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In this paper, we propose a low-complexity transmit antenna selection algorithm for MIMO multiuser channels. This algorithm greedily finds the optimal transmit antenna subset in base station. When the transmit power for individual data streams is equal, the proposed algorithm can be applied to the zero-forcing and the MMSE precoding schemes to further simplify the computational complexity. Simulation results show that the proposed low-complexity suboptimal antenna selections can achieve very close performance with the optimal antenna selection scheme in. As a result, a good trade-off between complexity and performance is attained by the proposed antenna selection schemes.