Signal Detection in Complex Structured Para Normal Noise

In this paper, we address target detection in correlated non-Gaussian noise. We introduce a new class of multivariate complex valued distributions 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 estimation of the noise parameters, and derive the maximum likelihood formulations. We evaluate the merit of our approach using numerical simulations on synthetic and real data, and clearly demonstrate the advantage of using both correlations and non-Gaussianity.