[en] Training-based estimation of channel state information in multi-antenna systems is analyzed herein. Closed-form expressions for the general Bayesian minimum mean square error (MMSE) estimators of the channel matrix and the squared channel norm are derived in a Rayleigh fading environment with known statistics at the receiver side. When the second-order channel statistics are available also at the transmitter, this information can be exploited in the training sequence design to improve the performance. Herein, mean square error (MSE) minimizing training sequences are considered. The structure of the general solution is developed, with explicit expressions at high and low SNRs and in the special case of uncorrelated receive antennas. The optimal length of the training sequence is equal or smaller than the number of transmit antennas.
G. J. Foschini and M. J. Gans, "On limits of wireless communications in a fading environment when using multiple antennas," Wireless Personal Commun., vol. 6, pp. 311-335, 1998.
E. Telatar, "Capacity of multi-antenna Gaussian channels," European Trans. Telecom., vol. 10, pp. 585-595, 1999.
M. Biguesh and A.B. Gershman, "Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals," IEEE Trans. Signal Process., vol. 54, pp. 884-893, 2006.
J.H. Kotecha and A.M. Sayeed, "Transmit signal design for optimal estimation of correlated MIMO channels," IEEE Trans. Signal Process., vol. 52, pp. 546-557, 2004.
E. De Carvalho and D.T.M. Slock, "Cramer-Rao bounds for semi-blind, blind and training sequence based channel estimation," in Proc. IEEE SPAWC'97, 1997.
F.A. Dietrich and W. Utschick, "Pilot-assisted channel estimation based on second-order statistics," IEEE Trans. Signal Process., vol. 53, pp. 1178-1193, 2005.
E. Björnson and B. Ottersten, "Pilot-based Bayesian channel norm estimation in Rayleigh fading multi-antenna systems," in Proc. Nordic Radio Science and Commun. (RVK'08), 2008.
E. Björnson and B. Ottersten, "A unified framework for training-based estimation in arbitrarily correlated Rician MIMO channels with Rician disturbance," IEEE Trans. Signal Process., Submitted for publication.
B. Hassibi and B.M. Hochwald, "How much training is needed in multiple-antenna wireless links?," IEEE Trans. Inf. Theory, vol. 49, pp. 951-963, 2003.
S.M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall, 1993.
E. Björnson and B. Ottersten, "Post-user-selection quantization and estimation of correlated Frobenius and spectral channel norms," in Proc. IEEE PIMRC'08, 2008.
S.L. Loyka, "Channel capacity of MIMO architecture using the exponential correlation matrix," IEEE Commun. Lett., vol. 5, pp. 369-371, 2001.
