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We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.