Closed-form error exponent for the Neyman-Pearson fusion of Markov local decisions

In this correspondence, we derive a closed-form expression of the error exponent associated with the binary Neyman-Pearson test performed at the fusion center of a distributed detection system where a large number of local detectors take dependent binary decisions regarding a specific phenomenon. We assume that the sensors are equally spaced along a straight line, that their local decisions are taken with no kind of cooperation, and that they are transmitted to the fusion center over an error free parallel access channel. Under each one of the two possible hypothesis, H₀ and H₁ the correlation structure of the local binary decisions is modelled with a first-order binary Markov chain whose transition probabilities are linked with different physical parameters of the network. Through different simulations based on the error exponent and a deterministic physical model of the aforementioned transition probabilities we study the effect of network density on the overall detection performance.