Page 503 - Fundamentals of Radar Signal Processing

ground clutter renders the interference nonhomogeneous in Doppler and

possibly in range.

6.5.3 Analysis of Cell-Averaging CFAR
The intent of the adaptive calculation of the threshold is to provide a constant
false alarm rate despite varying interference power levels. In this subsection,
the detector performance is analyzed for the case of a square law detector to see
if this goal has been achieved. The threshold computed according to Eq. (6.129)

will be a random variable, and therefore so will be the probability of false
alarm. The detector will be considered to be CFAR if the expected value of P FA

does not depend on the actual value of .
Combining Eqs. (6.128) and (6.129) gives an expression for the estimated
threshold

(6.130)

Define z = (α/N)x ; thus Standard results from probability theory and
i
i
Eq. (6.124) give the PDF of z i

(6.131)

The PDF of is the Erlang density

(6.132)

The P observed with the estimated threshold will be . This is now
FA
also a random variable; its expected value is

(6.133)

Completing this standard integral and performing some algebraic manipulations