Page 112 - Fundamentals of Radar Signal Processing

FIGURE 2.9 Relative RCS of the complex target of Fig. 2.8 at a range of 10 km

and radar frequency of 10 GHz.

The complicated variation of RCS with radar frequency and target aspect

angle observed for even moderately complex targets leads to the use of a
statistical description for radar cross section (Levanon, 1988; Nathanson, 1991;
Skolnik, 2001). This means that the RCS σ of the scatterers within a single
resolution cell is considered to be a random variable with a specified
probability density function (PDF). The mean or median RCS is typically used
for radar range equation calculations, but the full PDF is needed for detection
probability calculations, as will be seen in Chap. 6.

One of a variety of PDFs is used to describe the statistical behavior of the
RCS for different targets. Consider first a target consisting of a large number of
individual scatterers (similar to that of Fig. 2.8), each with its own individual
but fixed RCS and randomly distributed in space. Because of its high sensitivity
to small range changes, the phase of the echoes from the various scatterers can

be assumed to be a random variable distributed uniformly on (0, 2π]. Under
these circumstances, the central limit theorem guarantees that the real and
imaginary parts of the composite echo can each be assumed to be independent,
2
zero mean Gaussian random variables with the same variance, say α (Papoulis
and Pillai, 2001; Beckmann and Spizzichino, 1963). In this case, the squared-