Aerospace and Electronic Systems Magazine March 2017 - 42

Complementary Pair Radar Waveforms
gin, is -1.9 dB, reflecting loss due
to the weight window. The delay τ
axis is normalized by the code element duration tb, in order to obtain
dimensionless coordinates. For the
same purpose the Doppler ν axis
is normalized by multiplying it by
NTr the duration of the CPI, (recall that N = 64). Thus, if NTr is
in seconds, ν is in Hz. If NTr is in
milliseconds ν is in kHz, etc. The
observed response clearly shows
no near sidelobes on the delay axis
(zero-Doppler). Recurrent delay
lobes appear around delay τ = Tr
= 130tb, where one pulse of the
transmitted complementary pair
coincides with the wrong pulse
of the reference complementary
pair. The peak recurrent delay
sidelobe (-18.19 dB) is 16.25 dB
below the mainlobe (-1.933 dB),
as found also in Figure 1(c). The
Figure 2.
sidelobe-free recurrent delay peak
Delay-Doppler response, |τ| ≤ 2Tr + tp.
reappears at τ = 2Tr = 260tb, which
is the effective periodicity of the
signal (=2Tr).
A strong recurrent Doppler
peak appears on the Doppler axis
at ν = 1/Tr , namely at νNTr = 64.
At this Doppler shift the Doppler
induced phase ramp completes accumulating 2π between individual
pulses. Near range-sidelobes appear around that recurrent peak and
the peak value (= −2.5 dB) is only
slightly lower than the peak at the
origin (= −1.9 dB). Both are due to
the sensitivity of complementarypair waveform to Doppler. There
is also a relatively weak recurrent
Doppler ridge at νNTr = N / 2 =
32, namely at ν = 1 / (2Tr). At that
Doppler shift the Doppler induced
phase ramp accumulates π between
pulses, thus reversing polarity every pulse. This explains the null
Figure 3.
(hard to see) in that ridge on the
Delay-Doppler response, Doppler shift = 0, no pulse canceller. Zoom on |τ| ≤ tp.
Doppler axis. It is worth recalling
that a lobe at any coordinate (τ1,ν1)
A zoom in delay of the same delay-Doppler response is shown
of the delay-Doppler response imin Figure 3. The zoom allows us to see clearly the width of the
plies that a signal reflected with additional delay τ1 and additional
mainlobe at the origin. It is also easier to see the recurrent peak at
Doppler ν1 will be attributed to the nominal delay and Doppler
τ / tb = 0, νNTr = 64 compared with the null at τ / tb = 0, νNTr = 32.
(0,0). Along the Doppler axis (τ / tb = 0) we see the near-constant
−62 dB sidelobes of the mainlobe at the origin, predicted by the
(The corresponding data point was pulled slightly backward to τ / tb
chebwin(64,62) interpulse weight window.
= 0, νNTr = 29.5 to make it visible.)
42

IEEE A&E SYSTEMS MAGAZINE

MARCH 2017



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