Page 525 - Fundamentals of Radar Signal Processing

(6.166)

Utilizing integral 3.312(1) in Gradshteyn and Ryzhik (1980) gives

(6.167)

where B(·,·) is the beta function which in turn can be expressed in terms of the
gamma function Γ(·) as shown. For integer arguments, Γ(n) = (n – 1)! and Eq.

(6.167) reduces for integer α to
os

(6.168)

Figure 6.29 plots as a function of α for two choices of OS windows,
OS
one with N = 20 and one with N = 50. In the first case, the k = 15th order
statistic is chosen to set the threshold, while in the second the k = 37th order
statistic is selected. Plots such as these can be used to determine the threshold
multiplier needed to achieve a specified for a given OS CFAR window
configuration. For example, with N = 20 and k = 15, a multiplier of α = 6.857
OS
gives .