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 dependent on the radio interface and we pose special attention to the effect of the propagation delays 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 achieved for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We also provide a closed form expression for the global consensus, showing that the effect of delays is, in general, to introduce a bias in the final decision. The closed form expression is also useful to modify the consensus mechanism in order to get rid of the bias with minimum extra complexity. © 2007 IEEE.
Distributed decision through self-synchronizing sensor networks in the presence of propagation delays and nonreciprocal channels / Scutari, Gesualdo; Barbarossa, Sergio; Pescosolido, Loreto. - (2007), pp. 1-5. (Intervento presentato al convegno IEEE 8th Workshop on Signal Processing Advances in Wireless Communications, 2007 tenutosi a Helsinki; Finland nel June 17 - 20, 2007) [10.1109/SPAWC.2007.4401363].