IEEE Geoscience and Remote Sensing Magazine - June 2017 - 61

of the feedthrough signal is much lower than that of the
desired returns from snow at ranges of 250 m or more.
The feedthrough signal can thus be effectively filtered
at the IF stage. Figure 3 shows an example of the beatfrequency spectrum for a long-range FM-CW system with
a feedthrough signal. The feedthrough signal here is 15 dB
higher than the desired signal return, and its beat frequency is much lower than that of the desired target's return.
Although the feedthrough signal is out-of-band at the IF,
its presence can still saturate the radio-frequency (RF) portion of the receiver, and it also increases the noise floor of
the system. The effect of the feedthrough signal can thus
only be mitigated by minimizing the transmitter-receiver
leakage. For the Snow Radar systems in this article, this
was achieved by reducing the mutual coupling between
transmit and receive antennas to be less than −50 dB using
a custom-built antenna enclosure with microwave-absorbing material lining [23].
fM-CW RADAR fOR SNOW MEASUREMENT
Measuring the thickness of snow on sea ice and mapping internal layers to determine snow accumulation on glaciers and
ice sheets with FM-CW radars involves measuring the time
delay between the radar and dielectric discontinuities, such
as the air-snow and snow-ice interfaces of snow-covered sea
ice and layers within polar firn. The radar's ability to accurately map these interfaces depends upon three primary factors: SNR, surface conditions, and range resolution. The SNR
of an FM-CW radar can be determined using the standard radar equation, where the received power can be written as [37]
Pr =

Pt G t G r G pc m 2 v
Pt G t G r G pc m 2 v 0
= ##
dS
3 4
^ 4π h R
^4π h3 R 4
A

(4)

and the system noise can be written as
N = kTBFN .

air-snow and snow-ice or snow-ground interfaces are electrically smooth over the Fresnel zone of the radar. The diameter of a Fresnel zone, D Fresnel, is given by
D Fresnel = 2

Rm
2 .

(8)

For a surface to be electrically smooth, its root-meansquare (rms) height must satisfy the Fraunhofer criterion,
i.e., h < m/ (32 cos i), where h is the rms height of the surface and i is the angle of incidence [38]. In this case, a
majority of the backscattered energy is confined to the
specular direction. When the interfaces are not electrically
smooth, the backscattering coefficient v 0 can be broken
down into the coherent component v 0coh and the incoherent component v 0incoh. Detailed expressions of these two
terms were presented by Ulaby et al. [39]. As the surface
gets rougher, the coherent term decays rapidly, while the
incoherent term becomes dominant and the overall backscatter shows less dependence on the incident angle, because the incident wave energy is scattered and reradiated
in all directions. Figure 4 shows the backscattering coefficient as a function of the incident angle for different
surface-roughness scenarios. The radar's ability to clearly
map the air-snow and snow-ice interfaces, thus, heavily depends upon the interface roughness. In some cases,
synthetic aperture radar (SAR) processing may be required
to enhance the SNR of rough interfaces by integrating the
backscattered energy over a larger distance. For typical processing, unfocused SAR processing is applied to the Snow
Radar data; in other words, the data in the along-track are
coherently averaged over a length that is not longer than the
Fresnel zone. This is acceptable because, for most cases, the
snow interfaces are relatively smooth, and most of the reflected signal is limited to small angles. Also, unfocused SAR

(5)

Hence, the radar's SNR can be expressed as
Pt G t G r G pc m 2 v
Pt G t G r Tpd m 2 v
=
,
3 4
^ 4π h R kTBFN
^4π h3 R 4 kTFN

where Pt is the transmitted power; G t and G r are the gain of
the transmit and receive antennas, respectively; G pc = Tpd
B is the pulse compression gain; v is the radar scattering
cross section of the target and v 0 is the backscattering coefficient; A 0 is the illuminated area; k is the Boltzmann constant; T is the temperature; and FN is the receiver noise figure. The equation shows that the pulse-compression gain,
or the time-bandwidth product, is the key radar-design
parameter to enable low-power, long-range remote sensing
with FM-CW radars.
For a perfectly flat planar target, (4) can be rewritten as
Pr =

Pt G t G r G pc m 2 C 2
,
^ 4π h2 (2R) 2

ieee Geoscience and remote sensing magazine

Feedthrough Signal
Target Return

-10
-20
-30
-40
-50
-60

0.2
0.4
0.6
0.8
Normalized Beat Frequency (Hz/Hz)
With Feedthrough

Without Feedthrough

(7)

where C 2 is the reflection coefficient of the planar interface. This equation is a good approximation when the
june 2017

(6)
Normalized Magnitude (dB)

SNR =

fIgURE 3. A comparison of the beat-frequency spectrum illustrating the effect of the feedthrough signal.

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2017