Aerospace and Electronic Systems Magazine March 2017 - 43

sin ( 2

Levanon, Cohen, and Itkin
Figure 4 (bottom) shows the phase
ramp as function of time caused by
Doppler shift. The top subplot shows
the slow-time compensation provided
by the DFT in a conventional pulseDoppler processor. The intrapulse phase
ramp is not compensated, which results
in imperfect delay-sidelobe cancellation
and a rise in the near-sidelobes at nonzero Doppler, as shown in Figure 5.
Figure 5 displays the delay-Doppler
response at the output of a processor
matched to a Doppler shift of νNTr = 4.
A weak buildup of the range near-sidelobes is seen, but no significant change
is seen in the mainlobe height. The difference between the mainlobe and peak
sidelobe (≈ 50 dB) is still acceptable.
The range near-sidelobe will increase
with increasing Doppler.

TWO-PULSE CANCELLER
FOR COMPLEMENTARY-PAIR
WAVEFORM
In coherent pulse train constructed from
repeated pairs of complementary pulses,
the delay used in a two-pulse canceller
must be of length p2Tr, p = 1,2,.... Only
then the subtraction would be of returns
from an identically coded pulses. The
shortest delay is therefore 2Tr. A block
diagram of such a two-pulse canceller
appears in Figure 6. The response of a
2-pulse canceller is shown in Figure 7.
Log frequency scale was used because
we wish to emphasize low Doppler frequencies. The top subplot of Figure 7 describes the response of a 2-pulse canceller
when the delay is 2Tr. The first null occurs at ν = 1 / (2Tr) → νNTr = N / 2 = 32.
Recall that the frequency response of our
2-pulse canceller, whose delay equals 2Tr,
is given by (1), which explains the peak
of 6 dB in the top subplot of Figure 7.

Tr )

H (ν ) = 2 sin ( 2πν Tr ) → max H (ν ) = 2
(1)
→ max H ν = 2

( )

The middle subplot shows the response of the fourth Doppler filter out
of 64 DFT outputs. The peak level of
-1.93 dB reflects the loss caused by
the weight window. Cascading the two
top responses will result in the bottom
MARCH 2017

Figure 4.

Doppler induced phase ramp of the received complementary pulse train (bottom). Slow-time phase compensation provided by a conventional linear pulse-Doppler processor (top).

Figure 5.

Delay-Doppler response, Doppler shift νNTr = 4, no pulse canceller. Zoom on |τ| ≤ tp.

Figure 6.

The shortest two-pulse canceller for complementary pair
pulse train.

IEEE A&E SYSTEMS MAGAZINE

43



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