Page 524 - Fundamentals of Radar Signal Processing
P. 524
where p (T) is the PDF of the threshold. Because T is proportional to the kth-
T
ranked reference sample y , it is necessary to find the PDF of y , the kth
(k)
(k)
largest of N i.i.d. random variables. The result can be found in many textbooks
and is
(6.161)
where P (y) is the cumulative distribution function (CDF) of y . For complex
i
yi
WGN, the PDF and CDF of a single square-law detected and normalized
reference sample y are
i
(6.162)
Using Eq. (6.162) in Eq. (6.161) gives the PDF of the kth ranked sample:
(6.163)
(6.164)
Inserting this result into Eq. (6.160) gives
(6.165)
With the change of variable T′ = T/α this becomes the slightly more convenient
OS
form:
