Signal Detection In Para Complex Normal Noise

In this paper we address target detection in correlated non-Gaussian noise. We introduce a powerful class of multivariate complex valued distribution that allows us to specify flexible non-Gaussian marginals, as well as correlation between the variables, while preserving circular symmetry. For noise belonging to this class, we study the fundamental problem of signal detection under different settings, and develop the needed (generalized) likelihood ratio tests. We also consider the problem of estimation of the noise parameters, and derive the maximum likelihood formulations. We compare the performance of the proposed methods using numerical simulations on synthetic data, and demonstrate the importance of using both correlations and non-Gaussiantiy.