  We study the two-user multiple-input single-output (MISO) Gaussian
interference channel where the transmitters have perfect channel state
information and employ single-stream beamforming. The receivers are capable of
performing successive interference cancellation, so when the interfering signal
is strong enough, it can be decoded, treating the desired signal as noise, and
subtracted from the received signal, before the desired signal is decoded. We
propose efficient methods to compute the Pareto-optimal rate points and
corresponding beamforming vector pairs, by maximizing the rate of one link
given the rate of the other link. We do so by splitting the original problem
into four subproblems corresponding to the combinations of the receivers'
decoding strategies - either decode the interference or treat it as additive
noise. We utilize recently proposed parameterizations of the optimal
beamforming vectors to equivalently reformulate each subproblem as a
quasi-concave problem, which we solve very efficiently either analytically or
via scalar numerical optimization. The computational complexity of the proposed
methods is several orders-of-magnitude less than the complexity of the
state-of-the-art methods. We use the proposed methods to illustrate the effect
of the strength and spatial correlation of the channels on the shape of the
rate region.
