An optimal MIMO communication scheme was developed based on the ideal as- sumption that the knowledge of channel state information is perfect in the whole system. Upon this scheme, we consider the optimal precoding design problem when channel state information (CSI) is imperfect at the transmitter. In this thesis, the CSI error at the transitter is classi ed into two di erent types. We use random matrices analysis to investigate the system performance respectively with these types of error. For the purpose of mathematical tractibility, we try to use precoder design strategy to optimize the upperbound of system performance. When certain type of error is considered, we nd that the maximization of this upperbound do not gaurantee the enhancement of performance. On the other side, we con rm that the optimal solution for this type of error is the same with the so- lution derived under perfect CSI assumption. Also, for the other type of error, we alternatively propose a precoder design that can enhance the system performance.