Constant false alarm rate detection in Spherically Invariant Random Processes

In this paper, we use the theory of generalized likelihood ratio tests (GLRT) to study the adaptive version of the asymptotical Bayesian Optimum Radar Detector (BORD) built with a covariance matrix estimate. We investigate its properties, when the noise is modelled as a non-Gaussian complex process, such as Spherically Invariant Random Process (SIRP). We derive, for appropriate covariance matrix estimates, the analytical expression of the relationship between the Probability of False Alarm (PFA) and the detection threshold. We show that this detector is SIRP-CFAR: the GLR distribution does not depend on the SIRP characteristics.