Graphical generalization of power control in multiuser interference channels

In this paper, we present a graphical approach to the power control problem, and show how to find a near optimal solution to maximizing sum rate with individual power and user requirements by searching from the vertices of the power region. By leveraging our two previous results on the quasiconvexity and asymptotic nature of sum signal-to-interference-plus-noise ratio (SINR) and sum rate respectively, we determine an equivalency relationship between sum rate and sum SINR. As a related aside, we show that sum rate is indeed convex with respect to one varying power. Our conclusions are applicable to multiuser interference channels where resources are shared, and received powers vary by an order of magnitude or more, e.g., heterogeneous network whose transmitting powers span a magnitude of ranges.