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Multiple antennas play an important role in improving radio communications. In view of this role, the area of multiple antenna communication systems is in the forefront of wireless research. This article reviews two key related aspects of multiple antenna communication systems: multiple access interference mitigation at the receiver via multi-user beamforming; and space-time modulation and coding for MIMO systems. It is shown that both multi-user and MIMO receivers share similar signal processing and complexity tradeoffs.. Following that, a general unified framework for assessing different types of space-time modulation for MIMO systems is introduced. These space-time modulation methods are then compared in terms of Shannon capacity over multipath channels. Key MIMO system performance and implementation issues are also highlighted.