TY - JOUR
T1 - Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information
AU - Jorswieck, Eduard A.
AU - Boche, Holger
N1 - Funding Information:
Manuscript received June 30, 2003; revised November 28, 2003. This work was supported in part by the Bundesministerium für Bildung und Forschung (BMBF) under Grant BU150. Part of this work was presented at IEEE International Conference on Acoustics, Speech, and Signal Processing, April 6–10 2003, Hong Kong and IEEE International Symposion on Information Theory, Yokohama, Japan, June 29–July 4, 2003. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Behrouz Farhang-Boroujeny.
PY - 2004/12
Y1 - 2004/12
N2 - 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 eovariance 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.
AB - 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 eovariance 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.
KW - Beamforming
KW - Capacity
KW - Channel state information
KW - Covariance feedback
KW - Multiple-antenna systems
KW - Power allocation
KW - Spatial correlation
UR - http://www.scopus.com/inward/record.url?scp=9744221228&partnerID=8YFLogxK
U2 - 10.1109/TSP.2004.837415
DO - 10.1109/TSP.2004.837415
M3 - Article
AN - SCOPUS:9744221228
SN - 1053-587X
VL - 52
SP - 3440
EP - 3453
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 12
ER -