Page 156 - Fundamentals of Radar Signal Processing

assume a target is present within the range bin corresponding to that sample time

for the entire data collection time of mT seconds, meaning that R(t) remains in
8
the range interval [R –cτ/2, R ]. The mth sample in this range bin is then
s
s

(2.108)

The constant combines k′ and the amplitude of the sampled pulse envelope
A(·). The series of sampled echoes y[m] forms the slow-time series of samples
for that range bin, as will be described in Chap. 3.
The “stop” assumption applied in Eq. (2.98), when used across a series of
pulses as in (2.107), is called the stop-and-hop approximation. Relative to the
radar, the target is assumed to “stop” at the time of each pulse transmission at

the corresponding range R(mT) and then “hop” to the range at the next pulse
transmission time, rather than moving continuously.
Consider again a constant velocity target, R(t) = R – vt. The slow-time
0
data series becomes

(2.109)

The first exponential in Eq. (2.109) is a constant phase shift for all of the slow-
time samples y[m] and is of little consequence. The second exponential is a

discrete complex sinusoid with normalized frequency 2vT/λ cycles/sample,
corresponding to the expected Doppler frequency of 2v/λ Hz. Thus, the phase
history obtained from a moving target using a series of pulses provides a way to
measure the Doppler shift with good precision by observing the signal over an
observation time much longer than that of a single pulse.
The manifestation of the target Doppler shift in the slow-time phase history
is sometimes referred to as spatial Doppler. This terminology emphasizes the

fact that the Doppler shift is measured not from intrapulse frequency changes,
but rather from the change of phase of the echoes at a given range bin over a
series of pulses. Because of the inability to measure intrapulse Doppler
frequency shifts in most systems, the term “Doppler processing” in radar usually
refers to sensing and processing this spatial Doppler information.