Multi-User MISO Interference Channels with Single-User Detection: Optimality of Beamforming and the Achievable Rate Region

For a multi-user interference channel with multi-antenna transmitters and single-antenna receivers, by restricting each transmitter to Gaussian input and each receiver to a single-user detector, computing the largest achievable rate region amounts to solving a family of non-convex optimization problems. Recognizing the intrinsic connection between the signal power at the intended receiver and the interference power at the unintended receiver, the original family of non-convex optimization problems is converted into a new family of convex optimization problems. It is shown that, for such interference channels with each receiver implementing single-user detection, transmitter beamforming can achieve all boundary points of the achievable rate region.