Asymptotic locally optimal detector for large-scale sensor networks under Poisson regime

We consider the distributed detection problem with a large number if identical sensors deployed over a region where the phenomenon of interest (POI) has different signal strength depending on the location. Each sensor makes a decision based on its own measurement of the spatially varying signal and the local decision of each sensor is sent to a fusion center through a multiple access channel. The fusion center decides whether the POI has occurred in the region, under a global size constraint in the Neyman-Pearson formulation. Assuming that the initial distribution of sensors is a homogeneous spatial Poisson process, we show that the Poisson process of 'alarmed' sensors satisfies the locally asymptotic normality (LAN) condition as the number of sensor goes to infinity and derive a new asymptotically locally most powerful detector for the spatially varying signal. We show that (1) an optimal test statistic is a weighted sum of local decisions, (2) the optimal weight function is the shape of the spatial signal, and (3) the exact value of the spatial signal is not required. For the case of independent, identical distributed (i.i.d.) sensor observation, we show that the counting-based detector is also asymptotic locally optimal.