Differentiated Rate Scheduling for MIMO Broadcast Channels with Estimation Errors

We consider the throughput of a MIMO Gaussian broadcast channel with two generalizing assumptions: (1) differentiated quality of service, in the sense that the rates required by different users must satisfy certain rational constraints, and (2) imperfect channel side information (CSI), where we assume that the estimate of the underlying channel has some error with known distribution. Theoretically, with full and perfect CSI in hand, dirty paper coding (DPC) can achieve any point on the capacity region, including the non-symmetrical boundary points. However, the full CSI requirement and the computational complexity of DPC motivates the development of simpler schemes which require little feedback from the users and can obtain a large portion of the capacity of the channel. In this paper we will look at the throughput and rate ratio achieved by schemes based on the idea of opportunistic beam-forming and employing a rate back-off mechanism in order to maximize the throughput in the case of imperfect CSI. We will determine the optimal scheduling parameters and will show the order optimality of these schemes in the regime of large number of users.