  We consider a distributed detection problem where measurements at each sensor
follow a general parametric distribution. The network does not have a central
processing unit or fusion center (FC). Thus, each node takes some measurements,
does some processing, exchanges messages with its neighbors and finally makes a
decision (typically the same for all nodes) about the phenomenon of interest.
The problem can be formulated as a composite hypothesis test with unknown
parameters where, in general, a uniformly most powerful test does not exist.
This leads naturally to the use of the Generalized Likelihood Ratio (GLR) test.
As the measurements follow a general parametric distribution (which could model
spatial dependence of the data), the implementation of fully-distributed
detection procedures could be demanding in network resources. For this reason,
we study the use of a simpler test (referred as L-MP) which uses the product of
the marginals of the measurements taken at each node, where the unknown
parameters are easily estimated with only local measurements. Although this
simple proposal still requires network-wide cooperation between nodes, the
number of communications is significantly reduced with respect to the GLR test,
making it a suitable choice in severely resource-constrained sensor networks.
This simpler test does not exploit the full parametric model of data, so, it
becomes important to analyze its statistical properties and its potential
performance loss. This is done through the analysis of the L-MP asymptotic
distribution. Interestingly, despite the fact that the L-MP is simpler and more
efficient to implement than the GLR test, we obtain some conditions under which
the L-MP has superior asymptotic performance to the GLR test. Finally, we
present numerical results for a fully-distributed spectrum sensing application
for cognitive radios.
