Distributed power control for ad-hoc communications via stochastic nonconvex utility optimization

It is known that distributed power control in wireless ad-hoc networks is challenging, due to the inherent global coupling between concurrent transmissions interfering with each other. Observing that the globally optimal point lies on the boundary of the feasible region, we transform the utility maximization problem into a more structured problem in the form of maximizing the minimum weighted utility. Then, we develop a centralized algorithm for the minimum weighted utility maximization problem as a benchmark. Next, by using extended duality theory, we introduce penalty multipliers and decompose the minimum weighted utility maximization problem into subproblems for individual users. Appealing to the simulated annealing method, we propose a distributed stochastic power control algorithm, where each user stochastically adjusts its target utility to improve the overall system utility. Although the underlying optimization problem is nonconvex, our algorithm can guarantee global optimality although the convergence rate may be slow due to the usage of simulated annealing. We improve the convergence rate further by devising an enhanced algorithm based on the geometric cooling schedule.