Maximizing the sum rate in symmetric networks of interfering links under flat power constraints

We consider the power control problem of maximizing the sum rate of a symmetric network of interfering links in Gaussian noise. We consider a static network: there is no time-varying fading and the power allocation is also mandated to be time and frequency flat. All transmitters have a maximum allowable average transmit power, the same for all transmitters. We solve this nonconvex problem by identifying some underlying convex structure, and show that the solution is either one link blasting at full power, or all links blasting at full power. We provide a characterization of the solution in terms of the level of cross-gain between the interfering links. There is a phase transition between these two states, as the cross-gain traverses a threshold.