IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 11, NOVEMBER 2007 3519
Signal Processing for FMCW SAR
Adriano Meta, Member, IEEE, Peter Hoogeboom, and Leo P. Ligthart, Fellow, IEEE
Abstract—The combination of frequency-modulated
continuous-wave (FMCW) technology and synthetic aperture
radar (SAR) techniques leads to lightweight cost-effective imaging
sensors of high resolution. One limiting factor to the use of
FMCW sensors is the well-known presence of nonlinearities in the
transmitted signal. This results in contrast- and range-resolution
degradation, particularly when the system is intended for high-
resolution long-range applications, as it is the case for SAR.
This paper presents a novel processing solution, which solves the
nonlinearity problem for the whole range profile. Additionally,
the conventional stop-and-go approximation used in pulse-radar
algorithms is not valid in FMCW SAR applications under
certain circumstances. Therefore, the motion within the sweep
needs to be taken into account. Analytical development of the
FMCW SAR signal model, starting from the deramped signal
and without using the stop-and-go approximation, is presented
in this paper. The model is then applied to stripmap, spotlight,
and single-transmitter/multiple-receiver digital-beamforming
SAR operational mode. The proposed algorithms are verified by
processing real FMCW SAR data collected with the demonstrator
system built at the Delft University of Technology.
Index Terms—Doppler frequency correction, frequency-
modulated continuous wave (FMCW), nonlinearity correction,
synthetic aperture radar (SAR).
I. INTRODUCTION
T
HE COMBINATION of frequency-modulated
continuous-wave (FMCW) technology and synthetic
aperture radar (SAR) techniques leads to lightweight cost-
effective imaging sensors of high resolution. FMCW SAR
systems are going to play an important role in airborne Earth
observation fields, where frequent revisits at low cost are
needed or where small size is a requirement. In fact, differently
from pulse radars which require high peak transmission power,
FMCW systems operate with constant low transmission power,
which means lower cost and smaller size. FMCW radars
are, therefore, of great interest to the civil market for their cost
effectiveness and to military applications for their compactness.
Manuscript received September 29, 2006; revised March 9, 2007. This work
was supported in part by the Technology Foundation STW, by the Applied
Science Division of NWO, and by the Technology Program of the Dutch
Ministry of Economic Affairs.
A. Meta was with the International Centre for Telecommunication and Radar,
Delft University of Technology, 2600 GA Delft, The Netherlands. He is now
with the German Aerospace Center, Microwaves and Radar Institute, 82234
Oberpfaffenhofen, Germany (e-mail: adriano.meta@dlr.de).
P. Hoogeboom is with the TNO Defense, Security, and Safety, 2509 JG
The Hague, The Netherlands and also with the International Centre for
Telecommunication and Radar, Delft University of Technology, 2600 GA Delft,
The Netherlands.
L. P. Ligthart is with the International Centre for Telecommunication and
Radar, Delft University of Technology, 2600 GA Delft, The Netherlands.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TGRS.2007.906140
On the other hand, the low transmitted power limits the
maximum distance of interest to a few kilometers, which is,
however, enough for several imaging applications.
Conventional SAR algorithms have been developed for pulse
radar, therefore, when using FMCW sensors, proper algorithms
have to be used to achieve the expected results with the maxi-
mum resolution. Under certain circumstances, in fact, the stop-
and-go approximation used in conventional SAR algorithms
is no longer valid. An algorithm processing FMCW SAR
signals is presented in [1]; however, it requires the complete
bandwidth of the transmitted signal to be sampled and a single
long fast Fourier transform (FFT) to be performed over the
whole collected data for the processing. Differently, here we
propose an algorithm which uses the inherent FMCW deramp-
on-receive operation; in this way, the raw-data bandwidth can
be drastically reduced, particularly for high-resolution systems.
The presence of nonlinearities in the transmitted chirp signal
is limiting the use of cheap and simple high-resolution FMCW
systems with dechirp-on-receive to short-range applications.
Nonlinearities deteriorate the range resolution when deramping
techniques are used because they spread the target energy
through different frequencies [2], [3]. In fact, the beat frequency
corresponding to a target response is not constant. The conse-
quence is a more broadened response after a Fourier transform.
The nonlinearities in the beat signal are the difference be-
tween the transmitted and received nonlinearities; in the beat
signal, their influence is therefore greater for larger distance. In
fact, the transmitted and received nonlinearities are almost the
same for short-distance targets, and so, their difference results
in a compensation of a great part of the original nonlinearities.
This can be seen in Fig. 1, where the spreading of the beat signal
is greater in the target response at larger distance than the closer.
Hardware and software approaches are known in literature to
face the problem. Hardware solutions include the use of a pre-
distorted voltage-controlled oscillator (VCO) control voltage to
have a linear FM output and complex synthesizer concepts with
phase-locked loop [4], [5]. However, the former approach fails
when the external conditions, i.e., the temperature, are chang-
ing, while the latter requires quite costly devices. The use of
direct digital synthesizer offers quite cost-effective solution [6],
but the transmitted bandwidth is still limited when compared
to the one obtained by directly sweeping the VCO. Different
local oscillators could be used to transmit large bandwidths
at the cost of increased system complexity. Additionally, non-
linearities can be introduced by the system-transmitting chain
when using large bandwidths. Software solutions make use of
a reference response to estimate the frequency nonlinearities
directly from the acquired deramped data and partially com-
pensate them using different methods: Resampling of the data
in order to have a linear behavior [7] and matched filtering with
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