Highly Accurate Closed-Form Approximation for the Probability of Detection of Weibull Fluctuating Targets in Noncoherent Detectors

In this article, we derive a highly accurate approximation for the probability of detection of a noncoherent detector operating with Weibull fluctuation targets. To do so, we assume a pulse-to-pulse decorrelation during the coherent processing interval. Specifically, the proposed approximation is given in terms of a closed-form expression derived in terms of the Fox’s
$H$
-function, for which we also provide a portable and efficient MATHEMATICA routine, and a fast converging series obtained through a comprehensive calculus of residues. Both solutions are fast and provide very accurate results. In particular, our series representation, besides being a more tractable solution, also exhibits impressive savings in computational load and computation time compared to previous studies. Numerical results and Monte-Carlo simulations corroborated the validity of our expressions.