Maximum sum rates via analysis of 2-user interference channel achievable rates region

Treating the interference as noise, the paper studies the first derivative of the frontiers which trace the achievable rates region of the 2-user interference channel. The achievable rates region in this case was found to be the convex hull of the union of two regions, each is bounded by a log-defined line. Those log-defined lines are characterized by holding one of the transmitters at full power, while the other transmitter sweeps its full power range. Maximizing the sum rates for the 2-user interference channel translates to the study of the first intersection point with lines of slope -1 approaching the rates region from positive infinity. The paper achieves the same result reported, that the maximum sum rates solution is one of three points: one user transmitting with full power while the other user is silent, or both users transmitting at full power simultaneously. The result is achieved through analysis of the objective function, while the solution presented herein follows from analyzing the first derivative of the rates region frontiers.