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In the downlink of a broadcast fading channel, the base station can capitalize on multiuser diversity through channel aware scheduling. In MIMO systems, the design of the scheduler has to take into account the processing performed at the transmitter and the receivers. In this work, we consider channel aware scheduling for orthogonal linear precoding at the base station that guarantees interference free reception for each scheduled users. The problem is set in a novel mathematical framework and a scheduling algorithm is proposed that is shown by simulation to guarantee superior performance as compared to know techniques. Moreover, fairness constraints inspired by the proportional fair criterion are introduced in the scheduling process in order to guarantee the desired long term fairness properties.