Monotonic optimization framework for the MISO IFC

Resource allocation and transmit optimization for the multiple-antenna Gaussian interference channel are important but difficult problems. Recently, there has been a large interest in algorithms that find operating points which are optimal in the sum-rate, proportional-fair, or minimax sense. Finding these points entails solving a nonlinear, non-convex optimization problem. In this paper, we develop an algorithm that solves these problems exactly, to within a prescribed level of accuracy and in a finite number of steps. The main idea is to rewrite the objective functions so that methods for monotonic optimization can be used. More precisely, we write each objective function as a difference between two functions which are strictly increasing over a normal constraint set. The so-obtained reformulated, equivalent problem can then be solved efficiently by using so-called polyblock optimization. Numerical examples illustrate the advantages of the proposed framework compared to an exhaustive grid search.