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This paper proposes a novel downlink spatial scheduling algorithm in multiuser multiple-input--multiple-output (MIMO) systems, which selects a good combination of terminals and base station's (BS's) transmit beams so that the BS's beams nullify interstream interference at the selected terminals. In the derivation process, we reveal the new property that the optimization problem of downlink spatial scheduling is equivalent to that of uplink scheduling under the BS's zero-forcing beamforming. Using this property, an efficient downlink scheduling algorithm is presented, applying the principle of an uplink scheduling algorithm. Numerical results show that the presented spatial scheduling achieves a much higher system throughput than a multiuser MIMO system without spatial scheduling or with conventional spatial scheduling by linear processing. We also present a realistic control structure to achieve the uplink and downlink spatial scheduling in time-division duplex systems. [ABSTRACT FROM AUTHOR]