Optimal spectrum allocation in Gaussian interference networks

We consider a wireless network in which multiple users share a common spectrum band, modeled as a Gaussian interference network. Our objective is to choose the transmit power spectral density of each user to maximize the sum rate, subject to individual power constraints at each transmitter. This includes frequency-orthogonal transmissions and full-spreading with power control as special cases. Assuming single-user receivers and treating interference as noise, the resulting optimization problem is non-convex. Nevertheless, for a two-user model with flat-fading we completely characterize the optimal solution. In particular, we show that the optimal power allocation consists of each user using a piecewise constant power allocation over at most 3 frequency bands, where at most one band is shared by the two users. Extensions to more than two users and a distributed algorithm to implement the optimal allocation are also presented.