Efficient computation of the Pareto boundary for the MISO interference channel with perfect CSI

We consider the two-user multiple-input single-output (MISO) interference channel and the rate region which is achieved when the receivers treat the interference as additive Gaussian noise and the transmitters have perfect channel state information (CSI). We propose a computationally efficient method for calculating the Pareto boundary of the rate region. We show that the problem of finding an arbitrary Pareto-optimal rate pair, along with its enabling beamforming vector pair, can be cast as a sequence of second-order cone programming (SOCP) feasibility problems. The SOCP problems are convex and they are solved very efficiently using standard off-the-shelf (namely, interior-point) algorithms. The number of SOCP problems that must be solved, for the computation of a Pareto-optimal point, grows only logarithmically with the desired accuracy of the solution.