Uniformly Most Powerful CFAR Test for Pareto-Target Detection in Pareto Distributed Clutter

In the Radar context, Pareto distribution has been validated for both sea clutter and aircraft target under specific scenarios. Primarily, after the sea clutter is modeled as Pareto, some heuristic constant-false-alarm-rate (CFAR) processors appeared in the literature with the same form of adaptive thresholding that is derived for conventional exponential vs. exponential hypothesis testing (i.e., for detecting Swerling-I target in exponentially distributed clutter). Statistical procedures obtained under such idealistic assumptions cease to be optimal when applied to newer models esp. heavy tail distributions like Pareto. So, even to accommodate a wide range of application scenarios, in addition to Pareto modeled aircraft detection, we solve for heavy tail in Pareto vs. Pareto distributed lots from the composite hypothesis testing framework. Here, we derive the uniformly most powerful (UMP) test that complies CFAR property with-respect to the tail-index, using the least favorable density (lfd) concept. We further validate this CFAR property from extensive simulation results, and attribute that the geometric mean (GM)-CFAR is the optimal test in UMP sense.