Generalized CFAR property for radar detection

We consider adaptive detection of a signal embedded in additive disturbance whose multivariate distribution belongs to a very general class, including many statistical models commonly adopted for radar interference. We introduce the concept of generalized Constant False Alarm Rate (CFAR) and show that a class of receivers sharing some invariances complies with the quoted property. Then, we devise the Generalized Likelihood Ratio Test (GLRT) and prove that, under some mild technical conditions, it coincides with that obtained under the Gaussian assumption for the observations. At the analysis stage, we focus on a compound matrix variate model for the disturbance component, which is a natural generalization of the Spherically Invariant Random Vector (SIRV). In this context, we assess the performance of some well known invariant decision rules.