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Multiple-input multiple-output (MIMO) communication techniques have been an important area of focus for next-generation wireless systems because of their potential for high capacity, increased diversity, and interference suppression. For applications such as wireless LANs and cellular telephony, MIMO systems will likely be deployed in environments where a single base must communicate with many users simultaneously. As a result, the study of multi-user MIMO systems has emerged recently as an important research topic. Such systems have the potential to combine the high capacity achievable with MIMO processing with the benefits of space-division multiple access. In this article we review several algorithms that have been proposed with this goal in mind. We describe two classes of solutions. The first uses a signal processing approach with various types of transmitter beamforming. The second uses "dirty paper" coding to overcome the interference a user sees from signals intended for other users. We conclude by describing future areas of research in multi-user MIMO communications.