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Simulation and Modeling of Ground Penetrating
RADARs
M. Islam, M. U. Afzal, M. Ahmad, T. Taqueer
School of Electrical Engineering and Computer Science (SEECS)
National University of Sciences and Technology (NUST)
Islamabad, Pakistan
{10mseeaislam; usman.afzal; 10mseemuniba; tauseef.tauqeer} @seecs.edu.pk
Abstract -- This paper focuses on providing a design capable of
calculating range to target, material of target, Doppler shift of the
target, and gives the low cost implementation of the complete design
if hardware is also considered. The proposed model also provide
basis for designing ground penetrating Radars capable of detecting
underground metallic as well as non-metallic objects. While
selecting a frequency for the ground penetrating Radars water
absorption, attenuation, material of target and ground properties
should be kept in mind. 1 GHz frequency is therefore selected as it
can penetrate ground and is also sensitive to non-metallic targets.
For the Simulations Linear Frequency Modulation Continuous
Wave (FMCW) Radar principles are used as it is found that they
give good short range calculations and also have finer range
resolution as compared to pulsed Doppler radars. The overall
simulations are done on Advanced Design System (ADS) software.
Complete ground modeling is also done for the simulations. The
proposed ADS simulation model not only detects the presence and
relative frequency shift of the target, it can also deal with the
changing dielectric constant of target and ground, water content
and conductivity of ground. Range resolution up to 40cm can be
achieved if the proposed model is implemented.
Index Terms Frequency Modulated Continuous Wave, Ground
Penetrating Radar, Advanced Design System, Radar Cross
Section, Voltage Controlled Oscillator, Low Noise Amplifier, Free
Space Loss
I. INTRODUCTION
electromagnetic system for the detection and location of the
objects. It operates by transmitting a particular type of
waveform and detects the presence of a target based on the
received echo. It can measure the distance or range to the target
as well as the velocity of the target if it is non-stationary. The
Distance or Range to the target is given by measuring the round
trip time taken to reach the target [1].
eq-(1)
Where TR is the round trip time. This equation comes from the
R=cT equation if we take the round trip range. Once the radar
emits the transmitted pulse, a sufficient length of time must
elapse to allow any echo signals to return and detected before
the next pulse is transmitted. The longest range at which targets
are expected determines the rate at which the pulses may be
transmitted. If the target is non-stationary, it will experience
some Doppler shift in the frequency [2]. In case of Doppler
shift the frequency shifts by the amount given as
eq-(2)
Where is the frequency shift, d denoting the Doppler, is
the radial component of the velocity of target towards the
Radar, is the transmit frequency and c is the speed of light.
A. The Radar Equation
To determine the power levels and maximum range radar range
equation is used [3]. It relates the range of the Radar to the
characteristics of transmitter, receiver, antenna, target and the
environment. The measure of the amount of incident power
intercepted by the target and reradiated back in the direction of
the radar is denoted [1].
eq-(3)
Where is the projected area of the target as viewed from
the radar, is the reflectivity of the target at the polarization
of the Radar and is the target like gain in the direction of
the radar. The maximum Radar range at which the received
power becomes equal to the minimum detectable signal of the
Radar is given by
eq-(4)
Where is the effective area of the receiving antenna. For the
simulation purpose is also considered.
B. Frequency Modulated Continuous Wave (FMCW) Radar
For simulations and Design Frequency Modulated Continuous
Wave (FMCW) Radar was selected [4]. The transmit frequency
is continuously changed in a linear fashion [5]. This variation
can be of any form like saw tooth, sinusoidal pulse or
triangular. For the simulation purpose the triangular fashion
was selected so that there is a triangular like up and down
variation in the transmit frequency with respect to time. Figure-
1 further clarifies the change in frequency with respect to time.
The reason for selecting triangular wave FMCW Radar is that
the changing frequency serves as the timing mark which is not
present in case of Continuous Wave (CW) Radars. Thus in
978-1-4673-4451-7/12/$31.00 ©2012 IEEE
Continuous Wave Radars extracting targets range information
is not possible [4]. When we select Traingular or Sawtooth
variation in the frequency verses time plot the probability of
blind speed is also reduced [4]. With the help of this, both the
Doppler shift and the range to the target can be found.
Figure-1: Frequency vs. Time plot for Transmit and Receive Wave, Solid
line represents the transmitted signal, Dotted line represents the received
signal after some interval T [6]
By subtracting the two signals, the beat frequency can be
found. In figure-2 denotes the beat frequency.
Figure-2: Beat Frequency [4]
In case of Non-stationary targets, the beat frequency will have
the information of both the shift in frequency due to range and
the shift in frequency due to Doppler Shift. The frequency
verses time plot for transmit and receive frequency will become
as shown in Figure-3.
Figure-3: (a) Transmitted solid curve and echo dashed frequencies varying
with time. (b) Resulting beat frequency varying with time [1]
If the target is moving there will be two changes in the beat
frequency, Change in the beat frequency due to the distance
of the target form the Radar and is the change in the beat
frequency due to the speed of the target. The Doppler shift
causes the frequency-time plot to be shifted up or down
depending upon the direction of the moving target. On one
portion of the frequency modulation cycle the beat frequency is
increased by the Doppler shift while on the other portion it is
decreased. In case of short range targets . If the target is
approaching the Radar we will have the following two
equations.
fb (up)= fd fr eq-(5)
fb (down)=fd+fr eq-(6)
Using the equations 5-6, we can get both the range and the
Doppler Shift as shown in equations 7 and 8.
eq-(7)
eq-(8)
is the beat frequency produced for the increasing
transmit and receive frequencies and is the beat
frequency produced when the frequencies are decreasing. Using
and we can find the range as given in equation-9
eq-(9)
Where N= , is the average beat frequency in one period
and , where is the highest transmit frequency
and is the lowest transmit frequency. Using the velocity of
the target can also be found using the eq-(2). can be related
to beat frequency as given in equation-10 [7-9].
eq-(10)
The above calculations show that by implementing linear
FMCW Radar we can get both the information about the range
as well as velocity of the target.
C. Basic Block Diagram Of FMCW Radar
Figure-4: Basic Block Diagram
For producing the varying frequencies with time, Voltage
Controlled Oscillator (VCO) is used [6, 10]. The block diagram
shows that a triangular or ramp input is given to the VCO. Its
output frequency changes according to the input voltage. If the
input voltage is zero, VCO will output its free running
frequency that is actually the center frequency for a VCO.
The term k is the change in frequency according to the
voltage. K has the units of volts/second while is the change
per volts in frequency. is the characteristic of a particular
VCO. At the input of Low Noise Amplifier (LNA) we get the
signal that is reflected by the target that is the underground
hidden metallic or non-metallic mine, in the direction of the
Radar. The beat frequency can be extracted from the received
signal by mixing it with the transmitted waveform using a
frequency Mixer [10].
D. Advanced Design System Simulations
Microwave design and simulation tool capable of performing
system level, circuit level, Electromagnetic (EM),
communication system, Device level and complete RF system
Design level simulations [11]. ADS also have very powerful
Data handling and Data display window. Radar complete
results like transmitted waveforms, link budget, received
echoes, and component designing can be done on ADS and
analyzed in its data display window.
E. Ground Penetrating Radars (GPR)
The proposed simulation Model for an FMCW Radar is
focusing on detection of hidden metallic and non-metallic
mines under the ground. Such Radars are termed as Ground
Penetrating Radars (GPR). GPR systems are also capable of
detecting the ground structure and its geological properties.
They also used in sedimentary geology and glacier studies. The
wave that penetrates the ground hits the object underground
and based on the conductivity of the object and its cross
sectional area it is reflected back. Beat frequency can then be
analyzed for range and relative velocity of the transmitter and
the object as discussed in Section II-B. The Section II of the
paper deals with the implementation of the overall proposed
model, Section III discusses the results obtained and finally
Section IV gives the conclusions.
II. PROPOSED ADS MODEL
ADS already has an FM-CW Radar Simulations Model. It is
using envelope simulator to demonstrate a simple Doppler
Radar working. The variables considered in the Model are
targets cross section, velocity and range of the target form the
Radar. The existing design is modified for the application as a
GPR. The proposed Model is also ground properties dependent,
which are not being dealt in previously proposed models [6].
A. Frequency Selection
As mentioned earlier in the paper, that the basic application
considered here is the ground penetrating Radars. Furthermore,
another requirement is that the Radar should be capable of
determining range as well as the velocity of the target if the
target is non-stationary or we have our Radar in motion with
respect to the stationary underground target. For this reason, a
number of parameters need to be considered while selecting
the appropriate frequency. ADS existing design is working on
10GHz frequency. Designing or purchasing components at
10GHz is very expensive. Another problem with 10GHz
frequency is that it does not penetrate the ground much and
causes reflections from the ground. When dealing with
frequencies and distance Free Space Loss (FSL) is a very
dominant factor that also increases with frequency.
B. Modeling Free Space in ADS
FSL is derived from the Friis transmission formula and is given
by
Free Space Loss = 32.45 + 20log(d) + 20log(f) dB [5] eq-(12)
Where d is in km and f is in MHz. As we are not dealing with
free space, atmosphere has oxygen and water in it. Their
specific attenuation is also frequency dependent [1]. Specific
attenuation due to water molecules become 0.001dB/km at
4GHz, while due to oxygen, it is 0.01dB/km at 20GHz.
Resonance or maximum attenuation for water vapor is most
significant at 22.3, 183.3 and 323.8 GHz and those of Oxygen
it is maximum between 57 and 63 GHz with another maxima at
118.74 GHz. Water heating also starts at 2.4 GHz as in our
microwave ovens [12]. For a generalized design equation-12
has been implemented on ADS to represent FSL.
C. Modeling the Ground
Reflection and absorption of an electromagnetic wave from a
ground depends greatly on the dielectric constant and
conductivity of the ground. Dielectric constant and conductivity
depends upon the water content of the ground and the
frequency of the transmitted wave [13, 14]. This is the first
model in ADS that deals with different types of ground
materials. The proposed ADS model incorporates different
attenuations to the signal depending upon the water content of
the ground and the frequency of transmitted wave. The signal
decays exponentially when it penetrates the surface of ground.
The round trip attenuation loss when signal enter the ground is
given by [15]
eq-(11)
Where D is the round trip distance below ground and is the
attenuation constant. It is given by equation 13
eq-(13)
is the 2 x frequency, is the dielectric constant, is the
conductivity of the soil. The value for dielectric constant and
conductivity now depends on different types of ground and
water content of the ground. For the simulation purpose the
proposed values in [12] has been used for dielectric constant
and conductivity. These values are listed in the Table-1
Table-1: Ground Parameters [12, 16]
Surface Conductivity Relative Dielectric
Constant
Dry Ground 0.001 4-7
Average Ground 0.005 15
Wet Ground 0.02 25-30
Sea Water 5 81
Fresh Water 0.01 81
Another advantage of the proposed simulation method is that
the design becomes more close to the practical GPR systems if
the parameters of a specific ground are known.
Here we also come to know that lower frequencies are more
appropriate if we need to deal with a ground penetrating Radar
as it can be seen in equation-13 that attenuation constant
increases with frequency. Furthermore, we also need to avoid
the frequency where maximum attenuation in atmosphere
occurs. Our frequency should be such that the target lies in the
far field for accurate range measurements [1]. Another
restriction is the selecting the frequency of the triangular wave
that is given as an input to the VCO to control its output
frequency. This frequency sets the maximum unambiguous
range of target or mine detection for our Radar. The maximum
unambiguous range is given by equation 14.
eq-(14)
Where is the frequency of the modulating signal given as an
input to the VCO to control its output frequency. For the
proposed design, this signal is the triangular wave. The
maximum unambiguous range defined here is different from
the range given in equation-4 that depends upon the minimum
detectable signal level by the receiver. Minimum detectable
signal of receiver is above its noise threshold given by equation
-15 [6]. This Threshold helps in selection of LNA.
eq-(15)
D. ADS Simulated Design
Frequency of the triangular wave was taken as 50KHz. This
gives the maximum unambiguous range of 3km. This range is
very large for the Ground Penetrating Radars but they give
good resolution when used on ADS as compared to higher
frequencies. Another advantage of using high frequency is its
easier implementation. As we are dealing with ground
penetrating Radar we need to model two types of velocity of
propagation of wave: propagation velocity above ground and
propagation velocity below ground. In ADS two types of
transmission lines are used to introduce the delay in the signal
based on the Range of the target. The electrical length of the
TL1 is taken according to the range in free space. Here D is the
distance above ground and lambda is c/f where f=1GHz. Free
space has been considered for simplicity instead of atmosphere.
TL2 has the electrical length such that it corresponds to the
range below ground. D2 is the distance below ground.
Lambda2 is the wavelength calculated using /f for velocity of
wave in ground. Propagation velocity is given by equation -16.
eq-(16)
is 1, while can be substituted using Table-1. FSL and
ground loss has been implemented using two different
attenuators. Target cross section is modeled using an amplifier
and setting its gain as given in equation-(17). This technique
for modeling the target is same as in the existing model in
ADS.
eq-(17)
Figure-5 The complete ADS implemented Design
III. RESULTS AND DISCUSSION
The design operates at 1 GHz as this frequency can penetrate
ground and is suitable to keep the target in far filed region of
the antenna. The antenna used has the gain of 10dB. So the
diameter of antenna with 10dB gain and 55% efficiency is
0.41m [3]. The minimum distance of the target to be in the far
filed region of an antenna is 1.12m.
For the simulations the values of power level and component
properties are selected according to the components available in
the market for easier implementation. All the values can be
changed according to the availability. For the design simulated
VCO outputs +9dBm power. 10dB coupler is used to couple
10% of the power in the Local Oscillator port of the mixer.
Rest of the power is amplified by a 40dB gain amplifier and is
transmitted by an antenna having gain of 10dB. At the
receiving end, Antenna with a gain of 10dB is used. It is
amplified by an LNA of 20dB gain. Beat frequency can be
obtained at the intermediated frequency port of MIXER.
A. Range Simulations for stationary targets
Once we get the beat frequency at the output of the mixer,
range can be calculated by using equation-(9). The theoretical
and calculated values for different ranges are discussed in
Table-2. Here the above ground distance is taken as 2m,
keeping in view that the ground should be in the far filed of the
antenna.
Table-2: Comparison of Simulated and theoretical Beat
Frequencies S.NO Range
Above
Ground (m)
Range
Below
Ground (m)
Theoretical
(MHz)
Simulation
Results
(MHz)
1 4 0.25 0.091 0.1
2 4 1.2 0.704 0.750
3 4 1.6 0.8506 0.850
4 4 2 0.996 1
5 4 2.5 1.17 1.2
6 4 3 1.36 1.4
7 4 3.5 1.53 1.5
Assuming that due to the range above ground a fixed beat
frequency is produced that can be found in ADS by keeping
distance below ground as zero. This beat frequency is shown in
figure-6 is 250KHz. The Figure-6 also shows the decrease in
amplitude and shift in beat frequency when it hits some target
below ground at a distance of 25cm. The beat frequency has
now shifted to 350KHz.
Figure-6: Beat Frequency without the ground Distance considered and
with target 25cm below ground
Subtracting 250KHz frequency from the results each time will
give the desired range. In case of underground mine the shift in
the beat frequency can be seen as shown in figure-7. It can be
seen that the shift varies with the distance. The amplitude of
beat frequency is also decreasing exponentially.
Figure-7: Change in beat frequency due to range of target
Table-3: Error in theoretical and Simulation Ranges
S.No Theoretical
Range Below
Ground
(m)
Range found
by
Simulations
Below
Ground (m)
Error
(%)
1 1 1.09 8.25
2 1.2 1.24 3.22
3 1.6 1.64 3.22
4 2 2.05 2.4
5 2.5 2.55 2.06
Table-3 shows the theoretical and simulated ranges.
B. Range and Speed Simulations for Non-Stationary
Radars
In case of GPR usually the mine is stationary, while the Radar
moves with certain speed over the ground surface. As a result,
due to very low relative speed of the Radar very low frequency
change is observed in the beat frequency. Normally if even the
Radar is moving at the speed of 20km/hour, than the beat
frequency produced is only 20Hz. To view small changes in
beat frequency the step size in transient solver needs to be
decreased causing greater number of points and heavier data
files. For this reason currently Doppler shift has been ignored.
However if Doppler shift is higher for example 20MHz the
shift in the beat frequency becomes prominent. In that case the
difference of two frequencies gives the beat frequency while
average gives the Doppler Shift. The following figure-8 shows
the two different beat frequencies produced in first and second
half cycle of the triangular wave.
Figure-8: Doppler Shift for Non-stationary radars
Transient Solver has been found better than the harmonic
balance or envelope simulator as overall time domain
waveforms can be viewed. A problem associated with
harmonic balance is that the triangular wave generator of ADS
does not work in Harmonic Balance Simulator causing
problems in Simulations. On the other hand Harmonic Balance
Simulator can perform both frequency as well as time domain
analysis with greater accuracy and lesser data points.
The errors found in range measurements are very low and close
to the theoretical results. The only problem that needs
improvement is accuracy in range and speed measurements so
that smaller frequency shifts in terms of Hz can be seen.
IV. CONCLUSION
Range Shift can be measured with more accuracy and range
resolution. It can also measure short range as 40cm. The beat
frequency produced is a very low frequency which can be
analyzed easily giving easier hardware implementation. An
advantage of FMCW Radars over Pulsed Doppler Radars is
that they do not have any theoretical range resolution. It just
depends on our sampling [17, 18]. As our focus in GPR is
Range of the target underground, FMCW Radars are preferred.
For a GPR frequency of 1GHz is selected keeping in view
factors like attenuation due to ground, absorption by water
molecules and antenna dimensions. Another advantage of using
the particular frequency is detection of non-metallic mines that
is not possible on higher frequencies.
All the values of transmitted power and other component
parameters are considered according to the practically available
components. If practical simulations are required, component
delays need to be added to make the model close to practical.
Circulators need to be added in order to protect the components
from the part of transmitted power reflected from ground
towards transmitters.
The proposed model is the ADS solution to GPR that also deals
with properties of a soil. The attenuation due to ground depends
on its conductivity, relative permittivity and permeability.
These parameters are also frequency dependent. Targets
reflectivity of power also depends on the targets material and
cross section. The proposed design deals with complete
modeling of effect of different Ground as well as target
material properties like relative permittivity and conductivity.
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