Differentiated Rate Sceduling for MIMO Broadcast Channels

We consider the problem of differentiated rate scheduling for the fading MIMO Gaussian broadcast channel, in the sense that the rates required by different users must satisfy certain rational rate constraints. When full channel state information (CSI) is available at the transmitter, the problem can be readily solved using dirty paper coding (DPC) and con- vex optimization techniques on the dual multiple-access channel (MAC). However, since in many practical applications full CSI is not feasible, and since the computational complexity may be prohibitive when the number of users is large, we focus on two simple schemes that require very little CSI: time-division opportunistic (TO) beamforming where in different time-slots the transmitter performs opportunistic beamforing only to users requiring the same rate, and weighted opportunistic (WO) beamforing where the random beams are assigned to those users having the largest weighted SINR. In both cases we determine explicit schedules to guarantee the rate constraints and show that, in the limit of a large number of users, the throughput loss compared to the unconstrained sum-rate capacity tends to zero. As a side result, we show that, in this regime, the sum-rate of opportunistic beamforming converges to the optimal sum-rate achieved by DPC, which is a stronger result than the order-optimal results of (10, 13).