Asymptotic Performance of the Geometric Mean Detector in Pareto Distributed Clutter

Several independent investigations have demonstrated the validity of the Pareto distribution as a model for X-band high-resolution maritime surveillance radar intensity clutter returns. This has included validation of it for data collected from fixed costal surveillance radars, as well as airborne maritime surveillance radars. Consequently, there has been a steady development of radar detection schemes under such a clutter model assumption, both from a coherent and noncoherent detection perspective. One of the major initiatives at the Australian Defence Science and Technology Group has been to investigate the development of sliding window constant false alarm rate detectors for operation in a Pareto distributed clutter. A transformation approach has provided this capability, and one of the observations has been that a geometric mean detector, derived via this approach, tends to perform ideally when the number of clutter statistics in the clutter range profile is large. This letter examines this phenomenon and provides a mathematical explanation for it.