IEEE Aerospace and Electronic Systems Magazine - October 2020 - 8

Feature Article:

DOI. No. 10.1109/MAES.2020.2975355

Noise vs. Deterministic Waveform
Radar-Possibilities and Limitations
- ukasz Maslikowski,
Mateusz Malanowski, Krzysztof Kulpa, Marcin Baczyk,
˛
L
Warsaw University of Technology Institute of Electronic Systems

INTRODUCTION
There are numerous types of radars using different waveforms, operating in various time regimes and applying different signal processing schemes in order to obtain
information on the observed target. One of the most commonly used radars is a pulse radar, which sends short
bursts of electromagnetic waveforms and then listens to
the echo. The simplest form of the pulse used is a carrier
wave that is switched ON and OFF, without any additional
modulation. The range resolution, which is the radar's
ability to distinguish the targets in the range dimension,
depends on the length of the pulse. In order to obtain finer
range resolution, a shorter pulse should be applied. A
shorter pulse results in a broader spectrum. This has turned
out to be the general rule. If fine range resolution is
desired, the signal spectrum should be wide. Achieving
this by shortening the pulse is not always possible, mainly
due to the high amplitude of the pulse required to maintain
pulse energy sufficient for the desired detection range.
Higher bandwidth, and therefore fine range resolution, is
obtained by applying modulation to the pulse. The most
common form of modulation is the linear frequency modulation (LFM), which consists in changing the instantaneous frequency linearly during the pulse duration. The
radars that use LFM signals, also known as chirps, can be
thought of as the most common and classical radars used.
Another type of radar that is used very often is the frequency modulated, continuous-wave (FMCW) radar. It
also uses chirp-like signals, but the signal is transmitted

continuously; once the chirp signal is over, it is repeated
immediately. The reason for applying the modulation to
the signal is the same as in the pulse chirp radar, which is
to obtain fine range resolution. The main difference
between a pulse LFM radar and an FMCW radar is that in
the former, the signal is received only between sending
the pulses, whereas in the latter, the signal is received
continuously.
The two radar types mentioned can be described as
deterministic-wave systems. This means that the properties
of the signals are known, and there is no randomness in their
design. The noise radar, on the other hand, uses a truly random waveform, or a waveform that resembles a random signal, such as a computer-generated pseudo-random sequence
[1]. The noise radar can operate in pulse or continuouswave mode, just like the deterministic radar.
Having the two representatives of deterministic radar,
namely the LFM pulse radar and FMCW, a question
arises: how does the noise radar compare to the classical
approaches?
The aim of this article is to analyze the similarities and
differences between the deterministic and noise radar from
the point of view of waveform design and analysis.

RADAR WAVEFORM ANALYSIS
A standard way of assessing a radar waveform is the ambiguity function [2], [3]. It can be defined as
Z
xðt; fd Þ ¼

Authors' current addresses: Mateusz Malanowski,
Krzysztof Kulpa, Marcin Baczyk,
˛
and L- ukasz
Maslikowski, Warsaw University of Technology, Institute of Electronic Systems, Warsaw 00-665, Poland
(e-mail: m.malanowski@elka.pw.edu).
Manuscript received September 8, 2019, revised
December 13, 2019, and ready for publication
February 18, 2020.
Review handled by Richard Linares.
0885-8985/20/$26.00 ß 2020 IEEE
8

þ1

À1

xðt À t ÞxÃ ðtÞexpðÀj2pfd tÞdt

(1)

where xðtÞ is the baseband representation of the analyzed
signal, t is the delay and fd is the frequency shift.
The reason why the ambiguity function of the signal is
useful for analysis in radar is the fact that what happens
with the signal during normal radar operation is emulated
during the calculation of the ambiguity function. The echo
signal is delayed and shifted in the frequency (due to the
Doppler effect), which is also represented in the ambiguity
function. The ambiguity functions show the similarity of

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