Aerospace and Electronic Systems Magazine March 2017 - 50

Complementary Pair Radar Waveforms
B. M. Popovic [10] pointed out that the order of the sequences
in a complementary set, containing more than two sequences, can
significantly reduce the ambiguity function (Doppler) sidelobes.
In order to achieve useful Doppler resolution the CPI should
contain many periodic repetitions of the complementary pulse pair
{s1 s2}. A. Pezeshki et al. [11] provided a comprehensive analysis of reordering complementary pairs to reduce Doppler induced
range sidelobes. For example a Doppler resilient reordering of four
pairs would be {s1 s2 s2 s1 s2 s1 s1 s2}. Reference [11] also lists many
related references.
In our tutorial we elected not to elaborate on the Doppler resilient reordering concept because its contribution is lost when interpulse amplitude weighting is applied on receive. This point is
demonstrated in Figure 18. A ten element binary complementary
code pair was used. It was either periodically repeated 16 times, for
a total of 32 pulses (left side), or reordered for Doppler resilience
(right side). The top row represents the delay-Doppler responses
when the processor does not include interpulse amplitude weighting. In the bottom row the processor includes Hamming interpulse
weighting. Without weighting the reordered sequences produced
considerable sidelobe reduction at low Doppler shifts (top right).
With weighting the original periodic repeat yields the best response (bottom left) in which the Doppler sidelobes remain low
also at high Doppler shifts.

tained, but a penalty of variable amplitude is incurred. This is in
contrast to constant-amplitude, spectrally efficient representations,
which, however, do not maintain the perfect cancellation of the
range near-sidelobes.
Recently proposed Doppler resilient reordering of binary complementary pairs, when the CPI contains many pairs, was also addressed. It was shown to underperform, compared with repetitions
of the same pair, when the receiver's matched processor includes
interpulse amplitude weight window.

REFERENCES
[1]

[2]
[3]

[4]
[5]

[6]

CONCLUSIONS

[7]

Drawbacks of complementary-pair radar waveforms were discussed and evaluated. Methods to mitigate some drawbacks were
suggested. Doubling the delay in a two-pulse canceller allows applying it, as an MTI measure, to a coherent pulse train constructed
from repeated binary complementary pairs. The classical presentation of the Doppler frequency response of the pulse canceller is
augmented by the delay-Doppler response, which shows what happens to the range near-sidelobes at higher Doppler shifts. The emphasis in the displayed responses was on slow targets, where MTI
is most needed, in order to prevent stationary clutter returns from
penetrating into higher Doppler outputs through the Doppler sidelobes of the following processing stage - the weighted DFT processor. The MTI example used in the article was a two-pulse canceller.
It can easily be extended to the more complex three-pulse canceller
and to a modified three-pulse canceller [12].
Spectral efficiency improvement was obtained by altering the
code element (bit) representation from rectangular to GWS. It was
shown that the cancelling property of range near-sidelobes is main-

50

[8]

[9]

[10]
[11]

[12]

IEEE A&E SYSTEMS MAGAZINE

O'Donnell, R. M., Muehe, C. E., Labitt, M., Drury, W. H., and Cartledge, L. Advanced signal processing for airport surveillance radars.
EASCON 1974, Washington, DC, 1974, 71A-71F.
Richards, M. A. Fundamentals of Radar Signal Processing (2nd ed.)
New York: McGraw Hill, 2014.
Cook, M., Blunt, S., and Jakabosky, J. Optimization of waveform diversity and performance for pulse-agile radar. IEEE Radar Conference, Kansas City, MO, 2011, 812-817.
Levanon, N., and Mozeson E. Radar Signals. New York: Wiley, 2004.
Borwein, P. B., and Ferguson, R. A. A complete description of Golay
pairs for length up to 100. Mathematics of Computation, Vol. 73, 246
(2003), 967-985.
Chen, R., and Cantrell B. Highly bandlimited radar signals. IEEE Radar Conference, Long Beach, CA, 2002, 220-226.
Faust, H. H., Connolly, B., Firestone, T. M., Chen, R. C., Cantrell, B.
H., and Mokole, E. L. A spectrally clean transmitting system for solidstate phased-array radars. IEEE Radar Conference, Philadelphia, PA,
2004, 140-144.
Blunt, S., Cook, M., Perrins, E., and de Graff, J. CPM-based radar
waveform for efficiently bandlimiting a transmitted spectrum. IEEE
Radar Conference, Pasadena, CA, 2009.
Taylor, J. W., and Blinchikoff, H. J. Quadriphase code: A radar pulse
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Popovic, B. M. Complementary sets of chirp-like polyphase sequences. Electronics Letters, Vol. 27, 3 (1991), 254-255.
Pezeshki, A., Calderbank, A. R., Moran, W., and Howard, S. D. Doppler resilient Golay complementary waveforms. IEEE Transactions
on Information Theory, Vol. 54, 9 (2008), 4254-4266.
Cohen, I., and Levanon, N. Adjusting 3-pulse canceller to enhance
slow radar targets. IEEE International Conference on Microwaves,
Communications, Antennas and Electronic Systems (COMCAS), Tel
Aviv, Israel, 2015.

MARCH 2017



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