Geoscience Reference
In-Depth Information
in section 2.1 and 2.2, respectively. The readers are recommended to refer Hocking (2011)
for the thorough development history of the radar interferometry techniques. Further
applications aiming at advanced probing of the atmosphere are presented in section 2.3.
2.1 Angular resolution enhancement using spaced receivers
2.1.1 Signal processing
Fig. 1. shows a conceptual drawing of CRI. In CRI, signals from the spaced receivers are
synthesized with appropriate weights in order to steer the radar beam in certain directions
with improved angular resolution. For CRI, the Capon method (Capon, 1969) is widely used
because it satisfies both high angular resolution and simple calculation. Hereafter signal
processing of CRI using the Capon method is described. The Capon method is described as
the problem of finding optimal weights. The optimal weights used in order to calculate the
weighted sum of signals which are received by the spaced receivers.
s
denotes a set of
signals associated with the
N
spaced receivers at an arbitrary range gate and expressed by
T
s
() ( (), (),...,
t
s
t
s
t
s
())
t
,
(1)
1
2
N
where
t
is the sampled time and T is the transpose operator.
w
denotes a set of weights
for summation and is expressed by
T
w
(,
ww
,...,
w
)
.
(2)
12
N
The optimal weight vector is given by a solution that minimizes the resulting average power
B
.
B
is expressed by
H
B
wRw
,
(3)
where H represents the Hermitian operator (conjugate transpose) and
R
is a covariance
matrix given by
RR
R
11
22
1
N
N
RR
R
21
22
2
R
,
(4)
RR
R
N
2
N
2
NN
i
R
is a covariance between
s
and
s
. The length of time used for calculating
R
should be
determined by considering the accuracy of covariance value and the time resolution.
w
is
constrained by the condition of constant gain to waves coming from the target volume, and
the constraint is given by
H
ew
,
1
(5)
where
j
kD kD
j
j
kD
T
e
(
e
,
e
,
,
e
)
,
(6)
1
2
N
