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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