Page 142 - Fundamentals of Radar Signal Processing

reflectivity. If the scene being viewed by the radar is nonhomogenous, then the

characteristics of the RCS observed in one resolution cell might vary
significantly from those of another. For example, the dominant clutter observed
by a scanning radar at a coastal site might be an urban area in one look direction
and the sea in another. Another example occurs when scattered rain cells occupy
only part of the scanned region, so that some resolution cells contain rain while
others are clear.

This situation can be modeled by letting the slowly decorrelating term x in
the product model represent spatial variations in the local mean of the received
voltage. If the PDF of x is log-normal with a large variance and the PDF of ζ
conditioned on x is gamma distributed (which includes Rayleigh as a special
case), then the overall PDF of the product ζx has a lognormal distribution
(Lewinski, 1983). Consequently, the product model implies that lognormal
variations of the local mean from one resolution cell to another could account

for the log-normal variation often used to model ground clutter returns. A
similar argument can be used to justify the log-normal model for target RCS by
modeling the variation of RCS with aspect angle as a log-normal process.

2.4 Noise Model and Signal-to-Noise Ratio
The echo signal received from a target or clutter inevitably competes with
noise. There are two sources of noise: that received through the antenna from
external sources, and that generated in the radar receiver itself.

External noise is a strong function of the direction in which the radar
antenna is pointed. The primary contributor is the sun. If the antenna is directed
toward the night sky and there are no interfering microwave sources, the
primary source is galactic (also called cosmic) noise. Internal noise sources
include thermal noise (also called Johnson noise) due to ohmic losses, shot
noise and partition noise due to the quantum nature of electric current, and

flicker noise due to surface leakage effects in conducting and semiconducting
devices (Carlson, 1976).
Of these various sources, thermal noise is normally dominant. The theories
of statistical and quantum mechanics dictate that the thermal noise voltage in an
electronic circuit is a zero-mean Gaussian random process (Curlander and
McDonough, 1991). The mean energy of the random process is kT/2 joules,
where T is the temperature of the noise source in kelvins (absolute temperature)

–23
and k = 1.38 × 10 J/K is Boltzmann’s constant. The power spectrum S (F) of
n
the thermal noise delivered to a matched load is

(2.76)