IEEE Geoscience and Remote Sensing Magazine - March 2020 - 47

linear track, the synthetic aperture length is only the length
of the track during the scanning process. The radar antenna
moves along the linear track, and the antenna beam is perpendicular to the track so as to irradiate the target area. The
slant range of point target P can be expressed as
R(t) = (R 0 sin a)2 + (R 0 cos a - Va t)2 , (8)

	

where R 0 is the range between the coordinate origin and
point target P, and a is the squint angle.
Figure 7 shows the geometric model of the arc scanning mode GB-DInSAR system. It forms an arc-synthetic
aperture by rotating the antenna on the horizontal plane.
The radar antenna rotates with the rotating arm in the XOY
plane to scan the target area. The slant range of point target P [38] can be expressed as
R(t) = R 20 + r 2 - 2rR 0 cos(i - b) , (9)

	

where R 0 represents the range between target P and the rotating center O of the radar platform, r represents the length
of the rotating arm, b represents the angle between the OP
and the x-axis, and i represents the angle between the antenna and the x-axis, given as
	

i = ~t. (10)

fr
t
	 ss(t, fr; i) = rect c B m $ rect ` T j $ exp" j 6-2r( f0 + fr) x T@,,
r

where B r is the bandwidth of transmitted signal fr = K r # x d .
IMAGING PROCESS
After the system completes its echo data acquisition and demodulation, the imaging process is implemented to obtain
the complex data image of the observation area. The imaging algorithms used by GB-DInSAR are mainly derived
from the methods of spaceborne or airborne SAR systems,
in which the azimuth resolution depends only on antenna
length. However, because GB-DInSAR cannot obtain full
synthetic aperture, the azimuth resolution is affected by the
observation distance.
INTERFEROMETRY PROCESS
After the imaging process obtains multiple complex data
images of the observation area, the complex images are
utilized to perform the interferometry process that generates the interferometry phase. Then, the interferometry
phase can further be used to estimate the deformation.
Unlike spaceborne or airborne SAR, the GB-DInSAR interferometry process generally does not require image
coregistration due to the high accuracy of the antenna

SIGNAL MODEL
Using the FMCW system as an example, the signal model
of the GB-DInSAR system is introduced in (11)-(14). The
echo signal of a stationary target is expressed as
	

x - xp
t
ss(t, x; i) = rect a T k $ rect ` T j
p
a

$ exp " j $ 62rf0(x - x p) + rK r (x - x p)2@,,

Radar Beam

P

Y
R0

(11)

where t is the time in azimuth and Ta is the scanning time
along the azimuth. The dechirp-on-receive technique is
used to reduce the sampling requirements by mixing the
received and transmitted signals [45]. To demodulate the
frequency spectrum of echo signals to the baseband, the
reference signal is
	

a

(14)

R (t )

α
-Ls /2

Ls /2

O

X

FIGURE 6. The geometric model of linear scanning mode.

s ref = exp " j 62rf0(x - x c) + rK r (x - x c)2@,, (12)

where x c = 2rc /c is the time delay of the reference signal0

P
R0

)

ss IF(t, x; i) = ss(t, x; i) $ s ref
x -x
t
= rect a d T T k $ rect ` T j
p
a
$ exp " j 6-2rf0 x T - 2rk r x d x T@, $ exp " - j 6rK r x T2 @,.

R (t )

Y

Radar Beam
β

(13)

θ

r

The last exponential term is the well-known residual
video phase (RVP). It can be eliminated by a method called
deskew, which comprises the FT, phase multiplication, and
inverse FT. After the RVP removal, we obtain
MARCH 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

O

X

FIGURE 7. The geometric model of an arc scanning mode.

47
IEEE Geoscience and Remote Sensing Magazine - March 2020

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