Topology Optimization For Energy-Efficient Communications In Consensus Wireless Networks

Over the past years there has been an increasing interest in developing distributed computation methods over wireless networks. A new communication paradigm has emerged where distributed algorithms such as consensus have played a key role in the development of such networks. A special case are wireless sensor networks (WSN) which have found application in a large variety of problems such as environmental monitoring, surveillance, or localization, to cite a few. One major design issue in WSNs is energy efficiency. Nodes are typically battery-powered devices and thus, it is critical to make a proper use of the scarce energy resources. This fact motivates the search for optimal conditions that favor the communication environment. It is well known that the rate at which the information is spread across the network depends on the topology of the network and that finding the optimal topology is a hard combinatorial problem. However, using convex optimization tools, we propose a method that tries to find the optimal topology in a consensus wireless network that uses broadcast messages. Our results show that exploiting the broadcast nature of the wireless channel leads to more energy efficient configurations than using dedicated unicast messages and that our algorithm performs very close to the optimal solution.