Consensus Based Detection in Sensor Networks : Topology Optimization under Practical Constraints

We consider a distributed hypothesis testing problem in sensor networks with possibly correlated sensor observations. The intersensor communication is constrained by the underlying communication network to sensors exchanging information only with their neighbors. The network has no central fusion center. We show that, under reasonable assumptions, the global test statistic can be computed locally at each sensor by a distributed iterative consensus algorithm. We consider the problem of optimizing the sensor network topology with respect to the rate of convergence of iterative consensus under different practical design constraints. For nonrandom topologies with fixed intersensor communication costs, the class of Ramanujan graphs is optimal when the underlying communication graph is regular, the communication is noiseless, and the intersensor communication costs are constant across the network. In contrast, when communication among links exhibits different costs, links may fail, the optimal topology under an overall communication cost constraint is obtained by solving a semidefinite programming optimization problem.