Capacity Bounds on MIMO Relay Channel With Covariance Feedback at the Transmitters

In this paper, the source and relay transmit covariance matrices are jointly optimized for a fading multiple-antenna relay channel when the transmitters only have partial channel state information (CSI) in the form of covariance feedback. For both full-duplex and half-duplex transmissions, we evaluate lower and upper bounds on the ergodic channel capacity. These bounds require a joint optimization over the source and relay transmit covariance matrices. The methods utilized in the previous literature cannot handle this joint optimization over the transmit covariance matrices for the system model considered in this paper. Therefore, we utilize matrix differential calculus and propose iterative algorithms that find the transmit covariance matrices to solve the joint optimization problem. In this method, there is no need to specify first the eigenvectors of the transmit covariance matrices. The algorithm updates both the eigenvectors and the eigenvalues at each iteration. Through simulations, we observe that lower and upper bounds are close to each other. However, the distance between the lower and upper bounds depends on the channel conditions. If the mutual information on the source-to-relay channel and the broadcast channel get closer to each other, the bounds on capacity also get closer.