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Rapid growth in mobile computing and other wireless multimedia services is inspiring many research and development activities on high-speed wireless communication systems.Main challenges in this area include the development of efficient coding and modulation signal processing techniques for improving the quality and spectral efficiency of wireless systems. The recently emerged space-time coding and signal processing techniques for wireless communication systems employing multiple transmit and receive antennas offer a powerful paradigm for meeting these challenges. This paper provides an overview on the recent development in space-time coding and signal processing techniques for multiple-input multiple-output (MIMO) communication systems. We first review the information theoretic results on the capacities of wireless systems employing multiple transmit and receive antennas. We then describe two representative categories of space-time systems, namely, the BLAST system and the space-time block coding system, both of which have been proposed for next-generation high-speed wireless system. Signal processing techniques for channel estimation and decoding in space-time systems are also discussed. Finally, some other coding and signal processing techniques for wireless systems employing multiple transmit and receive antennas that are currently under intensive research are also briefly touched upon.