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. Thus the random source is either noise only or a deterministic signal plus noise. In particular, noise models for which the optimal system employs marginal likelihood ratio tests are characterized. A sufficient condition is obtained on the noise mean and covariance under which the optimal binary quantizers are contiguous partitions of the marginal observation space. It is also examined whether the sufficient condition discussed is necessary. A subsequent question is asked whether the symmetry in the signal and noise models imply symmetry in the optimal solution. This is found to be true. Hence, an optimal design is further simplified.