Multiuser MIMO relaying under quality of service constraints

We consider a wireless communication scenario with K source-destination pairs communicating through several half-duplex amplify-and-forward relays. We design the relay beamforming matrices by minimizing the total power transmitted from all the relays subject to quality of service constraints on the received signal to interference-plus-noise ratio at each destination node. We propose a novel method for solving the resulting nonconvex optimization problem in which the problem is decomposed into a group of second-order cone programs (SOCPs) parameterized by K real parameters. Grid search or nested bisection can be used to search for the optimal values of these parameters. We provide numerical simulations showing the superior performance of the proposed algorithms compared to earlier suboptimal approximations and their ability to approach the globally optimal solution of the non-convex problem.