Max-min weighted SIR for MIMO downlink system: Optimality and algorithms

Designing fast algorithms that adapt the transmit and receive power and beamformers to optimize performance for different users is important in wireless MIMO downlink systems. This paper studies the max-min weighted SIR problem in the downlink, where multiple users are weighted according to priority and are subject to a total power constraint. The difficulty of this nonconvex problem is compounded by the coupling in the transmit and receive beamformers, thereby making it hard to optimize in a distributed fashion. We first show that this problem can be optimally and efficiently computed using a fast algorithm when the channels are rank-one. The optimal transmit and receive power and beamformers are also derived analytically. We then exploit the MIMO uplink-downlink duality to adapt our algorithm to compute a local optimal solution for channels with general rank.