Max-min utility optimization in load coupled interference networks

We propose a novel utility optimization algorithm for wireless networks modeled by systems of nonlinear equations based on the load at the base stations. Unlike previous studies, the algorithm solves a max-min utility optimization problem over the joint space of network load, transmit power, and rates. In more detail, our first main contribution is to show that, in the optimum, users operate at the same rate, base stations are fully loaded, and at least one base station transmits at the maximum power. This characterization of the optimal solution enables a reformulation of the optimization task as a conditional eigenvalue problem associated with a concave mapping that relates the transmit power to the network load. With this reformulation, an efficient iterative solver becomes readily available. Our second main contribution is the derivation of a simple lower bound for conditional eigenvalues of general positive concave mappings. These bounds are of particular interest to network designers, because conditional eigenvalues can often be related to the optimal rates (or the optimal signal-to-interference-noise ratio) of a large class of utility optimization problems, and, in this paper, these bounds are used to derive performance limits of load coupled networks.