Sensor Networks With Random Links: Topology Design for Distributed Consensus

• Published in: IEEE transactions on signal processing Vol. 56; no. 7; pp. 3315 - 3326
• Main Authors: Kar, S., Moura, J.M.F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Applied sciences; Consensus; Convergence; Cost function; Costs; Distributed algorithms; Distributed computing; distributed decision; Exact sciences and technology; Failure; graph; Information, signal and communications theory; Iterative algorithms; Laplacian; Links; Miscellaneous; Network topology; Networks; Operations research; Optimization; sensor networks; Sensors; Signal processing; Signal processing algorithms; spectral graph theory; Studies; Sufficient conditions; Telecommunication network reliability; Telecommunications and information theory; Topology; Performance evaluation; Necessary and sufficient condition; convergence; topology; Information rate; Graph theory; sensor networks; Algorithm; Failures; Convex programming; Information transmission; Laplacian; Consensus; graph; Optimal design; Constrained optimization; spectral graph theory; Simulation; Spectral theory; Convergence rate; Signal processing; Data communication; Sensor array; distributed decision
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2008.920143

In a sensor network, in practice, the communication among sensors is subject to: 1) errors that can cause failures of links among sensors at random times; 2) costs; and 3) constraints, such as power, data rate, or communication, since sensors and networks operate under scarce resources. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. We model the network as a Bernoulli random topology and establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail. In particular, a necessary and sufficient condition is for the algebraic connectivity of the mean graph topology to be strictly positive. With these results, we show that the topology design with random link failures, link communication costs, and a communication cost constraint is a constrained convex optimization problem that can be efficiently solved for large networks by semidefinite programming techniques. Simulations demonstrate that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the performance of a non-random network at a fraction of the communication cost.