Page 513 - Fundamentals of Radar Signal Processing

multiplier α. Approximately the same relationship will determine the detection

probability attained with the new threshold multiplier α′ and SNR . will
equal if

(6.150)

Using Eq. (6.148) in Eq. (6.150) leads to

(6.151)

Figure 6.23b plots the approximate “target masking loss” in decibels for the
same conditions as in Fig. 6.23a.

The results given in Eqs. (6.149) and (6.151) are only approximations. A
more careful analysis would mimic the basic CA CFAR analysis of Sec. 6.5.3
by finding the PDF of the threshold in the presence of an interfering target, then
using that PDF to find the expected values of P and P . This approach is
D
FA
complicated by the fact that the interfering target changes the PDF of the cell
containing it. For instance, if the interferer is nonfluctuating the PDF of the
power in its cell will be a generalized noncentral chi-squared, while all of the
remaining cells will still be exponentially distributed. The PDF of the threshold

will be a mixture of the noncentral chi-squared and exponential PDFs. To avoid
calculating this PDF, the expected value of the threshold was used in the
expressions for the case of no interfering target. This gives a simple
approximation that behaves correctly in the limits of large and small mean
interferer SNR .

Figure 6.24 illustrates a related phenomenon, self-masking by a distributed
target. The interference, detector, and target characteristics are the same as in
Fig. 6.20, with the exception that the physical extent of the target is now greater
than a range bin so that the target signature is spread over three consecutive
cells. Figure 6.24a shows the effect when no guard cells are used. When one of
the three target cells is the test cell, the other two contaminate the interference
estimate, raising the threshold just enough to prevent detection. This effect is the

reason for using guard cells. Their impact is illustrated in Fig. 6.24b, where
three guard cells are used to each side of the test cell. This lengthens the total
CFAR window slightly, but assures that when the test cell is centered on the
target, the adjoining target cells do not contaminate the interference estimate and
the target is now detected.