Egalitarian fairness framework for joint rate and power optimization in wireless networks

How do we efficiently and fairly allocate the resource in a wireless network? We study a joint rate and power control optimization to achieve egalitarian fairness (max-min weighted fairness) in multiuser wireless networks. The key challenge to optimizing the fairness of maximizing the data rates for all the users is the nonconvexity and of the problem. We exploit the nonlinear Perron-Frobenius theory and nonnegative matrix theory to solve this nonconvex resource control problem. A fixed-point algorithm that resembles a nonlinear version of the Power Method in linear algebra and converges very fast to the optimal solution is also proposed.