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In this work, the Multiple transmit antennas Multiple Access Channel is considered. A construction of a family of distributed space-time codes for this channel is proposed. No Channel Side Information at the transmitters is assumed and users are not allowed to cooperate together. It is shown that the proposed code achieves the Diversity Multiplexing Tradeoff of the channel. As an example, we consider the two-user MIMO-MAC channel. Simulation results show the significant gain offered by the new coding scheme compared to an orthogonal transmission scheme, e.g. time sharing.

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