Maximizing Sum Rates in Gaussian Interference-limited Channels

We study the problem of maximizing sum rates in a Gaussian interference-limited channel that models multiuser communication in a CDMA wireless network or DSL cable binder. Using tools from nonnegative irreducible matrix theory, in particular the Perron-Frobenius Theorem and the Friedland-Karlin inequalities, we provide insights into the structural property of optimal power allocation strategies that maximize sum rates. Our approach is similar to the treatment of linear models in mathematical economies, where interference is viewed in the context of competition. We show that this maximum problem can be restated as a maximization problem of a convex function on a closed convex set. We suggest three algorithms to find the exact and approximate values of the optimal sum rates. In particular, our algorithms exploit the eigenspace of specially crafted nonnegative {\it interference matrices}, which, with the use of standard optimization tools, can provide useful upper bounds and feasible solutions to the nonconvex problem.