Page 255 - Fundamentals of Radar Signal Processing
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Suppose the radar can be expected to receive significant clutter returns at ranges
up to P · t , and consider the clutter component of the slow-time signal for a
ua
given range bin in the pulse-by-pulse processing viewpoint. When the range bin
of interest is sampled at delay t < T after the first pulse is transmitted, only
0
clutter echoes from the corresponding range ct /2 will be sampled at the
0
receiver. When the range bin is sampled again after the second pulse, the clutter
component will include echoes from the second pulse and range ct /2 as well as
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from the first pulse and range c/2(t + T). These two contributions represent
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echo from two physically different patches of clutter scatterers. The first slow-
time sample, which includes echoes from only the nearer patch, may differ
significantly in power and statistical behavior from the second slow-time
sample, which includes echoes from both. The Pth and subsequent slow-time
samples will contain contributions from all P contributing range intervals and
therefore exhibit the consistent clutter power levels and statistical behavior
needed for effective clutter filtering and target detection. Extending the
transmitted waveform to M + P – 1 pulses as above therefore allows collection
of M steady-state clutter measurements. In Chap. 5 these additional pulses will
be called “clutter fill” pulses. The first P – 1 slow-time samples will be
discarded in each range bin and only the remaining M samples will be used in
clutter filtering, coherent integration, and detection processing.
4.5.4 Doppler Response of the Pulse Burst Waveform
To consider the effect of a Doppler mismatch on the pulse burst waveform and
its matched filter, consider a target moving toward the radar at velocity v meters
per second so that its range is R – vt meters at time t. Assume that the “stop-
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and-hop” approximation is valid and that the target motion does not exceed one
range bin over the CPI, that is, MvT < cτ/2; this ensures that all echoes from a
given target appear in the same range bin over the course of a CPI. The
demodulated echoes will have a phase shift of –(4π/λ)R(t) = –(4π/λ)(R – vt).
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Adopting the pulse-by-pulse processing viewpoint and absorbing the phase
exp(–j4πR /λ) due to the nominal range R into the overall gain, the individual
0
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matched filtered outputs for each pulse become
(4.67)
The corresponding slow-time sequence is
(4.68)