Assuming a base station with multiple antennas, we propose two channel-assigning strategies based on spatial multiplexing with threshold-based user selection at the uplink. Allowing multiple chosen users to access the channel, we obtain additional multiplexing gain and a reduced feedback complexity, compared to the conventional greedy approach. We prove that the proposed system outperforms the greedy approach also with respect to the degree of fairness among users, measured by the variance of the time averaged throughput. For practical uplink multiuser systems, we show that the standard greedy scheme may not be the optimal policy in terms of the minimization of average BER. The numerical results corroborate our findings.