Distributed stochastic power control in ad hoc networks: a nonconvex optimization case

Signal-to-interference-plus-noise-based power allocation in wireless ad hoc networks is inherently a nonconvex optimization problem because of the global coupling induced by the co-channel interference. To tackle this challenge, we first show that the globally optimal point lies on the boundary of the feasible region. This property is utilized to transform the utility maximization problem into an equivalent max-min problem with more structure. By using extended duality theory, penalty multipliers are introduced for penalizing the constraint violations, and the minimum weighted utility maximization problem is then decomposed into subproblems for individual users to devise a distributed stochastic power control algorithm, where each user stochastically adjusts its target utility to improve the total utility by simulated annealing (SA). The proposed distributed power control algorithm can guarantee global optimality at the cost of slower convergence due to SA involved in the global optimization. The geometric cooling scheme with suitable choice of penalty parameters is then used to improve the convergence rate. Next, by integrating the stochastic power control approach with the back-pressure algorithm, we develop a joint scheduling and power allocation policy to stabilize the queueing systems under random packet traffic. Finally, we generalize the above distributed power control algorithms to multicast communications, and show their global optimality for multicast traffic.