Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
On Limits of Wireless Communications in a Fading Environment when UsingMultiple Antennas
Wireless Personal Communications: An International Journal
Blind channel estimation and equalization of multiple-input multiple-output channels
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
Practical Optimization: Algorithms and Engineering Applications
Practical Optimization: Algorithms and Engineering Applications
Training Signal Design for Estimation of Correlated MIMO Channels With Colored Interference
IEEE Transactions on Signal Processing
On Superimposed Training for MIMO Channel Estimation and Symbol Detection
IEEE Transactions on Signal Processing
Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing - Part I
Optimal training for MIMO frequency-selective fading channels
IEEE Transactions on Wireless Communications
Optimal training signals for MIMO OFDM channel estimation
IEEE Transactions on Wireless Communications
Transactions Papers - Space-time-frequency characterization of MIMO wireless channels
IEEE Transactions on Wireless Communications
Mutual information and minimum mean-square error in Gaussian channels
IEEE Transactions on Information Theory
A simple transmit diversity technique for wireless communications
IEEE Journal on Selected Areas in Communications
A stochastic MIMO radio channel model with experimental validation
IEEE Journal on Selected Areas in Communications
Multiple antenna spectrum sensing in cognitive radios
IEEE Transactions on Wireless Communications
Communications over the best singular mode of a reciprocal MIMO channel
IEEE Transactions on Communications
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In this paper, we design the training signal for a multi-input multi-output (MIMO) communication system in a colored medium. We assume that the known channel covariance matrix (CM) is a Kronecker product of a transmit channel CM and a receive channel CM. Similarly, the CM of the additive Gaussian noise is modeled by a Kronecker product of a temporal CM and a spatial CM. We maximize the differential entropy gained by receiver for a limited energy budget for training at the transmitter. Using, singular value decomposition of the involved CMs, we tum this problem into a convex optimization problem. We prove that the left and right singular vectors of the optimal training matrix are eigenvectors of the channel transmit CM and the noise temporal CM. In general case, this problem can be solved numerically using efficient methods. The impact of the optimal training is more significant in environments with larger eigenvalue spread. The expression of the optimal solution is interesting for some specific cases. For uncorrelated receive channel, the optimal training looks like water filling, i.e., more training power must be invested on the directions which have more impact. For high signal-to-noise ratios (SNRs), any orthogonal training is optimal; this means that if large amount of energy is available, it must be invested uniformly in all directions. In low SNR scenarios where low amount of energy is available for channel training, all the energy must be allocated to the best mode of channel (which has the highest ratio of the received channel variance to the received noise power).