Biparametric Linear Estimation for CFAR against Weibull Clutter

The authors deal with constant false alarm rate (CFAR) procedures against nonstationary clutter, modeled as a Weibull distributed process whose scale parameter alpha and shape parameter beta are both variable. It is shown that conventional CFAR procedures, which compensate only for alpha , degrade intolerably as beta deviates from beta =2, namely, as the Rayleigh distributional assumption is violated. A biparametric CFAR procedure is shown to be suited to such situations. The authors introduce a logarithmic transformation to reduce the Weibull probability density function (pdf) to a Gumbel pdf, i.e., to the location-scale type, and then exploit the best linear unbiased estimation (BLUE) of location-scale parameters to adjust the detection threshold. True CFAR is thus achieved when the clutter is locally homogeneous. Resilience against local inhomogeneities can also be conferred since BLUE lends itself to censoring. Through a performance analysis, the influence of various system and distributional parameters is elicited.