Distributed power control in wireless ad hoc networks using message passing: Throughput optimality and network utility maximization

This paper presents an algorithm for distributed power control and scheduling over wireless ad hoc-networks, where the data rate on each link depends on the transmission power levels at interfering links (non-convex coupling between link data rates). In this paper, we first consider a K-hop interference model. We describe a message passing algorithm that finds an optimal power allocation (schedule) in the case of line networks with a time complexity (in number of nodes N) that grows as N for line networks. Further, we show that this algorithm, when combined with appropriate congestion-control and routing algorithms results in throughput-optimality and utility maximization over wireless networks. We further study a complete physical interference model, where our algorithms provide e-optimal solutions. Our results can also be extended to grid networks.