Globally optimal tin strategies with time-sharing in the MISO interference channel

The capacity region of the two-user multiple-input single-output (MISO) interference channel is an open problem, and various achievable rate regions have been discussed in the literature. In this paper, we assume that the transmit signals are Gaussian and that the receivers treat interference as noise (TIN), i.e., we focus on the TIN rate region with Gaussian inputs. Our aim is to compute the rate region boundary for the case of proper Gaussian signaling with time-sharing, i.e., the data rates and required transmit powers may be averaged over several transmit strategies. To this end, we apply methods from convex optimization (in particular Lagrange duality and the cutting plane algorithm), and propose the novel mixed monotonic programming (MMP) framework to treat the arising nonconvex subproblems. The obtained TIN rate region with proper Gaussian signals and time-sharing is significantly larger than previously computed TIN rate regions with proper Gaussian signals, and can even outperform TIN strategies with improper signaling.