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In this paper, the authors solve the problem of linear precoding for the downlink in multiuser Multiple-Input Multiple-Output (MIMO) systems. The transmitter and the receivers may be equipped with multiple antennas and each user may receive multiple data streams. Their objective is to jointly optimize the power allocation and transmit-receive filters for all users. They develop the optimization for two different criteria; minimizing the total transmitted power while satisfying SINR constraints and minimizing the sum mean squared error given a total power budget. They take advantage of the duality between the uplink and downlink to derive the solution.
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