Aerospace and Electronic Systems Magazine March 2017 - 49

Levanon, Cohen, and Itkin
riphase implementation maintains the
cancellation of the ACF near-sidelobes,
but the mainlobe width is doubled, with
the null at |τ| = 2tb. The pulse amplitude
is uniform except for the first and last
bit. The spectral sidelobes decay rate
is in between the rectangular bit implementation and GWS.

NEAR-SIDE LOBES OF CONCATENATED COMPLEMENTARY CODES
The Doppler-induced near delay-sidelobes (see Figures 5 and 8) exhibit an
interesting pattern when code pairs are
created by concatenating an existing
pair. The concatenating rule says that
if a pair {[s1] [s2]} is complementary
then a new pair, created as {[s1, s2] [s1,
-s2]}, will also be complementary. So
will also be the pair {[s2, s1] [s2, -s1]}.
The unique symmetry between the two
codes in the new pair, combined with
the Doppler generated linear phase
ramp, added identically to each code in
the new pair, cancel out the distant Doppler-induced near-sidelobes. This phenomenon is demonstrated in Figure 17,
which used code pairs of length 52 elements each, created by concatenating
the 26 element codes used so far.
In Figure 17 the floor at −65 dB
was removed to expose the grid lines. It
should be compared with Figures 5 and
8, where a basic kernel code of length
26 was used. In Figures 5 and 8 the
near sidelobes at νNTr = 4 and at νNTr
= 68 extend for the entire pulsewidth (=
code length). In Figure 17 those sidelobes extend for only the near half of
the pulsewidth. It is expected that complementary codes created by repeated
concatenations will exhibit more complicated on-off sidelobe patterns.

Figure 17.

Delay-Doppler response, 52 element code, Doppler shift νNTr = 4, 2-pulse canceller, N=64 pulses. Zoom on
|τ| ≤ tp.

OTHER APPROACHES
So far we have described the complementary pair's sensitivity to Doppler
shift and its effect on the delay-Doppler
response, as obtained with a conventional linear pulse-Doppler processor.
We did not suggest any mitigation approach. However, mitigation schemes
were described in the literature. In 1991
MARCH 2017

Figure 18.

Delay-Doppler response of 16 complementary pairs (32 pulses), with 10 code elements in each pulse. (Left)
Conventional periodic repeats. (Right) Doppler resilient reordering. (Top) No amplitude weighting. (Bottom) Hamming amplitude weighting on receive.

IEEE A&E SYSTEMS MAGAZINE

49



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