Page 532 - Fundamentals of Radar Signal Processing

on clutter samples taken from the CUT but on previous time intervals. Thus,

spatial homogeneity is not required, but homogeneity in time, i.e., statistical
stationarity, is. Both types of CFAR require that the clutter samples be
uncorrelated (in space or Doppler for CA CFAR, in time for clutter mapping)
for the analyses given here to be valid. Finally, Eq. (6.176) shows that the
threshold is based on an infinite, weighted sum of previous samples rather than
the finite sums of CA CFAR and its variants.

It is also possible to estimate the clutter mapping threshold using a simple
average of a finite number of previous measurements. One version of the
moving target detector (MTD) is said to have used an eight-scan average,
covering about 32 seconds of data (Skolnik, 2001). In this case, the CA CFAR
analyses would apply to the clutter map as well. However, for computational
simplicity the recursive filter of Eq. (6.173) is most often used. The average
probabilities of false alarm and detection when the threshold is computed with

the recursive scheme are (Nitzberg, 1986)

(6.177)

(6.178)

These formulas are slow to converge in practice; a more rapidly converging
variation is given in Levanon (1988). Again, α can be varied to generate curves

of versus and CFAR loss can then be determined by comparing these
curves to the case where the interference is known exactly. The case γ = 0 in
fact corresponds to the ideal case. For every increase of 0.2 in γ, the CFAR loss
increases approximately 3 dB. A crude approximate formula for the CFAR loss
is (Taylor, 1990)

(6.179)

This formula is of limited accuracy, especially for large γ, but may be
useful for rough calculations. Another implementation of the MTD used a
recursive filter as described previously with a feedback coefficient of γ = 7/8
(Nathanson, 1991). A rational value of γ with a denominator that is a power of
two was particularly amenable to the fixed point implementations used in early
versions of the MTD, since the division by the denominator value (eight in this