Exact Closed-Form P_fa Expressions for CA- and GO-CFAR Detectors in Gamma-Distributed Radar Clutter

In this correspondence, two exact closed-form expressions for the probability of false alarm have been derived assuming a homogeneous Gamma distributed clutter. These expressions concern both the cell averaging CFAR (CA-CFAR) and the greatest of CFAR (GO-CFAR) detectors. As it will be shown, the proposed expressions are given in terms of the Gauss hypergeometric function and the second Appell function. Our expressions are then examined and validated numerically, by comparing them to their counterparts computed using numerical integrals and Monte-Carlo simulations, considering various scenarios.