A joint scheduling and grouping technique provides uplink throughput maximization for space-division multiple access (SDMA) systems under proportional fairness constraints. In a slow-fading narrowband MIMO multiple access channel (MAC) multiple users, each equipped with multiple transmit antennas, communicate to a receiver equipped with multiple receive antennas. The users are unaware of the channel state information (CSI) whereas the receiver has perfect CSI and employs a successive group decoder (SGD). For an open-loop system, an optimum successive group decoder (OSGD) simultaneously minimizes the common outage probability and the individual outage probability of each user, over all SGDs of permissible decoding complexity. For each channel realization, the OSGD maximizes the error exponent of the decodable set of users. An adaptive SGD retains the outage optimality of the OSGD and minimizes decoding complexity. The SGD yields symmetric capacity gains commensurate with the decoding complexity allowed. The OSGD offers significantly improved performance at low decoding complexity.