Relaying MIMO channel capacity with imperfect channel knowledge at the receiver

In this paper, we study a scenario of multiple input multiple output system using relays in an angle showing how the topology of the system can play its role in the situation. We assume perfect channel knowledge at the transmitter and the relay(s) which is represented by a matrix of zero mean circularly symmetric complex Gaussian (ZMCSCG) random variables with known covariances, but imperfect channel state information (CSI) at the receiver. The imperfect CSI at the receiver causes errors to the received signal and as a consequence the channel capacity saturates. We derive the channel capacity formulas for two different transmission algorithms; uniform and waterfilling. Finally we simulate and compare the results