Page 263 - Fundamentals of Radar Signal Processing

FIGURE 4.21 Relationship between pulse burst waveform parameters and
range and Doppler resolution and ambiguities.

4.5.6 The Slow-Time Spectrum and the Periodic Ambiguity Function
It would seem that the DTFT Y [l, ω ) of the slow-time sequence y[l, m] should
D
be related to the variation of the complex ambiguity function Â(t, F ) in
D
Doppler. The slow-time sequence y[l, m] is obtained by sampling the output of
the simple pulse matched filter output s (t) at the same delay after transmission
p
on each pulse. If the target motion across the CPI is small compared to the range
resolution (i.e., the target moves only a small fraction of a range bin during the
CPI), the amplitude of the sample taken on each pulse will be the same. This
amplitude will be the maximum value s (0) if the sampling time exactly
p
corresponds to the target range; if the sampling time differs from that
corresponding to the target range by Δt seconds the measured amplitude on each
pulse will be s (Δt). Thus, the slow-time sequence in a given range bin will
p
have constant amplitude but the ambiguity function of the waveform will
determine that amplitude based on the alignment of the target range and the range
bin sampling times.
If there is relative motion between the radar and target, there will be a

sample-to-sample decrease in the phase of the slow-time samples of the form –
4πmvT/λ. If the target is within the first unambiguous range interval the target
echo will be present in all M slow-time samples for the appropriate range bin
and the magnitude of the DTFT will have the |sin(πF MT)/sin(πF T)|form seen
D
D
i n Eq. (4.80). However, the|sin(πF τ)/πF τ|term of the AF Doppler response
D
D
due to the individual pulse shape will not be observed in the DTFT; rather, this
term will weight the overall amplitude of the DTFT. Finally, if the target range