  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.
