Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.

[1]  Holger Boche,et al.  Behavior of outage probability in MISO systems with no channel state information at the transmitter , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[2]  J. H. Winters,et al.  The diversity gain of transmit diversity in wireless systems with Rayleigh fading , 1994, Proceedings of ICC/SUPERCOMM'94 - 1994 International Conference on Communications.

[3]  Joseph M. Kahn,et al.  Fading correlation and its effect on the capacity of multielement antenna systems , 2000, IEEE Trans. Commun..

[4]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .

[5]  J. W. Silverstein,et al.  On the empirical distribution of eigenvalues of a class of large dimensional random matrices , 1995 .

[6]  E.A. Jorswieck,et al.  Multiuser MIMO systems, worst case noise and transmitter cooperation , 2003, Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology (IEEE Cat. No.03EX795).

[7]  Andrea J. Goldsmith,et al.  Adaptive multirate CDMA for uplink throughput maximization , 2003, IEEE Trans. Wirel. Commun..

[8]  H. Boche,et al.  Uplink sumrate maximization with different types of channel state information at the transmitters , 2003, Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology (IEEE Cat. No.03EX795).

[9]  Björn E. Ottersten,et al.  Analytic approximations of eigenvalue moments and mean channel capacity for MIMO channels , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[11]  Andrea J. Goldsmith,et al.  Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information , 2005, IEEE Transactions on Wireless Communications.

[12]  John M. Cioffi,et al.  Uniform power allocation in MIMO channels: a game-theoretic approach , 2003, IEEE Transactions on Information Theory.

[13]  Leandros Tassiulas,et al.  Transmit beamforming and power control for cellular wireless systems , 1998, IEEE J. Sel. Areas Commun..

[14]  Holger Boche,et al.  Solvability of coupled downlink beamforming problems , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[15]  Arogyaswami Paulraj,et al.  Adaptive transmitting antenna methods for multipath environments , 1994, 1994 IEEE GLOBECOM. Communications: The Global Bridge.

[16]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[17]  Gregory W. Wornell,et al.  Efficient use of side information in multiple-antenna data transmission over fading channels , 1998, IEEE J. Sel. Areas Commun..

[18]  Chen-Nee Chuah,et al.  Capacity scaling in MIMO Wireless systems under correlated fading , 2002, IEEE Trans. Inf. Theory.

[19]  Joseph M. Kahn,et al.  Fading correlation and its effect on the capacity of multi-element antenna systems , 1998, ICUPC '98. IEEE 1998 International Conference on Universal Personal Communications. Conference Proceedings (Cat. No.98TH8384).

[20]  I. M. Pyshik,et al.  Table of integrals, series, and products , 1965 .

[21]  A. Goldsmith,et al.  On optimality of beamforming for multiple antenna systems with imperfect feedback , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[22]  H. Boche,et al.  Stability region of arrival rates and optimal scheduling for MIMO-MAC-a cross-layer approach , 2004, International Zurich Seminar on Communications, 2004.

[23]  John M. Cioffi,et al.  Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization , 2003, IEEE Trans. Signal Process..

[24]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[25]  Holger Boche,et al.  Optimal Transmission with Imperfect Channel State Information at the Transmit Antenna Array , 2003, Wirel. Pers. Commun..

[26]  H. Boche,et al.  Optimal transmission strategy for multiple antenna systems with uninformed transmitter and correlation , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[27]  Aris L. Moustakas,et al.  MIMO capacity through correlated channels in the presence of correlated interferers and noise: a (not so) large N analysis , 2003, IEEE Trans. Inf. Theory.

[28]  Lizhong Zheng,et al.  Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels , 2003, IEEE Trans. Inf. Theory.

[29]  Giuseppe Caire,et al.  Limiting performance of block-fading channels with multiple antennas , 2001, IEEE Trans. Inf. Theory.

[30]  Helmut Bölcskei,et al.  Tight lower bounds on the ergodic capacity of Rayleigh fading MIMO channels , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[31]  Upamanyu Madhow,et al.  Space-Time transmit precoding with imperfect feedback , 2001, IEEE Trans. Inf. Theory.

[32]  Ingram Olkin,et al.  Inequalities: Theory of Majorization and Its Application , 1979 .

[33]  M. Godavarti,et al.  Min-capacity of a multiple-antenna wireless channel in a static Rician fading environment , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[34]  Gregory W. Wornell,et al.  Performance limits of coded diversity methods for transmitter antenna arrays , 1999, IEEE Trans. Inf. Theory.

[35]  Holger Boche,et al.  A new approach to power adjustment for spatial covariance based downlink beamforming , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[36]  E. Biglieri,et al.  Limiting performance of block-fading channels with multiple antennas , 1999, Proceedings of the 1999 IEEE Information Theory and Communications Workshop (Cat. No. 99EX253).

[37]  Holger Boche,et al.  Transmission strategies for the MIMO MAC with MMSE receiver: average MSE optimization and achievable individual MSE region , 2003, IEEE Trans. Signal Process..