Monotonic Optimization Framework for the Two-User MISO Interference Channel

Resource allocation and transmit optimization for the multiple-antenna Gaussian interference channel are important but difficult problems. The spatial degrees of freedom can be exploited to avoid, align, or utilize the interference. In recent literature, the upper boundary of the achievable rate region has been characterized. However, the resulting programming problems for finding the sum-rate, proportional fair, and minimax (egalitarian) operating points are non-linear and non-convex. In this paper, we develop a non-convex optimization framework based on monotonic optimization by outer polyblock approximation. First, the objective functions are represented in terms of differences of monotonic increasing functions. Next, the problems are reformulated as maximization of increasing functions over normal constraint sets. Finally, the idea to approximate the constraint set by outer polyblocks is explained and the corresponding algorithm is derived. Numerical examples illustrate the advantages of the proposed framework compared to an exhaustive grid search approach.