Fading MIMO relay channels with channel estimation error

In this paper, we consider a full-duplex, decode-and-forward, fading MIMO relay channel where the transmitters have partial channel state information (CSI) and the receivers have noisy channel estimates. Under block fading assumption, we divide the transmission block into two parts: training phase and data transmission phase. The destination and relay receivers estimate the instantaneous channel realizations during the training phase by using linear minimum mean square error (MMSE) estimation, extract the covariance information of the channel, and feed it back to the source and relay transmitters. We obtain a lower bound expression to the relay channel capacity in terms of a max-min optimization problem over channel estimation and data transmission parameters. By applying matrix differential calculus, we jointly optimize this achievable rate over source and relay transmit covariance matrices, training phase length, training phase powers and training sequences.