New Saddle-Point Technique for Non-Coherent Radar Detection With Application to Correlated Targets in Uncorrelated Clutter Speckle

This paper presents a novel implementation of the saddle-point technique for calculating the non-coherent detection probability of targets by airborne surveillance radar in the presence of pulse-to-pulse correlation. It is based on the inverse Laplace transform of the moment generating function for the returned power distribution by means of integration along the path of steepest descent. To illustrate the methodology, the problem of non-coherent pulse integration for a target with gamma-fluctuating partially correlated radar cross-section embedded within compound surface clutter with uncorrelated speckle is revisited. This situation arises for maritime or overland surveillance radar with sufficient frequency agility to fully decorrelate the clutter speckle but not the fluctuations of the target radar cross-section. An exact method and a hierarchy of approximations are described, all of which perform well for this problem. Monte Carlo simulation at the quadrature component level is used to verify the results.