  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.
