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In the multiuser spatial multiplexing multiple-input multiple-output (MIMO) system, the joint transmitter-receiver (Tx-Rx) design is investigated to minimize the weighted sum power under the post-processing signal-to-interference-and-noise rate (post-SINR) constraints for all subchannels. Firstly, we show that the uplink-downlink duality is equivalent to the Lagrangian duality in the optimization problems. Then, an iterative algorithm for the joint Tx-Rx design is proposed according to the above result. Simulation results show that the algorithm can not only satisfy the post-SINR constraints, but also easily adjust the power distribution among the users by changing the weights accordingly. So that the transmitting power to the edge users in a cell can be decreased effectively to alleviate the adjacent cell interference without performance penalty.