Highly accurate closed-form approximation for the probability of detection of Weibull fluctuating targets in non-coherent detectors

TL;DR

This paper presents a highly accurate, closed-form approximation for the probability of detection of Weibull fluctuating targets in non-coherent radar detection, using advanced mathematical functions and series expansions.

Contribution

The paper introduces a novel approximation method using Fox's H-function and a converging series, improving accuracy and computational efficiency over previous approaches.

Findings

The approximation closely matches Monte Carlo simulations.

The series representation significantly reduces computation time.

The method is validated for various Weibull parameters.

Abstract

In this paper, we derive a highly accurate approximation for the probability of detection (PD) of a non-coherent detector operating with Weibull fluctuation targets. To do so, we assume a pulse-to-pulse decorrelation during the coherent processing interval (CPI). Specifically, the proposed approximation is given in terms of: i) 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 ii) 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.