Page 277 - Fundamentals of Radar Signal Processing

attenuated output from the matched filter and will likely go undetected. An LFM

pulse of the same duration will still produce a significant output peak for a much
broader range of Doppler shifts, even though the peak will be mislocated in
range. Nonetheless, the target will be more likely to be detected. The LFM
waveform is said to be more Doppler tolerant than the simple pulse. This
makes it a good choice for surveillance applications because a relatively large
range of Doppler shifts can be searched with an LFM pulse. The range error can

be eliminated, at least for isolated targets, by repeating the measurements with
an LFM pulse of the opposite slope, e.g., an upchirp followed by a downchirp.
In this case the sign of the range error will be reversed. Averaging the two
measurements will give the true range and also allow determination of the
Doppler shift.

4.6.5 Stretch Processing
LFM waveforms are often the waveform of choice for exceptionally wideband

radar systems where the swept bandwidth β may be hundreds of megahertz or
even exceed 1 GHz. Digital processing can be difficult to implement in such
systems because the high instantaneous bandwidth of the waveform requires
equally high sampling rates in the A/D converter. It is difficult to obtain high-
quality A/D converters at these rates with wordlengths longer than perhaps 8
bits with current technology; wordlengths at 1 GHz are expected to reach only

about 11 bits by 2020 (Jonsson, 2010). In addition, the sheer number of samples
generated can be stressing for the signal processor.
Stretch processing is a specialized technique for matched filtering of
wideband LFM waveforms. It is also called deramp processing, deramp on
receive, dechirp, and one-pass processing. It is essentially the same as the
processing used with linear frequency-modulated continuous wave (FMCW)
radar. Stretch processing is most appropriate for applications seeking very fine

range resolution over relatively short range intervals (called range windows or
range swaths).
Figure 4.30 shows the scenario for analyzing stretch processing. The
central reference point (CRP) is in the middle of the range window of interest
at a range of R meters, corresponding to a time delay of t seconds. Consider a
0
0
scatterer at range R and time delay t = t + δt . The problem will be analyzed
b
b
b
0
in terms of differential range or delay relative to the CRP, denoted δR and δt .
b
b
The transmitted waveform is the LFM pulse of Eq. (4.84). The echo from the
scatterer, with the carrier frequency included, is