Page 90 - Fundamentals of Radar Signal Processing

received signal resulting from a single pulse echoing from a scatterer at range R 0

= ct /2 can be modeled as
0

(2.2)

where n(t) = receiver noise

echo amplitude factor due to propagation losses and target
k =
reflectivity
ϕ(t) = echo phase modulation due to target interaction

The important parameters of are the delay time t , the echo component
0
amplitude k · |a(t)| and its power relative to the noise component, and the echo

phase modulation function θ(t – t ) + ϕ(t). These characteristics are used to
0
estimate target range, scattering strength, and radial velocity, suppress jamming
and clutter, form images, and so forth.
The amplitude and phase modulation functions also determine the range
resolution ΔR of a measurement. For example, ΔR = cτ/2 if θ(t) is a constant
and is a simple constant-frequency pulse of length τ seconds. Resolution in
angle and cross range is determined by the 3-dB width of the antenna pattern in
a nonimaging radar.

In order to design good signal processing algorithms, good models of the
signals to be processed are needed. In this chapter, an understanding of common
radar signal characteristics pertinent to signal processing is developed by
presenting models of the effect of the scattering process on the amplitude, phase,
and frequency properties of radar measurements. While deterministic models

suffice for simple scatterers, it will be seen that complicated real targets require
statistical descriptions of the scattering process.

2.2 Amplitude

2.2.1 Simple Point Target Radar Range Equation
T he radar range equation (Richards et al., 2010; Skolnik, 2001) is a
deterministic model that relates received echo power to transmitted power in
terms of a variety of system design parameters. It is a fundamental relation used
for basic system design and analysis. Since the received signals are narrowband

pulses of the form of Eq. (2.2), the received power P estimated by the range
r
equation can be directly related to the received pulse amplitude.
To derive the range equation, assume that an isotropic radiating element
transmits a waveform of power P watts into a lossless medium. Because the
t
transmission is isotropic and no power is lost in the medium, the power density
at a range R is the total power P divided by the surface area of a sphere of
t