Likelihood ratio partitions for distributed signal detection in correlated Gaussian noise

A distributed detection system is considered in which two sensors and a fusion center jointly process the output of a random data source. It is assumed that the null and alternative distributions are spatially correlated Gaussian, differing in the mean; thus the random source is either noise only or a deterministic signal plus noise. The authors characterize noise models for which the optimal system employs marginal likelihood ratio tests. In the setup where each sensor draws one local observation, we succeed in obtaining a sufficient condition on the noise mean and covariance under which the optimal binary quantizers are contiguous partitions of the marginal observation space