GLRT-Based Coherent Detection in Sub-Gaussian Symmetric Alpha-Stable Clutter

Abstract

This letter presents a generalized likelihood ratio test (GLRT)-based adaptive detector specially for the sub-Gaussian symmetric alpha-stable (SGS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \text{S}$ </tex-math></inline-formula> ) sea clutter background. Since the probability density function (PDF) of SGS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \text{S}$ </tex-math></inline-formula> distribution cannot be expressed as a closed-form expression in terms of the elementary function, the research on target detectors in alpha-stable clutter background is very limited. In this letter, firstly, the Fox’s H-function is adopted to formulate the PDF of the SGS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \text{S}$ </tex-math></inline-formula> distribution so that the PDF of SGS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \text{S}$ </tex-math></inline-formula> distribution can be expressed as a closed form in terms of H-function. Then, the GLRT-based detector in alpha-stable clutter is designed based on the two-step GLRT criterion and the closed-form expression of the test statistics in terms of the H-function is given. Experimental results based on the simulated data and the measured data verify the effectiveness of the proposed detector.