  In this article, we consider the detection of a localized source emitting a
signal using a wireless sensor network (WSN). We consider that geographically
distributed sensor nodes obtain energy measurements and compute cooperatively
and in a distributed manner a statistic to decide if the source is present or
absent without the need of a central node or fusion center (FC). We first start
from the continuous-time signal sensed by the nodes and obtain an equivalent
discrete-time hypothesis testing problem. Secondly, we propose a fully
distributed scheme, based on the well-known generalized likelihood ratio (GLR)
test, which is suitable for a WSN, where resources such as energy and
communication bandwidth are typically scarce. In third place, we consider the
asymptotic performance of the proposed GLR test. The derived results provide an
excellent matching with the scenario in which only a finite amount of
measurements are available at each sensor node. We finally show that the
proposed distributed algorithm performs as well as the global GLR test in the
considered scenarios, requiring only a small number of communication exchanges
between nodes and a limited knowledge about the network structure and its
connectivity.
