Multi-antenna downlink precoding with individual rate constraints: power minimization and user ordering

This paper addresses the problem of achieving a specified information rate for every user in a multi-user MIMO broadcast channel. We propose two methods for finding the set of transmit covariance matrices that minimizes the transmit power subject to the dirty-paper coding rates equal to some specified values. The first method applies to the case with a fixed encoding order and each receiver has one antenna. The second applies to the general case without a fixed encoding order and with time sharing taken into account, and has a complexity polynomial in the number of users