Broadcasting with channel state information

We consider the problem of transmit downlink beamforming for wireless transmission in the context of certain broadcasting or multicasting applications wherein channel state information (CSI) is available at the transmitter, and a common message is to be transmitted to the users. Unlike the usual "blind" isotropic broadcasting scenario, the availability of CSI allows transmit optimization. We adopt a minimum transmission power criterion, subject to prescribed minimum received signal-to-noise ratio (SNR) at each of the intended receivers. We also consider a related max-min SNR "fair" problem formulation subject to a transmit power constraint. The basic problem is non-convex and thus difficult to solve; however, we show that a suitable reformulation allows the application of semidefinite relaxation (SDR) techniques. SDR yields a (generally approximate) solution, but in many cases our solution is optimal, and in most cases it is within 3-4 dB from the optimal solution, which is often good enough in our intended applications. While the focus of the paper is on a wireless communication scenario, we also discuss related problems in downstream preceding for broadcasting in digital subscriber line systems.