In this thesis, we introduce the performance degradation due to the correlations of the transmit antennas for MIMO systems. In order to resolve this problem, the feedback information at the transmitter can be employed. We first estimate the channel covariance matrix, and then send this matrix back to the transmitter and apply the specific linear precoder which is known at the receiver as well. Some papers have suggested the linear precoding for the space-time block codes and the spatial multiplexing, but they required the high complexity for implementing. Therefore, we will propose a linear precoder which can improve the performance for STBC (Space Time Block Codes) and spatial multiplexing respectively. In case of STBC, we formulate the closed-form linear precoder for two transmit antennas system. And we propose also the sub-optimal closed-form linear precoder for spatial multiplexing. The main contribution is that we developed very simple and practical precoder for spatial multiplexing. Simulation results show that the proposed linear precoder can achieve the performance very close to the optimal linear precoder which is hard to implement practically.