Aerospace and Electronic Systems Magazine March 2017 - 46

Complementary Pair Radar Waveforms
Figure 11 shows the two
complementary base-band signals
using the rectangle shaped element (dash) and the GWS shaped
element with M = 4 (solid). Since
the GWS representation extends
over 4 bits the duration of the
GWS shaped complementary signal extends over 26+3 = 29 bits.
In practice the transmitter and
the receiver are likely to be bandwidth limited by the hardware,
which will further modify the
waveforms in Figure 11 as if they
passed through a low-pass filter
(LPF). It is therefore expected that
the waveform in the upper subplots of Figures 11 and 12 will be
smoothed as shown in the bottom
subplot of Figure 12. Figure 13
shows the spectrum change between the original complementary signal, with rectangle element
shape, and the 4 samples/bit GWS
element shape after LPF. The LPF
was a simple first order Butterworth filter with cutoff frequency
νn = 5 / tb.
We find it important to clarify
that the LPF is not an intended part
of the processing. It was added
to represent a likely effect of the
hardware's limited bandwidth. It
is also important to point out that
the waveform seen in Figure 12
(bottom) is the complex envelope
of the signal, which happens to be
real, that coherently modulates (in
both amplitude and phase) a carrier frequency. Noncoherent amplitude modulation only will exclude
Doppler processing and Doppler
information.
The next obvious question is
how the bandwidth reduction affected the autocorrelation and how
well the zero range-sidelobe property was preserved. The answers
are given in Figures 14 and 15.
Figure 14 shows the periodic autocorrelation (linear scale) of the
26 element complementary pair
when the element shape is 4 samples/element GWS, followed by
LPF. Note that the only deviations
from the ideal zero near-sidelobes
46

Figure 11.

The two complementary base-band waveforms, each with the two sequence element shapes: rectangle (dash),
GWS with 4 samples per code element (solid).

Figure 12.

The first complementary base-band waveforms with 4 samples/bit GWS, before (top) and after LPF (bottom).

IEEE A&E SYSTEMS MAGAZINE

MARCH 2017



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