To achieve high performance, in terms of reliability and throughput, in future multiple-antenna communication systems, it is essential to fully exploit the spatial dimensions of the wireless propagation channel. In multiuser communication systems, the throughput can be significantly increased by simultaneously transmitting to several users in the same time-frequency slot by means of spatial-division multi-access (SDMA). A major limiting factor for downlink SDMA transmission is the amount of channel-state information (CSI) that is available at the transmitter. In most cases, CSI can be measured/estimated only at the user terminals and must be fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed to the base station. Herein, we develop several low-complexity, as well as optimized, SDMA downlink resource-allocation schemes that are particularly suitable for systems utilizing statistical channel information and partial CSI feedback. A framework is proposed for combining statistical channel information with a class of instantaneous channel norms. It is shown that, in wide-area scenarios, the feedback of such a scalar norm provides sufficient information for the proposed resource-allocation algorithms to perform efficient SDMA beamforming (BF) and scheduling.