Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Asymmetric Channels

Abstract

In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights (possibly) dependent on the radio channels and we pose special attention to the effect of the propagation delay occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is reached with exponential convergence speed for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We provide a closed form expression for the global consensus, showing that the effect of delays is, in general, the introduction of a bias in the final decision. Finally, we exploit our closed form expression to devise a doublestep consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters.

Hopfield-Like Neural Nets and Sensor Networks

“…This issue is considered in [6] in the case of linear non-reciprocal sensor networks. The convergence time is shown to be inversely proportional to the second smallest eigenvalue of a suitable matrix associated with the graph modelling the interaction among sensors.…”

Distributed Estimation of Channel Gains in Wireless Sensor Networks

“…For communications between the nodes during the training phase and the channel estimation phase which follows the training phase, we use TDMA based medium access control [9] which increases the energy savings by avoiding collisions and retransmissions. These energy savings result at the cost of synchronization which could be achieved using the schemes proposed in the literature [10] [11] [12] [13].…”

Dynamic average consensus over random networks with additive noise

“…It is well known that if the graph is strongly connected, the corresponding Laplacian matrix has only one eigenvalue of zero and all other eigenvalues are in open right half plane. 1 Although weaker assumptions on connectivity leads to consensus, e.g., the topology only contains a spanning tree, such assumption does not ensure that the final consensus value contains information of all nodes, see, e.g., [16]. Besides, the eigenvector associated with the zero eigenvalue is 1.…”