| Cellular wireless communication systems are becoming increasingly interference-limited due to shrinking cell sizes that are needed to accommodate growing user density. Similarly, in dense ad hoc network interference rather than the thermal noise often limits performance. Handling interference optimally by techniques such as coding and multi-user detection remains a theoretical challenge and computationally complex, and therefore current generation wireless systems typically treat the interference as noise.;We study a simple n---user interference channel where there are n transmit-receive links which interfere with each other. The interference is treated as noise, and the transmitters are subject to a maximum power constraint. The achievable rates region is found as the convex hull of n hyper-surfaces, characterized with each user transmitting at full power. The convex hull dictates time-sharing to be employed depending on the convexity characterization of such hyper-surfaces.;Hence, the characteristics of the interference rates region are studied to determine the conditions when convex, concave or mixed regions occur. Specific operating point solution on the frontier of the achievable rates region is then derived to meet metrics of interest such as the maximum sum rates (greedy scheme), and the maximum minimum rate (fairness scheme). For the 2---user interference channel, the maximum sum rates is shown to always result in a binary power control solution (nodes transmitting at maximum power or being silent). While this solution is easy to find in a 2---user channel, for the n---user channel, a sequential geometric programming is applied to solve the problem efficiently. The maximum minimum rate problem, on the other hand results in solutions that need transmit power control, and sometimes, also time sharing. Geometric programming is used in conjunction with evaluating time-sharing options to determine the solution.;Constraining the transmitters to use only zero or full power results in the formation of 2n -- 1 corner points in the rates region. A crystallized rates region is constructed by forming the convex hull of connecting those corner points via time-sharing. We use game theoretic concepts such as correlated equilibrium to converge to an operating point on the crystallized frontier.;We thus show that power control and time sharing are the tools to optimize throughput for the interference channel under study. Finally, we demonstrate an application of these concepts to cellular communication systems to significantly improve their performance. |
