Square-Law Detection of Exponential Targets in Weibull-Distributed Ground Clutter

Abstract

Modern radar systems use square-law detectors to search and track fluctuating targets embedded in Weibull-distributed ground clutter. However, the theoretical performance analysis of square-law detectors in the presence of Weibull clutter leads to cumbersome mathematical formulations. Some studies have circumvented this problem by using approximations or mathematical artifacts to simplify calculations. In this work, we derive a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-form</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exact</i> expression for the probability of detection (PD) of a square-law detector in the presence of exponential targets and Weibull-distributed ground clutter, given in terms of the Fox H-function. Unlike previous studies, no approximations nor simplifying assumptions are made throughout our analysis. Furthermore, we derive a fast convergent series for the referred PD by exploiting the orthogonal selection of poles in Cauchy’s residue theorem. In passing, we also obtain closed-form solutions and series representations for the probability density function and the cumulative distribution function of the sum statistics that govern the output of a square-law detector. Numerical results and Monte Carlo simulations corroborate the validity of our expressions.