IEEE Geoscience and Remote Sensing Magazine - June 2017 - 60

0
-5
Normalized Magnitude (dB)

Normalized Magnitude (dB)

0
-5
-10
-15
-20
-25
-30
-35
-40
-45

-10
-15
-20
-25
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-45

-50
0.985

0.99
0.995
1
1.005
1.01
Normalized Beat Frequency (Hz/Hz)

10% AM

20% AM

100% AM

1.015
No AM

(a)

-50
0.985

0.99
0.995
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1.005
1.01
Normalized Beat Frequency (Hz/Hz)
0.1% FM

0.2% FM

1% FM

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No FM

(b)

fIgURE 2. The FM-CW radar system response with (a) amplitude modulation and (b) frequency modulation superimposed to the
radar signal.

shows that the beat frequency, fb, is directly proportional to
the time delay, t aud, between the transmitted and received
signals, which can be written as
fb = x d K = x d

f1 - f0
2R
B
Tpd = ` c ja Tpd k,

(2)

where R is the range to the target, B is the bandwidth of the
transmitted signal, and c is the speed of light. Given the radar parameters, the range to the target can be precisely determined by analyzing the frequency of the beat signal. The
mixing operation in the receiver is equivalent to pulse compression in hardware, which significantly improves the range
resolution and the signal-to-noise ratio (SNR) of the system.
SYSTEM EFFECTS AND THEIR REMOVAL
As mentioned in the previous section, frequency estimation
is critical in determining the range with FM-CW radars, and
it can be performed conveniently and efficiently with the
Fourier transform. For an ideal point target, the radar output is a pure single-tone beat-frequency signal. The Fourier
transform of this signal gives the ideal system response of
the radar, which is shown by the solid blue line in Figure 2(a).
However, in practical systems, signal reflections between
nonideal radar components and the frequency nonlinearity
of the chirp generator can easily introduce undesirable amplitude modulation or frequency modulation to the radar
signal, which modifies the transmitted chirp signal, x m (t), to
K
x m ^ t h = 61 + m a (t)@ cos :2π a f0 t + 2 t 2 + fT

#0 t m f ^xhdx kD,
(3)

60

where m a (t) is the amplitude-modulated (AM) waveform, fT
is the maximum frequency deviation, and m f (t) denotes the
FM waveform. The equation shows that the resultant beatfrequency signal is no longer a pure single-tone signal and
that the primary radar response is accompanied by ambiguous lobes, as shown in Figure 2. These ambiguous lobes, or
sidebands, can be misinterpreted as false targets and degrade
the overall radar performance. As shown in Figure 2, the
system response is less susceptible to amplitude modulation
[Figure 2(a)] than frequency modulation [Figure 2(b)]. For
example, a 10% amplitude modulation in the beat-frequency signal would result in a −26-dB lobe, but it would only
require less than 0.1% frequency modulation to achieve a
similar effect.
If the amplitude and frequency modulations are small,
they can be removed effectively by system-response deconvolution at a small expense of the system SNR. The system response of the radar can either be measured in the laboratory
in a loopback mode or estimated using a known radar target,
such as a corner reflector or a large, electrically-smooth surface. The details on system response deconvolution are discussed further in the "Snow Radar Data Processing" section.
In short-range FM-CW systems, the radar sensitivity is
often limited by the feedthrough signal caused by the leakage between the transmitter and the receiver, which is a
result of the finite isolation between transmit and receive
ports of a circulator used in single-antenna systems or the
mutual coupling between transmit and receive antennas
in dual-antenna systems. Very often, such a feedthrough
signal is much stronger than the desired target return and
can mask the desired signal. However, in long-range FMCW systems such as the Snow Radar, the beat frequency
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2017
