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The authors consider the power control problem of maximizing the sum rate of a symmetric network of interfering links in Gaussian noise. They 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. They solve this non-convex problem by indentifying some underlying convex structure, and show that the solution is either one link blasting at full power, or all links blasting at full power. They 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 cases, as the cross-gain traverses a threshold.
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