In multiuser multiple-input multiple-output (MIMO) systems, transmit beamforming can be used to realize spatial division multiple access which significantly increases system throughput. The beamforming vector is generally determined by exhaustive search in a codebook in the receiver and sent back to the transmitter. In this paper, we propose some low-complexity schemes for joint design of transmit and receive beamforming. A minimum mean square error (MMSE) receive beamforming is developed which minimizes multiuser interference caused by potential difference between the optimal transmit beamforming vector and the code selected from the codebook. Based on the MMSE beamforming, we developed algorithms which notably reduce the computation complexity in codebook searching. Simulation results show that the proposed schemes can achieve even better performance than existing schemes at reduced complexity.
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