Page 484 - Fundamentals of Radar Signal Processing

and the RCS of a group of N samples follows either the uncorrelated or fully

correlated model as described in Chap. 2. Note that using a fluctuating target
model has no effect on the probability of false alarm. P is determined only by
FA
the PDF when no target is present; thus Eq. (6.79) still applies.
The strategy for determining the probability of detection depends on the
target fluctuation model used. Figure 6.13 illustrates the approach. In all cases,
the PDF of the magnitude-squared of a single sample of signal + noise is a

generalized noncentral chi-squared so that the CF of a single square-law
detected sample is still given by Eq. (6.83). However, the SNR in that
expression is now a random variable because the target RCS is a random
variable.

FIGURE 6.13 Strategy for computing P for fluctuating target models.
D

In a fully correlated case (e.g., Swerling 1 or 3) the target RCS is a fixed
value for all N pulses integrated to form z′. Thus, the CF of z′ is the N-fold
product of Eq. (6.83) with itself

(6.93)

This is the same expression as Eq. (6.84) except that now C is written
z′
explicitly as a function of all of q, χ, and N. Next take the expected value of the
CF over the SNR