In the downlink of a multi-user MIMO system over a fading channel, the base station can assign the available spatial streams to different users by capitalizing on multiuser diversity or enforcing fairness constraints. Assuming linear precoding (beamforming) at the base station, the problem amounts to the joint design of precoding matrices and channel aware scheduling, according to the cross-layer paradigm. In this paper we formulate the joint optimization of scheduling and linear precoding within a physical layer-oriented framework, where the performance metric is the transmission rate. Moreover, we constraint the preceding scheme to ensure interference-free reception of spatial streams (Orthogonal Space Division Multiple Access, OSDMA). Fairness constraints are either inspired by the max-min or the proportional fair criterion. Performance of different schemes is evaluated by numerical simulations allowing to assess the trade-offs between sum-rate (multi-user diversity) and fairness.