IEEE Aerospace and Electronic Systems Magazine - October 2020 - 30

Feature Article:

DOI. No. 10.1109/MAES.2020.3022485

Pseudonoise Waveform Design for Spectrum Sharing
Systems
Janusz S. Kulpa, Embry-Riddle Aeronautical University; Warsaw University of
Technology
Grzegorz Krawczyk, Anna Kurowska, Warsaw University of Technology

INTRODUCTION
Demand on the frequency spectrum is rising due to the
need for both high-resolution radars and high-throughput
wireless networks. For such systems to coexist, a way to
minimize the intersystem interference is necessary. Some
of the current designs rely on the spatial properties of the
transmitted signals, employing various beamforming algorithms [1], [2]. Such an approach blinds the radar system
in the direction of the communication transmitters. An
alternative approach is to encode the radar signal and the
communication codewords in such a way that those two
does not interfere with each other. Such a solution requires
knowledge about the communication receiver position and
the transmission channels, as presented in [3], and is not
always applicable. The simplest solution is the design of a
radar waveform with spectral nulls [4] for the frequencies
occupied by the communication service. Various signals
can be used by the radar as a sounding signal: a liner or a
nonlinear frequency modulation signals, as well as phase
and amplitude coded ones, each having its benefits and
drawbacks. However, noise radars deter from using highly
structured signals. The two most commonly used ones are
Gaussian noise, and a unimodular pseudonoise, i.e., signal
with a constant amplitude and a random phase. The noise

Authors' current addresses: Janusz S. Kulpa is with the
College of Engineering, Embry-Riddle Aeronautical
University, Daytona Beach, FL 32114 USA, and also
with the Institute of Electronic Systems, Warsaw University of Technology, 00-665 Warsaw, Poland (e-mail:
janusz.s.kulpa@gmail.com). Grzegorz Krawczyk and
Anna Kurowska are with the Institute of Electronic Systems, Warsaw University of Technology, 00-665 Warsaw, Poland.
Manuscript received September 6, 2019, revised
January 14, 2020, and ready for publication September
4, 2020.
Review handled by Christoph Wasserzier.
0885-8985/20/$26.00 ß 2020 IEEE
30

or pseudonoise signal can be regarded as a coded signal
with up to infinite code space. In practical design, a code
space is limited by system requirements, and or by analog-to-digital converters' bit depth.
The usage of noise-like waveforms provides good electromagnetic compatibility with other transmitters operating
at a given frequency range, as their signal does not correlate
with other radar or communication signals. However, the
presence of a radar signal increases the noise level, which
may be seen as an increase of the thermal noise level of
other antennas operating in the same band. Noise radars are
preferable as low probability of detection radars. The major
disadvantage of such radars is the masking effect, i.e., when
a weak echo is masked by residual correlation of the signal
originating from strong reflections.
The processing scheme in modern noise radars [5] is
based on a cross-ambiguity function (CAF) calculation
between digitized transmitted (xt ) and received (xr )
signals, given by formula [6]
xxt xr ðm; fd Þ ¼

NÀ1
X

xr ½n xt Ã ½n À mej2pfd n=N

(1)

n¼0

where m is time delay related to the range of the target, fd
is normalized Doppler frequency shift, and N is the number of samples in the integration block.
The resulting CAF is a superposition of the ambiguity
function of the sounding waveform (i.e., cross ambiguity
with itself), with respect to all reflecting points in the
observed scene. An ideal noise signal has a thumbtack
ambiguity function, with the maximum value at the origin,
and is zero-valued otherwise. In practical implementations, both time interval and frequency band of the integration is limited. Those limits generate a so-called noise
floor-sidelobes that spread infinitely in the range-Doppler plane. Contrary to FMCW or pulse radars, there is no
frequency or time separation between the reception of the
signals from nearby and far away targets. The close targets
and ground clutter produces strong echoes, sidelobes of
which can completely mask weaker echoes of far-away

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