Distributed detection of correlated random processes under energy and bandwidth constraints

We analyze a binary hypothesis testing problem built on a wireless sensor network (WSN). Using Large Deviation Theory (LDT), we compute the probability error exponents of a distributed scheme for detecting a correlated circularly-symmetric complex Gaussian process under the Neyman-Pearson framework. Using an analog scheme, the sensors transmit scaled versions of their measurements several times through a multiple access channel (MAC) to reach the fusion center (FC), whose task is to decide whether the process is present or not. In the analysis, we consider the energy constraint on each node transmission. We show that the proposed distributed scheme requires relatively few MAC channel uses to achieve the centralized error exponents when detecting correlated Gaussian processes.