On fully-distributed composite tests with general parametric data distributions in sensor networks

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.