New results on coherent radar target detection in heavy-tailed compound-Gaussian clutter

In this work we prove that if the texture of compound-Gaussian clutter is modeled by an Inverse-Gamma distribution, the optimum detector is the optimum Gaussian matched filter detector compared to a data-dependent threshold that varies linearly with a quadratic statistic of the data. The compound-Gaussian model presented here varies parametrically from the Gaussian clutter model to a clutter model whose tails are evidently heavier than any K-distribution model. Moreover, we also show that the GLRT, which is a popular suboptimum detector due to its CFAR property, is in fact an optimum detector for our clutter model in the limit as the tails get extremely heavy.