Page 140 - Fundamentals of Radar Signal Processing

of the received signal. For such a component to exist, both the amplitude and

phase of the reflectivity of the clutter scatterers involved must be constant. Thus,
the DC component is attributable to backscatter from elements such as bare
ground, rocks, and tree trunks. The AC term accounts for back-scatter from
moving elements such as leaves, branches, and blades of grass. Simple
autoregressive filters can be used to implement the model in simulations
(Mountcastle, 2004).

2.3.4 Compound Models of Radar Cross Section
As is seen in Chap. 6, radar detection performance predictions depend strongly
on the details of target and clutter RCS models. Furthermore, it is well known
that RCS statistics vary significantly with a host of factors such as geometry,
resolution, wavelength, and polarization. Consequently, the development of
good statistical RCS models is a very active area of empirical and analytical
research. Following are three brief examples of an extension to the basic

modeling approach described earlier, all motivated by the complexities of
modeling clutter. Because the literature regarding these models is developed
primarily in terms of the echo amplitude (voltage) ζ instead of RCS σ or power,
the remainder of this section also concentrates on amplitude PDFs.
Some amplitude PDFs are physically motivated, especially the Rayleigh
(exponential RCS) model (which follows from a central limit theorem

argument) and the Rice or Rician model (which corresponds to a Rayleigh
model with an additional dominant scattering source). Others, such as the log-
normal or Weibull, have been developed empirically by fitting distributions to
measured data. One attempt to provide a physical justification for a non-
Rayleigh model abandons the single-PDF approach, instead assuming that the
random variable representing echo amplitude can be written as the product of
two independent random variables, ζ = x · y. The PDF of ζ can then be

represented in a Bayesian formulation as

(2.74)

This model has been used to describe sea clutter (Jakeman and Pusey,
1976; Ward, 1981). The random variable x is identified with a slowly
decorrelating component having a voltage distribution following a central chi-
square of degree 2m with m ≥ 2.5. This component is introduced to account for
“bunching” of scatterers due to ocean swell structure and radar geometry, and

represents variation in the mean of the amplitude over time. The distribution
p (ζ|x) is assumed to represent the composite of a large number of independent
ζ|x
scatterers. Its amplitude distribution is therefore Rayleigh. The resulting overall
PDF p (ζ) can be shown to be the K distribution, which is given by
ζ