Modeling Information Flows in Distributed Sensor Networks: Chernoff Information Azimuth Spectrum

Consider a distributed sensor network (DSN) with randomly deployed sensors for binary detection of a phenomenon of interest (PoI). A fusion center (which may be a sensor itself) monitors the PoI using both the directly acquired PoI data and the wireless communication signals conveying binary decisions about the PoI from other distributed sensors. To address this problem, we first look into a PoI with specified statistics and present the modeling paradigm of Chernoff information azimuth spectrum (CIAS) to provide a compact, space-domain representation of asymptotic error exponents in DSNs. The CIAS is not only a function of DSN geometry but also tied inherently to the PoI and, in particular, its position and strength. This school of thought applies an analogous approach to the description method of directional propagation channels. Second, we propose the concept of outage classifier to characterize the detection performance when the PoI distribution is unspecified and define the corresponding outage CIAS (O-CIAS). Third, by specifying the decision strategies at intermediate cognitive sensors based upon either random selection of classifier outputs or Boolean operation in the receiver operating characteristics (ROC) space, we define the effective CIAS (E-CIAS). The above theoretical framework is then elaborated in light of geometry-based modeling of sensor placement. Finally, we present numerical results to exemplify the properties of the CIAS and explore its potential application for system design and analysis.