Page 113 - Fundamentals of Radar Signal Processing

magnitude σ has an exponential PDF:

(2.52)

where is the mean value of the RCS σ. The corresponding amplitude ζ
has a Rayleigh PDF:

(2.53)

The phase of the complex echo will be uniformly distributed over (0,2π].
While the exponential model for RCS is only strictly accurate in the limit
of a very large number of scatterers, in practice it can be a good model for a
target having as few as 10 or 20 significant scatterers. Figure 2.10 compares a
histogram of the RCS values from Fig. 2.9 to an exponential curve of the form of
Eq. (2.52) having the same mean . Even though only 50 scatterers are used, the
fit of the total RCS histogram to the Rayleigh/exponential distribution is quite

good. This same effect is observed when the randomly distributed scatterers
also have random individual cross sections drawn from the same Gaussian
distribution, a somewhat more general and plausible situation than the fixed-
RCS case.