Closed-form solutions to the Pareto boundary and optimal distributed strategy for the two-user MISO interference channel

In this paper, the achievable rate region of the two-user multiple-input single-output (MISO) interference channel (IC) is considered. All points on the Pareto boundary can be obtained by solving the weighted sum rate maximization problem for some weighted coefficients. Unfortunately, the problem is non-convex and difficult to solve without performing an exhaustive search. Through minimizing the interference power leaked to the other receiver for fixed useful signal power received at the intended receiver, the non-convex optimization problem can be converted into a family of convex optimization problems. After some conversion, the closed-form solutions to all Pareto optimal points are derived using the Lagrange duality theory for the two-user MISO interference channel, and the only computation involved is to solve a basic quadratic equation. In order to reduce the complexity of the algorithm, a distributed iterative beamforming strategy using only local channel state information (CSI) at each transmitter is proposed which can also achieves a Pareto optimal outcome when the iteration stepsize is small enough. The results are validated via numerical simulations.