Geoscience Reference
In-Depth Information
Note that dispersion of the pulse shape due to wave propagation effects has been neglected
in our model.
Denoting by
S
i
(
ω
)
the self-spectrum of the signal at the output of the
i
-th receiver and
applying Parseval's theorem, we have that
ˆ
d
2
2
|
v
i
(
t
)
|
=
S
i
(
ω
)
.
(82)
π
Likewise, the cross-spectrum
S
i
,
j
and the cross-correlation of the signals at the outputs of
the
i
-th and
j
-th receivers are related by
(
ω
)
ˆ
d
2
v
j
(
v
i
(
)
)
=
S
i
,
j
(
ω
)
t
t
.
(83)
π
Assuming that the ambiguity function is almost flat within the bandwidth of the RCS
spectrum
(which is a valid approximation in the case of short-pulse radar
applications), we can use equations (78) and (80) to obtain the following beam-weighted
spectrum and cross-spectrum models:
σ
v
(
k
,
ω
)
E
t
K
i
ˆ
ˆ
2
r
2
2
2
dr
|
χ
(
t
−
c
)
|
Ω
|T
(
r
)
|
|R
i
(
r
)
|
S
i
(
ω
)=
Γ
i
(
r
)
σ
v
(
k
,
ω
)
d
(84)
4
π
r
2
k
2
and
E
t
K
i
,
j
ˆ
ˆ
2
R
i
(
r
)
R
j
(
r
)
k
2
Ω
|T
(
r
)
|
2
r
c
2
dr
|
χ
(
t
−
)
|
S
i
,
j
(
ω
)=
d
Γ
i
,
j
(
r
)
σ
v
(
k
,
ω
)
,
(85)
4
π
r
2
where
1
T
f
∗
(
−
χ
(
t
)=
t
)
∗
f
(
t
)
(86)
(
)
is the normalized auto-correlation of the pulse waveform
f
t
. In the radar equations (84) and
Γ
i
(
r
)
Γ
i
,
j
(
r
)
(85), the polarization coefficients
effectively modify the radiation patterns;
thus, the spectrum shapes are dependent not only on the scattering process but also on the
modes of propagation. This dependence further complicates the spectrum analysis of radar
data and the inversion of physical parameters.
and
10. Summary
In this chapter we have described the operation of ionospheric incoherent scatter radars (ISR)
and the signal spectrum models underlying the operation of such radars. ISR's are the premier
remote sensing instruments used to study the ionosphere and Earth's upper atmosphere.
First generation operational ISR's were built in the early 1960's — e.g., Jicamarca in Peru and
Arecibo in Puerto Rico — and ISR's continue to play a crucial role in our studies of Earth's near
space environment. These instruments are primarily used to monitor the electron densities
and drifts, as well as temperatures and chemical composition of ionospheric plasmas. The
latest generation of ISR's include the AMISR — advanced modular ISR — series which are
planned to be deployed around the globe and then re-located depending on emerging science
needs. With increasing ISR units around the globe, there will be a larger demand on radar
engineers and technicians familiar with ISR modes and the underlying scattering theory. For
that reason, in our presentation in this chapter, as well as in our recent papers (Kudeki & Milla,
2011; Milla & Kudeki, 2011), we have taken an “engineering approach” to describe the theory
of the incoherent scatter spectrum. Complementary physics based descriptions of the same
processes can be found in many of the original ISR papers included in references.
