Dual Methods for Power Allocation for Radios Coexisting in Unlicensed Spectra

The power allocation that maximizes the sum rate of transceivers operating in the same frequency band is a difficult non-convex problem. Lack of a convex structure excludes the direct application of Lagrangian dual techniques as the duality gap might not be zero. This paper advances current knowledge by introducing three significant steps in finding a solution. First, we show that for transceivers operating under a total power constraint, the maximum sum rate occurs at the boundary of the feasible set formed by the hyper plane representing the power constraint. This conclusion is nontrivial considering that we are dealing with an interference limited system. Second, we prove that the duality gap is zero for this problem, despite the lack of concavity of the objective. We do this by showing that the maximum sum rate is concave in the power constraint. Third, we propose an iterative algorithm that finds the optimal power allocation by solving the dual problem. Simulation results are provided to support the theorems proven in the paper as well as to demonstrate the convergence of the algorithm to the global maximum sum rate. Results of the algorithm are also compared with solutions based on Game theory.