Optimal power control in interference-limited fading wireless channels with outage-probability specifications

We propose a new method of power control for interference-limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explicitly takes into account the statistical variation of both the received signal and interference power and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair. We establish several results for this type of problem. We establish tight bounds that relate the outage probability caused by channel fading to the signal-to-interference margin calculated when the statistical variation of the signal and interference powers is ignored. This allows us to show that well-known methods for allocating power, based on Perron-Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (i.e., minimal) outage probability. We show that the problems of minimizing the transmitter power subject to constraints on outage probability and minimizing outage probability subject to power constraints can be posed as a geometric program (GP). A GP is a special type of optimization problem that can be transformed to a nonlinear convex optimization problem by a change of variables and therefore solved globally and efficiently by interior-point methods. We also give a fast iterative method for finding the optimal power allocation to minimize the outage probability.