On the Optimality of Multiuser Zero-Forcing Precoding in MIMO Broadcast Channels

In this paper, we consider a multiuser Gaussian broadcast channel where the base station and the users both are equipped with multiple antennas. The problem of optimal zero-forcing (ZF) precoding design subject to sum power constraint is discussed. Block diagonalization (BD) is applied as the ZF precoding method. We consider two common optimization criteria: maximum throughput and maximal fairness, where by maximizing fairness we mean maximizing the minimum rate among all users. Under these criteria, the structure of the optimal BD precoders is presented and analyzed. It is shown that the conventional BD precoding design with sum power constraint is indeed optimal under the throughput and fairness criteria.