans. On Inform. Theory. Apr. 2003. 49:951-963.
[146] Baltersee J. Fock G. and Meyr H. Achievable rate of MIMO channels with data-aided channel estimation and perfect interleaving. IEEE J. Sel. Areas Commun. Dec. 2001. 19: 2358-2368.
[147] Svantesson T. Rao B.D. A framework for MIMO capacity Bounds based on the cramer-rao bound on the channel estimation error. 2005. Signals, Systems and Computer, 2005. Conference Record of the Thirty-ninth Asilomar conference on. Pp. 139-143.
[148] Svantesson T. Rao B.D. Capacity of spatio-temporally structured MIMO channels with estimation errors. 2005. IEEE international conference on Acoustics, speech and signal processing. Pp. 401-404.
[149] Baccarelli E. Biagi M. and Pelizzoni C. On the information throughput and optimized power allocation for MIMO wireless systems with imperfect channel estimation. Jul 2005. IEEE Trans. On Signal Processing. 53(7): 2335-2347.
[150] Yoo Taesang. Goldsmity A. Capacity of fading MIMO channels with channel estimation error. 2004. IEEE International Conference on Communications. pp.808-813.
[151] Yoo Taesang. Goldsmity A. Capacity and power allocation for fading MIMO channels with channel estimation error. May 2006. IEEE Trans. On Inform. Theory. 52: 2203-2214.
[152] Yoo Taesang. Goldsmity A. MIMO capacity with channel uncertainty: Does Feedback Help? 2004. Proc IEEE Global Telecommunications Conference. Pp. 96-100.
[153] Pascual-Iserte A. Palomar D.P. Perez-Neira A.I. and Lagunas M.A. A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization Jan 2006. IEEE Trans. On Signal Processing. 54(1): 346-360.
[2] 邬正义 范瑜 徐惠钢 现代无线通信技术 高等教育出版社 2006.
[3] 黄韬 袁超伟 杨睿哲等 MIMO 相关技术与应用 机械工业出版社 2007
[4] Telatar I.E. Capacity of Multi-antenna Gaussian Channels. AT&T-Bell Labs Technical Report. June 1995.
[5] Foschini G.J. Layered Space-Time Architecture for Wireless Communication in a Fading Environment When Using Multiple Antennas. Bell Labs Tech. J. , 1996, pp. 41-59
[6] Foschini G.J. Gans M.J. On Limits of Wireless Communications in a Fading Environment When Using Multiple Antennas. Wireless Personal Communications , 1998, vol.6, pp.311-335
[7] Alamouti S.M. A simple transmit diversity technique for wireless communications. IEEE Jounal on Select Areas in Communications, 1998, 16(8), pp. 1451-1458
[8] Tarokh V , Seshadri N , Calderbank A R. Space-Time Block Codes from Orthogonal Designs. IEEE Trans. On Inform. Theory, Jul. 1999, 45(5), pp. 1456-1467.
[9] Tarokh V., Naguib A., Seshadri N.etc. Space–Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction. IEEE Trans. On Inform. Theory, Mar. 1998, 44(2), pp. 744-765
[10] Wolniansky P.W., Foschini, G.J., Golden, G.D., etc. V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel. International Symposium on Signal, Systems, and Electronics. 1998, pp. 295-300
[11] Simon M.K. Alouini M.S Digital Communication over Fading Channels: A Unified Approach to Performance Analysis. John Wiley&Sons, 2000
[12] Rappaport T.S. Wireless Communication: Principle and Practice, Prentice Hall, 1996
[13] Jankiraman M. Space-time codes and MIMO systems Artech House. 2004
[14] Vucetic B. Yuan J.H, Space-Time Coding. Chichester U.K.: John Wiley & Sons. 2004
[15] Naguib A. Tarokh V. Seshadri N. etc. A space-time coding modem for high-data-rate wireless communications. IEEE Journal Select. Areas Commun. Oct. 1998, 16(10), pp. 1459-1478
[16] Baro S. Bauch G. Hansmann A. Improved codes for space-time trellis coded modulation. IEEE Comm. Lett. Jan 2000, 4(1), pp. 20-22
[17] Tarokh V., Naguib A., Seshadri N.etc. Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths. IEEE Trans. On Inform. Theory, Feb. 1999, 47(2), pp. 199-207.
[18] Tarokh V., Jafarkhani H. Calderbank A.R. Space–Time Block Coding for Wireless Communications: Performance Results Mar. 1999, IEEE Jounal on Selected Areas in Comm. 17(3), pp. 451-460
[19] Tse D. Viswanath P. Fundamentals of Wireless Communication. Cambridge University Press, 2004
[20] Goldsmith A. Wireless Communication. Cambridge University Press, 2005
[21] Cover T.M. Thomas J.A. Elements of Information Theory. John Wiley & Sons, 1991
[22] Jafar S.A. Fundamental Capacity Limits of Multiple Antenna Wireless Systems. PHD dissertation. 2003
[23] Chizhik D. Rashid-Farrokhi F. Ling J. etc. Effect of antenna sepapation on the capacity of BLAST in correlated channels. IEEE Commun. Letters, Nov. 2000, 4(11), pp. 337-339
[24] Chizhik D. Foschini G. Gans M. etc. Keyholes, correlations and capacities of multielement transmit and receive antennas. IEEE Trans. On Wireless Commun. Apr.2002, 1(2), pp. 361-368
[25] Shiu D.S. Goschini G. Gans M. etc. Fading correlation and its effect on the capacity of multielement antenna systems. IEEE Trans. On Commun. Mar.2000, 48(3), pp. 502-512
[26] Uysal M. Georghiades C.N. Effect of spatial fading correlation on performance of space-time codes. IEEE Electronics Letters. Feb.2001, 37(3), pp. 181-183
[27] Chuah C.N. Tse D.N.C. Kahn J.M. etc. Capacity scaling in MIMO wireless systems under correlated fading. IEEE Trans. On Inform. Theory. Mar.2002, 48(3), pp. 637-650
[28] Viswanathan H. Capacity of Markov channels with receiver CSI and delayed feedback. IEEE Trans. On Inform. Theory. Mar. 1999, 45, pp. 744-765.
[29] Caire G. Shamai S. On the capacity of some channels with channel state information. IEEE Trans. On Inform. Theory. Sep. 1999, 45, pp. 2007-2019
[30] Goldsmith A. Varaiya P. Capacity of fading channels with channel side information. IEEE Trans. On Inform. Theory. Nov. 1997, 43, pp. 1986-1992
[31] Venkatesan S. Simon S.H. Valenzuela A. Capacity of a Gaussian MIMO channel with nonzero mean. Proc. IEEE Vehicular. Tech. Conf. Oct. 2003, 3, pp. 1767–1771
[32] Hoesli D. Kim Y.H. Lapidoth A. Monotonicity Results for Coherent MIMO Rician Channels. IEEE Trans. On Inform. Theory. Dec. 2005, 51(12), pp. 4334-4339
[33] Visotsky E. Madhow U. Space-time Transmit Precoding with Imperfect Feedback. IEEE Trans. On Inform. Theory. Sep. 2001, 47(6), pp. 2632-2639
[34] Moustakas A.L. Simon S.H. Optimizing Multiple-Input Single-Output(MISO) Communicationsystems with general Gaussian channels: Nontrival covariance and NonzeroMean. Oct 2003. IEEE Trans. On Information Theory. 49(10): 2770-2780.
[35] Jafar S.A. Goldsmith A. Transmitter Optimization and Optimality of Beamforming for multiple antenna systems. IEEE Trans. on Wireless Comm., July 2004, 3(4), pp. 1165–. 1175
[36] Simon S.H. Moustakas A.L. Optimizing MIMO antenna systems with channel covariance feedback. Apr. 2003, IEEE Journal on Selected Areas in Comm. 21(3), pp. 406-417
[37] Jafar S.A. Goldsmith A. On optimality of beamforming for multiple antenna systems with imperfect feedback. Proc. IEEE Int. Symp.Information Theory, 2001, pp.321-321.
[38] Jafar S.A. Vishwanath S. Goldsmith A. Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback. Proc. IEEE. Int. Conf. Comm. 2001, pp. 2266-2270
[39] Jafar S.A. Goldsmith A. Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information. IEEE Trans. Wireless. Comm., May. 2005 4(3), pp.990–997,
[40] Goldsmith A. Jafar S.A. Jindal N. etc. Capacity Limits of MIMO Channels. IEEE Journal on Selected Areas in Communications. Jul 2003, 21(5), pp. 684-702
[41] Jorswieck E.A. Boche H. Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information. IEEE Trans. On Signal Processing. Dec 2004, 52(12), pp. 3440-3453
[42] Boche H. Jorswieck E.A. On the ergodic capacity as a function of the correlation properties in systems with multiple transmit antennas without CSI at the transmitter. IEEE Trans. On Communication. Oct 2004, 52(10), pp. 1654-1657
[43] Jorswieck E.A. Boche H. Channel capacity and capacity-range of beamforming in MIMO wireless systems under correlated fading with covariance feedback. IEEE Trans. On Wireless Comm. Sep 2004, 3(5), pp. 1543-1553
[44] Jorswieck E.A. Oechtering T.J. Boche H. Performance analysis of combining techniques with correlated diversity. Proc. IEEE Wireless Communication and Networking Conference. 2005, pp. 849-854.
[45] Jorswieck E.A. Boche H. On transmit diversity with imperfect channel state information. ICASSP’02, 2002, pp. 2181-2184
[46] Uthansakul P. Bialkowski M.E. Investigations into an Optimal Transmission Scheme for a MIMO System Operating in a Rician Fading Environment. in Proc. IEEE APCC2005, Oct 2005, pp. 339-343
[47] Ming K. Alouini M.S. Water-filling capacity and beamforming performance of MIMO systems with covariance feedback. In Proc. SPAWC2003, Jun 2003, pp. 556-560
[48] Li Y.P. Ye Z.F. Characterization of optimal power allocation at the transmit antennas in MIMOsystem with covariance feedback. In Proc. ECSP’04, Sep 2004, pp. 1910-1913
[49] Liang Y B. Veeravalli V.V. Correlated MIMO Rayleigh fading channels: capacity and optimal signaling. In Proc. of Asilomar Conference on Signals, Systems and Computers, Nov. 2003, pp. 1166-1170
[50] Mckay M.R. Collings I.B. General Capacity Bounds for Spatially Correlated Rician MIMO Channels. IEEE Trans. On Inform. Theory. Sep 2005, 51(9), pp. 3121-2145
[51] Gupta A.K., Nagar D. K., Matrix Variate Distributions. 2000. New York: Chapman & Hall/CRC
[52] Bolcskei H., Borgmann M., Paulraj A.J. Impact of the propagation environment on the performance of space-frequency coded MIMO-OFDM. IEEE J. Select. Areas Commun, 2003, 21(3), pp. 427-439
[53] Roh J.C. Rao B.D. An Improved Transmission Strategy for Multiple Antenna Channels with Partial Feedback. 2002. Asilomar Conference on Signals, Systems and Computer.
[54] Salo J. Mikas F. and Vainikainen P. An upper bound on the ergodic mutual information in Rician fading MIMO channels. Jun 2006. IEEE Trans. On Wireless Communications. 5(6): 1415-1421
[55] Prasad N. Varanasi M.K. Analysis of decision feedback detection for MIMO Rayleigh-fading channels and the optimization of power and rate allocations. Jun 2004. IEEE Trans. On Information Theory. 50(6): 1009-1025
[56] Zheng J and Rao B.D. Capacity analysis of MIMO systems with unknown channel state information. 2004. in IEEE information Theory Workshop. pp. 413-417
[57] Nguyen H.T. Andersen J.B. and Pedersen G.F. Capacity and performance of MIMO systems under the impact of feedback delay. 2004. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications. Pp. 53-57
[58] Kang M. Alouini M. Capacity of correlated MIMO Rayleigh channels. Jan 2006. IEEE Trans. On Wireless Communications. 5(1): 143-155.
[59] Kang M. Alouini M. Capacity of MIMO rician channels. Jan 2006. IEEE Trans. On Wireless Communications. 5(1): 112-122.
[60] Viswanathan H. Capacity of Markov channels with receiver CSI and delayed feedback. Mar 1999. IEEE Trans. On Information Theory. 45(2): 761-771
[61] Jayaweera S.K. Poor H.V. Capacity of multiple-antenna systems with both receiver and transmitter channel state information. Oct 2003. IEEE Trans. On Information Theory. 49(10): 2697-2709
[62] Tulino A.M. Lozano A. and Verdu S. Capacity-achieving input covariance for single-user multi-antenna channels. Mar 2006. IEEE Trans. On Wireless Communications. 5(3): 662-671
[63] Ivanis P. Drajic D. Combined optimal power allocation and adaptive modulation for MIMO systems with imperfect CSI. 2003. IEEE International Conference on Telecommunications in ModernSatellite, Cable and Broadcasting Services. Pp. 167-170.
[64] Liu J. Chen J. Host-Madsen A. and Fossorier M.P.C. Correlated MIMO Rayleigh fading systems with transmit channel state information. IEEE Vehicular Technology Conference. Pp. 26-29.
[65] Kiessling M. Speidel J. and Reinhardt M. Ergodic capacity of MIMO channels with statistical channel state information at the transmitter. 2004. ITG Workshop on Smart Antennas. Pp. 79-86.
[66] Jafar S.A. Fundamental Capacity Limits of Multiple Antenna Wireless Systems. 2003. Ph.d dissertation.
[67] Jorswieck E.A. Unified approach for optimization of single-user and multi-user multiple-input multiple-output wireless systems. 2004. Ph.d dissertation.
[68] Jayaweera S.K. Poor H.V. MIMO capacity results for Rician fading channels. 2003. IEEE Globecom. Pp. 1806-1810.
[69] Lebrun G. Faulkner M. Shafi M. and Smith P.J. MIMO Ricean channel capacity: an asymptotic analysis. Jun 2006. IEEE Trans. On Wireless Communications. 5(6): 1343-1350
[70] Kiessling M. Speidel J. Mutual Information of MIMO Channels in Correlated Rayleigh Fading Environments – a General Solution. 2004. ICC. pp. 814-818.
[71] Sagias N.C. Tombras G.S. and Karagiannidis G.K. New results for the Shannon channel capacity in generalized fading channels. 2005. IEEE Communications Letters. 9(2): 97-99
[72] Khan E. Heneghan C. Nonzero Mean Gaussian Mimo Channel Capacity. 2005. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications. pp. 146-150.
[73] Rosenzweig A. Steinberg Y. and Shamai S. On channels with partial channel state information at the transmitter. May 2005. IEEE Trans. On Information Theory. 51(5): 1817-1830.
[74] Li Y.P. Ye Z.F. On optimum transmission power strategy in MIMO systems with covariance feedback. May 2005. IEEE Communications Letters. 9(5): 444-446.
[75] Skoglund M. Jongren G. On the capacity of a multiple-antenna communication link with channel side information. Apr 2003. IEEE Journal on Selected Areas in Communications. 21(3): 395-405.
[76] Shin H. Win M.Z. Lee J.H. and Chiani M. On the capacity of doubly correlated MIMO channels. Aug 2006. IEEE Trans. On Wireless Communications. 5(8): 2253-2265
[77] Jayaweera S.K. Poor H.V. On the capacity of multi-antenna systems in the presence of Rician fading. 2002. in Proc. Of IEEE Vehicular Technology Conference. Pp. 1963-1967.
[78] Jayaweera S.K. Poor H.V. On the capacity of multiple-antenna systems in Rician fading. May 2005. IEEE Trans. On Wireless Communications. 4(3): 1102-1111.
[79] Jorswieck E.A. Sezgin A. Boche H. and Costa E. Optimal transmit strategies in MIMO Ricean channels with MMSE receiver. 2004. in Proc. of IEEE VTC. Pp. 3787-3791
[80] Moustakas A.L.Simon S.H. Optimizing multiple-input single-output (MISO) communication systems with general Gaussian channels: nontrivial covariance and nonzero mean. Oct 2003. IEEE Trans. On Information Theory. 49(10): 2770-2780.
[81] Luo J.H. Blum R.S. Cimini L. Greenstein L. and Haimovich A. Power allocation in a transmit diversity system with mean channel gain information. Jul 2005. IEEE Communications Letters. 9(7): 616-618.
[82] Kotecha J.H. Sayeed A.M. Transmit signal design for optimal estimation of correlated MIMO channels. Feb 2004. IEEE Trans. On Signal Processing. 52(2): 546-557.
[83] Caire G. Taricco G. and Biglieri E. Optimal power control over fading channels. Jul 1999. IEEE Trans. On Inform. Theory. 45: 1468-1489.
[84] Biglieri E. Caire G. and Taricco G. Limiting performance of block fading channels with multiple antennas. May 2001. IEEE Trans. On Inform. Theory. 47(4): 1273-1289.
[85] Jorswieck E.A. and Boche H. Behavior of outage probability in MISO systems with no Channel State Information at the transmitter. 2003. Proc. Inform. Theory Workshop. pp: 353-356.
[86] Boche H. and Jorswieck E.A. Outage probability of multiple antenna systems: optimal transmission and impact of correlation. 2004. International Zurich Seminar on Communications. pp: 116-119.
[87] Xie Y.Z. Georghiades C.N. and Araposathis A. Outage probability for MISO fading channels with imperfect feedback. 2003. IEEE Global Telecommunications Conference, pp. 1674-1678
[88] Xie Y.Z. Georghiades C.N. and Araposathis A. Minimum outage probability transmission with imperfect feedback for MISO fading channels. May 2005. IEEE Trans. On Wireless Communications. 4(3): 1084-1091
[89] Srinivasan R. Tiba G. Fast estimation of outage probabilities in MIMO channels. May 2004. IEEE Trans. On Communications. 52(5): 711-715.
[90] Wang Z.D. Biannakis G. Outage mutual information of space-time MIMO channels. Apr 2004. IEEE Trans. On Information Theory. 50(4): 657-662.
[91] Kandukuri S. Boyd S. Optimal power control in interference-limited fading wireless channels with outage-probability specifications. Jan 2002. IEEE Trans. On Wireless Communications. 1(1): 46-55.
[92] Laneman J.N. Limiting analysis of outage probabilities for diversity schemes in fading channels. 2003. in Proc. IEEE Global Comm. Conf. (GLOBECOM). Pp. 1242-1246.
[93] Ko Y. Alouini M. and Simon M.K. Outage probability of diversity systems over generalized fading channels. Nov 2000. IEEE Trans. On Communications. 48(11): 1783-1787.
[94] Mondal B. Jr R.W. A lower bound on outage probability of limited feedback MIMO beamforming systems. 2004. In Proc. Of IEEE Asilomar Conf. on Signals, Systems and Computers. Pp. 876-880
[95] Zhang Q.T. Cui X.W. Outage probability for optimum combining of arbitrarily faded signals in the presence of correlated Rayleigh interferers. Jul 2004. IEEE Trans. On Vehicular Technology. 53(4): 1043-1051.
[96] Perez J. Ibanez J. Vielva L. and Santamaria I. Closed-form approximation for the outage capacity of orthogonal STBC. Nov 2005. IEEE Communications Letters. 9(11): 961-963.
[97] Varadarajan B. Barry J.R. The Outage Capacity of Linear Space–Time Codes. Nov 2005. IEEE Trans. On Wireless Communications. 14(6):2642-2648.
[98] Sezgin A. Oechtering T.J. On the outage probability of quasi-orthogonal space-time codes. 2004. in Proc. IEEE Information Theory Workshop. pp. 381-386.
[99] Rajan D. Sabharwal A. and Aazhang B. Outage behavior with delay and CSIT. 2004. IEEE International Conference on Communications. pp. 578-582.
[100] Nabar R.U. Bolcskei H. and Paulraj A.J. Outage properties of space-time block codes in correlated Rayleigh or Rician fading environments. 2002. International Conference on Acoustics, Speech and Signal Processing. Pp. 2381-2384.
[101] Kamath K.M. Goeckel D.L. Adaptive modulation schemes for minimum outage probability in wireless systems
[102] Yang H. Alouini M. Closed-form formulas for the outage probability of wireless communication systems with a minimum signal power constraint. Nov 2002. IEEE Trans. On Vehicular Technology. 51(6): 1689-1698.
[103] Hjorungnes A. Gesbert D. Precoding of Orthogonal Space-Time Block Codes in Arbitrarily Correlated MIMO Channels: Iterative and Closed-Form Solutions. http://www.unik.no/personer/arehj/publications/i3etwcsep2005.pdf
[104] Hjorungnes A. Gesbert D. Akhtar J. Precoding of space-time block coded signals for joint transmit-receive correlated MIMO channels. IEEE Trans. On Wireless Comm. Mar 2006, 5(3), pp. 492-497
[105] Hjorungnes A. Gesbert D. Precoding of Orthogonal Space-Time Block Codes over Correlated Ricean MIMO Channels. IEEE Vehicular Technology Conference. 2005. pp. 3024-3028.
[106] Liu H.P. Song Y.Z. Qiu R.C. The impact of fading correlation on the error performance of MIMO systems over Rayleigh fading channels. IEEE Trans. On Wireless Comm. Sep. 2005, 4(5), pp.2014-2019
[107] Annamalai A. Tellambura C. Bhagava V.K. A General Method for Calculating Error Probabilities Over Fading Channels. IEEE Trans. On Comm. May 2005, 53(5), pp. 841-852.
[108] Zhang H. Gulliver T.A. Capacity and Error Probability Analysis for Orthogonal Space-Time BlockCodes Over Fading Channels. IEEE Trans. On Wireless Comm. Mar 2005, 4(2), pp. 808-819
[109] Xian L. Liu H.P. An adaptive power allocation scheme for space-time block coded MIMO systems. Proc. Of IEEE WCNC’05, Mar 2005, pp. 504-508
[110] Hedayat A. Shah H. Nosratinia A. Analysis of space-time coding in correlated fading channels. IEEE Trans. On Wireless Comm. Nov 2005, 4(6), pp. 2882-2891
[111] Zhou S.L. Giannakis G.B. Optimal transmitter eigen-beamforming and space-time block coding based on channel mean feedback. IEEE Trans. On Signal Precessing. Oct 2002, 50(10), pp. 2599-2613.
[112] Zhou S.L. Giannakis G.B. Optimal transmitter eigen-beamforming and space-time block coding based on channel correlations. IEEE Trans. On Inform. Theory. Jul 2003, 49(7), pp. 1673-1690
[113] Zerlin B. Joham M. Utschick W. and Nossek J.A. Covariance-Based linear precoding. Jan 2006. IEEE Journal on Selected Areas in Communications. 24(1): 190-199.
[114] Love D.J. Jr R.W. Limited feedback unitary precoding for orthogonal space-time block codes. Jan 2005. IEEE Trans. On Signal Processing. 53(1): 64-73.
[115] Akhtar J. Gesbert D. Spatial multiplexing over correlated MIMO channels with a closed-form precoder. Sep 2005. 4(5): 2400-2409
[116] Bahrami H.R. Le-Ngoc T. Nasrabadi A.M.N. Jamali S.H. Precoder design based on correlation matrices for MIMO systems. 2005. IEEE International Conference on Communications. pp. 2001-2005.
[117] Kim J.S. Nam H. and Kim H. Performance of adaptive precoding for wireless MIMO broadcast channels with limited feedback. 2005. Vehicular Technology Conference. Pp. 487-491.
[118] Wang J.Q. Zoltowski M.D. Capacity Analysis and Precoding for MIMO Channels with Covariance Feedback. 2005. Proceedings Asilomar Conference on Signals, Systems and Computer. Pp. 393-397.
[119] Huang K. Andrews J.G. Unified linear precoding for minimum SER. 2005. GLOBECOM. Pp. 1495-1499
[120] Zhao Y. Adve R. and Lim T.J. Precoding of orthogonal STBC with channel covariance feedback for minimum error probability. 2004. IEEE International Symposium on Personal Indoor and Mobile Radio Communications. pp. 503-507.
[121] Vu M. Paulraj A. and Evans R. Linear space-time precoding for Rician fading MISO channels. 2004. in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing. Pp. 461-464.
[122] Vu M. Paulraj A. Linear precoding for MIMO channels with non-zero mean and transmit correlation in orthogonal space-time coded systems. 2004. Vehicular Technology Conference. Pp. 2503-2507.
[123] Simon M.K. Alouini M.S. A unified approach to the performance analysis of digital communicationover generalized fading channels. Proc. IEEE, Sep 1998, pp.1860-1877
[124] Simon M.K. Alouini M.S. Digital Communication over Generalized Fading Channels: A unified Approach to the Performance Analysis. New York: Wiely, 2000
[125] Skoglund M. Jongren G. On the capapcity of a multiple-antenna communication link with channel side information. IEEE J. on Selected Area in Comm. Apr 2003, 21(3), pp. 395-405
[126] Jongren G. Sglund M. Ottersten B. Combining Beamforming and Orthogonal Space-Time Block Coding. IEEE Trans. On Inof. Theory. Mar 2002, 48, pp. 611-627
[127] Sampath H. Paulraj A. Linear precoding for space-time coded systems with known fading correlations. IEEE Comm. Lett., Jun 2002, 6, pp. 239-241
[128] Francisco R. Slock D. Linear precoding for MIMO transmission with partial CSIT. IEEE 6th workshop on signal Processing advances in wireless communications. 2005, pp. 660-664
[129] Love D.J. Heath R.W. Multimode precoding for MIMO wireless systems. IEEE Trans. On Signal Processiong. Oct 2005, 53(10), pp. 3674-3773
[130] Love D.J. Heath R.W. Diversity performance of precoded orthogonal space-time block codes using limited feedback. IEEE Comm. Letters. May 2004, 8(5), pp. 305-307
[131] Bahrami H.R. Le-Ngoc T. Nasrabadi A. etc. Precoder design based on correlation matrices for MIMO systems. IEEE International Conference on Communications. 2005, pp. 2001-2005.
[132] Sanayei S. Love D.J. Nosratinia A. On the design of linear precoders for orthogonal space-time block codes with limited feedback. IEEE Wireless Comm. and Networking Conference, 2005, pp. 489-493
[133] Huang K. Andrews J.G. Unified linear precoding for minimum SER. IEEE Globlecom 2005, pp. 1495-1499
[134] Zhao Y. Adve R. Lim T.J. Precoding of orthogonal STBC with channel covariance feedback for minimum error probability. IEEE International Symposium on Personal, indoor and Mobile Radio Communications. 2004, pp. 503-507
[135] Zhao Y., Adve R. and Lim T.J., Optimal STBC precoding with channel covariance feedback for minimum error probability. Eurasip Journal on Applied Signal Processing. 2004, 9, pp. 1257-1265
[136] Liu L. Jafarkhani H. Application of Quasi-Orthogonal Space-Time Block Codes in Beamforming. IEEE Trans. On Signal Processing, Jan 2005, 53(1), pp. 54-63
[137] Liu L. Jafarkhani H. Combining beamforming and quasi-orthogonal space-time block coding using channel mean feedback. IEEE Globecom 2003, pp. 1925-1930
[138] Graham A. Kronecker Products and Matrix Calculus with Applications. Ellis Horwood Ltd. 1981
[139] Marshall A.M. Olkin I. Inequalitilies: Theory of Majorization and Its Applications. Academic Press,1979.
[140] Medard M. The effect upon Channel Capacity in Wireless Communications of Perfect and Imperfect Knowledge of the Channel. IEEE Trans. Inform. Theory. May 2000. 46: 933-946.
[141] Klein T.E. Gallager R.G.. Power control for the additive white Gaussian noise channel under channel estimation errors. IEEE International Symposium on Information Theory. 2001, pp. 304.
[142] Lapidoth A. Shamai S. Fading Channels: How Perfect Need “Perfect Side Information” Be?. IEEE Trans. Inform. Theory. May 2002. 48: 1118-1134.
[143] Diaz J. Latinovic Z. and Bar-Ness Y. Impact of imperfect channel state information upon the outage capacity of Rayleigh fading channels. Global Telecommunications Conference, 2004. GLOBECOM '04. IEEE. 2004. 2: 887-892.
[144] Proakis J. Digital Communications. Third Edition. New York: McGraw-Hill, 1995.
[145] Hassibi B. Hochwald B. How much training is needed in multiple-antenna wireless links?. IEEE Trans. On Inform. Theory. Apr. 2003. 49:951-963.
[146] Baltersee J. Fock G. and Meyr H. Achievable rate of MIMO channels with data-aided channel estimation and perfect interleaving. IEEE J. Sel. Areas Commun. Dec. 2001. 19: 2358-2368.
[147] Svantesson T. Rao B.D. A framework for MIMO capacity Bounds based on the cramer-rao bound on the channel estimation error. 2005. Signals, Systems and Computer, 2005. Conference Record of the Thirty-ninth Asilomar conference on. Pp. 139-143.
[148] Svantesson T. Rao B.D. Capacity of spatio-temporally structured MIMO channels with estimation errors. 2005. IEEE international conference on Acoustics, speech and signal processing. Pp. 401-404.
[149] Baccarelli E. Biagi M. and Pelizzoni C. On the information throughput and optimized power allocation for MIMO wireless systems with imperfect channel estimation. Jul 2005. IEEE Trans. On Signal Processing. 53(7): 2335-2347.
[150] Yoo Taesang. Goldsmity A. Capacity of fading MIMO channels with channel estimation error. 2004. IEEE International Conference on Communications. pp.808-813.
[151] Yoo Taesang. Goldsmity A. Capacity and power allocation for fading MIMO channels with channel estimation error. May 2006. IEEE Trans. On Inform. Theory. 52: 2203-2214.
[152] Yoo Taesang. Goldsmity A. MIMO capacity with channel uncertainty: Does Feedback Help? 2004. Proc IEEE Global Telecommunications Conference. Pp. 96-100.
[153] Pascual-Iserte A. Palomar D.P. Perez-Neira A.I. and Lagunas M.A. A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization Jan 2006. IEEE Trans. On Signal Processing. 54(1): 346-360.