Probability of detection for χ2 radar target in Weibull clutter

This article presents a method for calculating the threshold level and probability of detection of χ² radar targets, in the presence of Weibull clutter. It is based on mathematical models for general χ² targets [1], of which the four Swerling models are special cases. The model used for the clutter, including both the ground reflection variations and near ground propagation effects, has Weibull distribution [2]. Assuming the returns of the clutter are so distributed, the distribution parameters can either be estimated by the land type, or calculated from clutter measurements. Using these parameters, an expression is obtained for the probability of false alarm, Pfa, for a given single pulse threshold T1. This is inverted to provide an expression for the threshold T1 for any given Pfa. The probability density function (pdf) for target + clutter, assuming the two are uncorrelated, is the convolution of the two marginal pdf´s. This density is given in an integral form that has no known analytical solution [3]. However, using the expression for this pdf, probability of detection, Pd, is expressed as a definite integral with finite limits of this pdf. Using advanced mathematical software, e.g. Matlab^®, the definite double integral for Pd is numerically calculated. Simplification and generalization of the convolution formula via normalization, and some computational results conclude the presentation. These computations, without the need for tables and graphs, enable the researcher to use it conveniently in system performance evaluations as well as in scenario simulations for given environments as required.