Multiple-input multiple-output (MIMO) systems have potential to provide the capacity needed for future generation wireless systems and have been adopted by 3GPP Long Term Evolution (LTE) system. However, due to several practical limitations the theoretical benefits of MIMO are not fully achieved. The degree of channel state information (CSI) at the transmitter is one key limiting factor when aiming at high performance. In this thesis, the performance possible to achieve under different CSI assumptions at the transmitter is studied. In the beginning, full CSI is assumed at the receiver and the problem of sum rate maximization for two multiplexed users with linear receiver and transmit processing is investigated. A new simple transmission s...