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

We consider a distributed detection system formed by a large number of local detectors and a fusion center that performs a Neyman-Pearson fusion of the binary quantizations of the sensor observations. The aforementioned local decisions are taken with no kind of cooperation and transmitted to the fusion center over error free parallel access channels. Furthermore, the devices are located on a rectangular lattice so that sensors belonging to a specific row or column are equally spaced. For each hypothesis Ho and H\, the correlation structure of the local decisions is modelled with a two-dimensional causal field where the rows and columns are outcomes of the same first-order binary Markov chain. Under this scenario, we derive a closed-form error exponent for the Neyman-Pearson fusion of the local decisions. Afterwards, using the derived error exponent we study the effect of different design parameters of the network on its overall detection performance.