Asymptotic performance of a distributed detection system in correlated Gaussian noise

In this correspondence we consider the detection of a constant signal in noise with a large set of geographically dispersed sensors. The noise at the sensors are correlated Gaussian. Two correlation models are considered: one where the correlation coefficient between any two sensors decreases geometrically as the sensor separation increases, and the other where the correlation coefficient between any two sensors is a constant. For both correlation models, the asymptotic (as the number of sensors becomes large) performances of a distributed detection system and a central system are examined.