Achieving the lower bound of fading MIMO relay channels with covariance feedback at the transmitters

In this paper, we consider a full-duplex mode MIMO relay channel for decode and forward strategy where the receivers have perfect channel state information (CSI) and the transmitters have only covariance feedback at the transmitters. We derive a lower bound to the ergodic capacity for this scenario and propose an iterative algorithm that finds lower bound achieving transmit covariance matrices of the source and relay nodes. The solution of the optimization problem in the lower bound expression is given for three cases depending on channel covariance matrices. For one of these cases, it seems that an efficient and fast algorithm achieving the lower bound is not possible. However, under a certain practical channel assumption, we propose a power allocation algorithm that gives a solution much faster than classical convex optimization methods. Moreover, we show that this fast algorithm results in a data rate which is very close to the lower bound to the capacity.