For a multi-user interference channel with multi-antenna transmitters and
single-antenna receivers, by restricting 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.