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

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 double-step consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters.

💡 Research Summary

The paper addresses the fundamental problem of achieving globally optimal estimation or detection in a distributed sensor network where each node possesses only its own local measurement. The authors propose a novel self‑synchronizing algorithm based on linearly coupled integrators. Each sensor runs a first‑order integrator whose state is initialized with its local observation. Nodes exchange their states over wireless links; the exchanged information is subject to asymmetric channel gains and bounded propagation delays that depend on the physical geometry of the network. The interaction topology is modeled as a directed weighted graph (G(V,E)) whose adjacency matrix captures both the channel‑induced asymmetry and the delay‑induced phase shift.

The dynamics of the whole network are described by a set of delay differential equations:

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