Page 280 - Fundamentals of Radar Signal Processing

FIGURE 4.32 Instantaneous frequency vs. time for an LFM transmitted pulse
and echoes from three scatterers. See text for details.

It is desirable that the reference LFM chirp completely overlap the echo
from a scatterer anywhere within the range window. If the range window is R =
w
cT /2 meters long the leading edge of the echo from a scatterer at the nearest
w
range, R – R /2, will arrive t – T /2 seconds after transmission as shown in
w
0
0
w
Fig. 4.32. The trailing edge of the echo from the scatterer at the far limit of the
range window, R + R /2, will arrive t + T /2 + τ seconds after transmission.
w
w
0
0
Thus, data from the range window have a total duration of T + τ seconds. To
w
ensure complete overlap of the reference chirp with echoes from any part of the
range window the reference chirp must be T + τ seconds long and so will
w
sweep over (1 + T /τ)β Hz.
w
Another issue evident in Fig. 4.32 is range skew. This is the phenomenon
whereby the beat frequencies for scatterers at different ranges, while all of the
same duration (provided the reference chirp is lengthened), start and stop at
different times. This complicates weighting of the mixer output prior to spectral
analysis for range sidelobe control. If the window is aligned with the beat
frequency for the center scatterer response, it will be misaligned with earlier
and later scatterer responses. If it is lengthened to cover the full mixer output
duration of T + τ seconds, none of the beat frequencies will be weighted by the
w
full window and each will have a different effective window function. In either
case, sidelobe suppression will be poor.

This problem can be solved by placing an additional filter between the
mixer output and the Fourier transform. Notice that the scatterer at delay δt b
relative to the patch center generates a beat frequency of –β · δt /τ Hz. What is
b
needed is a filter whose frequency response has unit magnitude for all