Page 94 - Fundamentals of Radar Signal Processing

show the effect of other variables, such as pulse length, intermediate frequency

(IF) bandwidth, or signal processing gains. Several such variations are given in
Richards et al. (2010). The range equation also provides the basis for
calibrating a radar system. If the system power, gain, and losses are carefully
characterized, then the expected received power of echoes from test targets of
known RCS can be computed. Calibration tables equating receiver voltage
observed due to those same echoes to incident power density can then be

constructed.
Signal processing techniques can increase the effective received power,
and therefore increase the obtainable range. The effect of each technique on
received power is discussed as they are introduced in later chapters.

2.2.2 Distributed Target Forms of the Range Equation
Not all scattering phenomena can be modeled as a reflection from a single point
scatterer. Ground clutter, for example, is best modeled as distributed scattering

from a surface, while meteorological phenomena such as rain or hail are
modeled as distributed scattering from a three-dimensional volume. The radar
range equation can be rederived in a generalized way that accommodates all
three cases.
Equation (2.3) is still applicable as a starting point. To consider
distributed scatterers, and because the gain of the antenna varies with azimuth

and elevation angle, Eq. (2.4) must be replaced with an equation that accounts
for the effect of the antenna power pattern P(θ, ϕ) on the power density radiated
in a particular direction (θ, ϕ):

(2.13)

Assume that the antenna boresight corresponds to θ = ϕ = 0. The antenna
boresight is normally the axis of maximum gain so that P(0, 0) = G.
Now consider the scattering from an incremental volume dV located at
range and angle coordinates (R, θ, ϕ). Suppose the incremental RCS of the
volume element is dσ square meters, and that dσ in general varies with position
in space. The incremental backscattered power from dV is

(2.14)

As before, dσ is defined such that it is assumed this power is reradiated
isotropically, and then collected by the antenna effective aperture, adjusted for
the angle of arrival. After substituting for effective aperture and accounting for
losses, this results in an incremental received power of