Achieving consensus in self-organizing wireless sensor networks: the impact of network topology on energy consumption

Achieving consensus on common global parameters through totally decentralized algorithms is a topic that has attracted considerable attention in the last few years. Several algo-rithms have been developed, among which the most popular is the average consensus method. The main advantage of these approaches is that they do not require a fusion center. But, on the other hand, they are typically based on iterative algo-rithms, whose energy consumption is proportional to the time necessary to achieve consensus. This time depends on the net-work topology, as well as on the transmit power of each node. In this paper, we show that there exists an optimal transmit power that minimizes the overall energy consumption neces-sary to achieve the global estimate within a given accuracy and that this power depends on the network topology. Index Terms — Average consensus, energy consumption, algebraic connectivity, distributed estimation