||THE REALIZATION OF WIRELESS COMMUNICATION providing high-speed, high-capacity and high-quality information exchange between two portable terminals that might be located anywhere in the world is still the communication challenge. This is also the ultimate goal of wireless system design. In this thesis, we study transmit signal processing for the downlink of multiuser systems, including MISO (multiple-input single-output) and MIMO (multiple-input multiple-output) systems, where instantaneous or long-term channel state information (CSI) is available at the transmitter. Our goal is to develop transmit processing techniques to overcome the difficulties of wireless communication, and thereby enhancing wireless communication. Several transmit schemes are proposed in this thesis. These include four schemes for multi-user MISO systems and four schemes for multi-user MIMO systems when instantaneous CSI is available at the transmitter. Besides, we provide a simple transmit scheme to study the potential of transmit processing for multi-user MIMO systems when only long term CSI is available at the transmitter. The multi-user MISO transmit schemes are 1) transmit MMSE (minimum mean square error) scheme in flat fading channels, 2) transmit MMSE with preFDE (frequency domain pre-equalization) scheme in frequency selective channels, 3) transmit Pre-BLAST-DFE (Pre-BLAST decision feedback equalization) in frequency selective channels, and 4) transmit MMSE processing in frequency selective channels for a TDD-CDMA system. The multi-user MIMO transmit schemes are 1) transmit MMSE with simple receive diversity scheme, 2) transmit multi-user MIMO decomposition scheme, 3) joint transmit and virtual receive multi-user MIMO decomposition scheme, and 4) joint transmit MMSE and virtual receive MMSE scheme. Numerical results and comparisons with various schemes are provided and these demonstrate the potential of our proposed techniques. In particular, it is shown that a multi-user MIS0 or MIMO system can provide improved throughput or capacity by utilizing the proposed techniques. The improvement is substantially enough to offset the cost of obtaining the CSI at the transmitter.