Constant false alarm rate detectors for pareto clutter models

Nonlinear Transformations and Radar Detector Design

“…The distribution function of Ξ can also be found in Ref. [20] for the case of interest. Figure 1 shows the pretransformed CUT as well as Eq.…”

“…Consequently, the Pareto distribution fits into the currently accepted radar clutter model phenomenology [19]. Hence, there have been a number of recent advances in the design of CFAR processes under a Pareto clutter model assumption [20][21][22][23][24][25].…”

“…This Pareto model possesses what is referred to as a duality property in Ref. [20]. To introduce this, recall that if Y is an Exponential random variable with unity mean, its cdf is given by…”

“…Then with an application of results from the proof of Corollary 3.1, since |E 2 − E 3 | has the same exponential distribution, one can apply statistical conditioning on E 1 and |E 2 − E 3 | to show that the distribution function of the transformed CUT is Gaussian process with inverse Gamma texture in the complex domain, and then taking modulus squared to produce the intensity measurement [20]. The distribution function of Ξ can also be found in Ref.…”

“…In the Pareto setting, it is shown in Ref. [20] that an ideal detector has its threshold set via β(Pfa) , this threshold is 0.8312 by contrast. Thus the nonlinear mapping, in the process of compressing the original data series, can be used to achieve the CFAR property with Eq.…”