PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
December 2014
1107
GPU Processing for UAS-Based
LFM-CW Stripmap SAR
Craig Stringham and David G. Long
Abstract
Unmanned air systems (
UAS
) provide an excellent platform
for synthetic aperture radar (
SAR
), enabling surveillance
and research over areas too difficult, dangerous, or costly
to reach using manned aircraft. However, the nimble nature
of the small
UAS
makes them more susceptible to external
forces, thus requiring significant motion compensation in
order for
SAR
images to focus properly.
SAR
backprojection
has been found to improve the focusing of low-altitude
stripmap
SAR
images compared to frequency domain al-
gorithms. In this paper we describe the development and
implementation of
SAR
backprojection appropriate for
UAS
based stripmap
SAR
that utilizes the unique architecture of a
GPU
in order to produce high-quality imagery in real-time.
Introduction
Unmanned air systems (
UAS
) carrying synthetic aperture radar
(
SAR
) can obtain high-quality high-resolution information over
areas too difficult, dangerous, or costly to reach using manned
aircraft.
SAR
systems are active radars that transmit and
receive microwave signals. The received signals are used to
create images of the surface and are able to operate regardless
of illumination or weather conditions. The nimble nature of a
small
UAS
makes it much more mobile but also more suscep-
tible to external forces, thus requiring significant motion com-
pensation in order for
SAR
images to focus properly. Low-al-
titude operation further complicates motion compensation
of stripmap
SAR
images, due to the large range of incidence
angles and increased range cell migration.
SAR
backprojection
inherently handles arbitrary aircraft motion and low-altitude
geometry and can form images directly along known topogra-
phy making it a particularly effective algorithm for
UAS
-based
SAR
. However, backprojection is much more computationally
demanding than frequency domain algorithms (Melvin and
Scheer, 2012). Fortunately, backprojection processing is easily
parallelized and computed efficiently on graphics processing
units (
GPU
). Several studies have been conducted on imple-
menting backprojection on
GPUs
, most notably Fasih and
Hartley (2010), Benson
et al
., (2012), Capozzoli
et al
. (2013),
and Nguyen
et al
. (2004), but these papers focus on the sim-
plest form of spotlight mode
SAR
backprojection and are not
directly applicable to stripmap
SAR
. In this paper we present
the development and implementation of a highly efficient
GPU
-based
SAR
backprojection processor for stripmap imag-
ing. In particular, we develop a stripmap processor for linear
frequency-modulated continuous-wave (
LFM-CW
)
SAR
systems
operated on a
UAS
.
This paper is organized as follows. We begin with a back-
ground discussing the
LFM-CW
signal, stripmap
SAR
, and a
brief introduction to the
NVIDIA GPU
architecture and Compute
Unified Device Architecture (
CUDA
). Then, we develop a
SAR
backprojection method that accounts for motion during the
pulse and the moving antenna pattern, which is suitable for
UAS
based stripmap
SAR
. This is followed by a discussion of
the implementation of the
SAR
processor on a
GPU
. Finally, we
use
SAR
data from
CASIE
2009 (Long
et al
., 2010) to analyze the
performance of the implementation and present the resulting
imagery.
Background
LFM-CW Signal
Modern
SAR
systems can be very small, low-power, and
lightweight such that they can be used on a small
UAS
. This
reduction in size has greatly been made possible by technol-
ogy advancements and the use of
LFM-CW
technology.
LFM-CW
radars maximize the signal to noise ratio (
SNR
) achievable for
a given peak transmit power by continuously transmitting,
maximizing the energy of the received signal. To achieve
high-resolution, the transmit signal is modulated over a wide
range of frequencies.
The transmit signal of an
LFM-CW
radar can be described as
the complex exponential:
s t
j
f t k t
t
r
η
π π ϕ
,
( )
= −
+ +
(
)
{
}
exp 2
0
2
(1)
where
f
0
is the carrier frequency,
k
r
is the chirp rate,
ϕ
is
the initial phase of the system, and
η
and
τ
are respectively
“slow-time” and “fast-time” which are typical
SAR
notation.
Slow-time changes discretely with each pulse while fast-time
ranges over the length of the pulse,
T
p
. The received signal
from a single scatterer with position,
x
, can be described as
an attenuated, time-delayed copy of the transmit signal. The
received signal can be written as:
r t A t s t
t
A t
j
f t
x
x
x t
x
x
x
η
η σ τ η
η σ
π
,
,
,
,
(
( )
=
( )
−
( )
(
)
=
( )
−
−
exp 2
0
τ η π τ η ϕ
x
r
x
t
k t
t
( , ))
(
( , ))
+ −
+
(
)
{
}
2
(2)
where
A
x
is an amplitude function due to the antenna pattern,
incidence angle, the distance to the scatterer, and the backscat-
ter from the target is
σ
x
, and
τ
x
(
η
,
t
) is the round-trip propaga-
tion time of the radar signal, which consists of the time for the
pulse to travel from the transmit antenna to the position
x
plus
the time for the backscatter to radiate back to the receive anten-
Brigham Young University, 459 Clyde Building, Provo UT
84602 (
.
Photogrammetric Engineering & Remote Sensing
Vol. 80, No. 12, December 2014, pp. 1107–1115.
0099-1112/14/8012–1107
© 2014 American Society for Photogrammetry
and Remote Sensing
