Based on real extremely heterogeneous synthetic aperture radar (SAR) urban clutter data and Cramer-Von Mises distance

the goodness-of-fit tests were done via Rayleigh distribution

Weibull distribution

K distribution and G distribution

respectively.It is shown that the Rayleigh distribution and Weibull distribution may be mismatched and the K distribution may be only partly matched

but the G distribution may model the real data very well.Furthermore

for the CFAR(Constant False Alarm Rate) detection under the G distributed clutter

the curves of the signal-to-noise ratio versus shape parameter and numbers of reference cells were presented to meet the given detection performance

and the reason was also analyzed that the CFAR losses decrease with the increasing of the distribution parameter.Also

an effective CFAR threshold calculating method was proposed at last.