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NAVAL

POSTGRADUATE

SCHOOL

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THESIS

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DESIGN A TRACKING SYSTEM WITH SINGLE

CHANNEL RSNS AND MONOPULSE DIGITAL

BEAMFORMING

By

ShihYuan Yeh

December 2010

Thesis Advisor: David C. JennThesis Co-Advisor: Roberto Cristi

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Approved for public release; distribution is unlimited

DESIGN A TRACKING SYSTEM WITH SINGLE CHANNEL RSNS AND

MONOPULSE DIGITAL BEAMFORMING

ShihYuan YehMajor, Taiwanese Army

B.S., Taiwanese National Defense University, 2001

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOL

December 2010

Author: ShihYuan Yeh

Approved by: David C. JennThesis Advisor

Roberto CristiThesis Co-Advisor

R. Clark RobertsonChairman, Department of Electrical and Computer Engineering

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TABLE OF CONTENTS

I.INTRODUCTION...........................................................................................................1

A. BACKGROUND...............................................................................................1

B. PREVIOUS WORK..........................................................................................2

C. SCOPE OF RESEARCH..................................................................................3

D. THESIS OUTLINE...........................................................................................4

II.DIRECTION FINDING AND ROBUST SYMMETRIC NUMERIC SYSTEM.....6

A.DIRECTION FINDING....................................................................................6

B. AMBIGUITY AND FOLDING WAVEFORMS............................................9

1. Ambiguity.............................................................................................10

2. Folding Waveforms..............................................................................12

C. QUADRATURE DEMODULATION...........................................................14

1. Signal Modulation................................................................................14

2. Quadrature Demodulation..................................................................15D. ROBUST SYMMETRIC NUMERIC SYSTEM THEORY........................17

1. Parameters Define................................................................................17

2. Interferometer Design.........................................................................19

III. TRACKING RADARS AND TECHNIQUES........................................................22

A. TYPES OF TRACKING RADAR SYSTEM...............................................22

1. Single-Target Tracker (STT)..............................................................23

2. Automatic Detection and Track (ADT).............................................23

3. Phased Array Radar Tracking...........................................................24

4. Track While Scan (TWS)....................................................................25

B. ANGLE TRACKING TECHNIQUES..........................................................25

1. Conical Scan.........................................................................................252. Sequential Lobing................................................................................25

3. Monopulse Tracking............................................................................26

a. Amplitude Comparison Monopulse.........................................26

b. Phase Comparison Monopulse................................................26

C. TRACKING ACCURACY.............................................................................26

1. Theoretical Angular Accuracy............................................................26

2. Limitations to Tracking Accuracy.....................................................26

a. Glint...........................................................................................26

b. Receiver Noise...........................................................................26

c. Amplitude Fluctuations............................................................26

d. Servo Noise...............................................................................26

IV. SINGLE CHANNEL RSNS COMPUTER SIMULATION AND HARDWARE

TESTING RESULTS..........................................................................................28

A.SINGLE CHANNEL RSNS DESIGN............................................................28

B. CALIBRATION..............................................................................................28

C. HARDWARE SETUP.....................................................................................28

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D. RSNS IN LABVIEW.......................................................................................28

E. MATLAB SIMULATION..............................................................................28

F. COMPARISON AND RESULTS..................................................................36

V. TRACKING WITH SINGLE CHANNEL RSNS AND MONOPULSE DIGITAL

BEAMFORMING TESTING RESULTS..........................................................38

A. ANECHOIC CHAMBER...............................................................................38B. HARDWARE SETUP.....................................................................................38

C. TRACKING PROGRAM IN LABVIEW.....................................................38

D. COMPARISON AND RESULTS..................................................................38

VI. CONCLUSIONS AND RECOMMENDATIONS..................................................40

A. CONCLUSIONS.............................................................................................40

B. RECOMMENDATIONS FOR FUTURE WORK.......................................40

LIST OF REFERENCES................................................................................................42

INITIAL DISTRIBUTION LIST...................................................................................45

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LIST OF FIGURES

FIGURE 1. INCIDENT PLANE WAVE ARRIVE TO TWO ELEMENT

ANTENNAS (AFTER [6]).....................................................................................7

FIGURE 2. I/Q SIGNAL DIAGRAM (FROM [10]).....................................................8

FIGURE 3. PHASE DIFFERENCE VS. AOA AT D= (AFTER [6]).........................10

FIGURE 4. PHASE DIFFERENCE VS. AOA AT D=(AFTER [6])..........................11

FIGURE 5. PHASE DIFFERENCE VS. AOA AT FREQUENCY=300MHZ..........11

FIGURE 6. PHASE DIFFERENCE VS. AOA AT FREQUENCY=900MHZ..........12

FIGURE 7. OUTPUT VOLTAGE VS. AOA AT (AFTER [6]).................................13

FIGURE 8. OUTPUT VOLTAGE VS. AOA AT (AFTER [6])..................................13

FIGURE 9. OUTPUT VOLTAGE VS. AOA AT (AFTER [6])..................................14

FIGURE 10. MODULATES WITH A SINUSOID CARRIER FREQUENCY........15

FIGURE 11. QUADRATURE DEMODULATION PROCESS (AFTER [10])........16

FIGURE 12. AD8347 QUADRATURE DEMODULATOR MADE BY ANALOG

DEVICES, INC. (FROM [10])............................................................................16

FIGURE 13. RSNS FOLDING WAVEFORMS FOR AND (FROM [12])...............20

FIGURE 14. AN/MPQ-53 (AFTER [13]).....................................................................22

FIGURE 15. AN/FPQ-6 (FROM [14]).........................................................................23

FIGURE 16. AN/SPY-1D (FROM [15]).......................................................................24FIGURE 17. DIFFERENCE BETWEEN IDEAL AOA, ESTIMATED AOA AND

MEASURED AOA AT SNR = 10.......................................................................28

FIGURE 18. DIFFERENCE BETWEEN IDEAL AOA, ESTIMATED AOA AND






FIGURE 21. DIFFERENCE BETWEEN IDEAL AOA, ESTIMATED AOA ANDMEASURED AOA AT SNR = 50.......................................................................32





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LIST OF TABLES

TABLE 1. RSNS SEQUENCE FOR MODULI SET [3,4] (FROM [6])....................18

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EXECUTIVE SUMMARY

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LIST OF ACRONYMS AND ABBREVIATIONS

ADC Analog to Digital Converter

ADT Automatic Detection and Track

AM Amplitude Modulation

AOA Angle of Arrival

ASR Air Surveillance Radar

ATC Air Traffic Control

COTS Commercial-of-the-shelf

DBF Digital Beamforming

DC Direct Current

DF Direction Finding

EM Electromagnetic

EW Electronic Warfare

FDM Frequency-Division Multiplexing

FM Frequency Modulation

FOV Field of View

G Gain

GUI Graphical User Interface

I In Phase

IC Integrated Circuit

IF Intermediate Frequency

LNA Low Noise Amplifier

LO Local Oscillator

LOS Line Of Sight

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LPF Low Pass Filter

NF Noise Figure

NI National Instruments

NPS Naval Postgraduate School

PM Phase Modulation

Q Quadrature Phase

RF Radio Frequency

RSNS Robust Symmetric Numeric System

RX Receiver

SNR Signal to Noise Ratio

STT Single Target Tracker

TWS Track While Scan

TX Transmitter

UAV Unmanned Aerial Vehicle

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ACKNOWLEDGMENTS

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I. INTRODUCTION

A. BACKGROUND

Passive Direction Finding (DF), later chapter mention DF would mean passive

DF, technique has been widely used in variety of fields such as communication,

navigation, Electronic Warfare (EW), Unmanned Aerial Vehicle (UAV), radar system

and lots of military applications. It is a method used to receive electromagnetic (EM)

wave which comes from the signal source or target and then use proper DF algorithm to

calculate the Angle of Arrival (AOA). Different DF algorithm can derive different angle

resolution and even use the same algorithm with different parameters could come into

different results. The goal is to use a better DF algorithm to improve angle resolution

accuracy.

DF, also named Electronic Support Measure (ESM), is a method used to derive

angle but not range. Unlike the common radar system that provides range and angle

information from a target. Radar system could use high gain antenna to provide better

angle accuracy but DF could not get any gain benefit from it. Further, with higher range

and angle resolution, it becomes possible to recognize individual targets. Even without

high resolution, DF has been able to recognize and identify a target by its general nature

or behavior in space. Because of its passive receive characteristic, it could not be used on

tracking a target. DF method could cooperate with other tracking systems to provide a

military air-defense radar system [1].

On the other hand, beamforming is a common technique used on tracking radar

system. With connection of a group of non-directional antennas and simulates as a large

directional antenna. By adjusting the phase, it could point the main beam electronically to

the desired azimuth or elevation angles without actually moving or rotating the antenna.

To steer the main beam point to the signal source could reduce interference and improve

Signal to Noise Ratio (SNR). Beamforming could also use in DF area, by pointing the

main beam to the signal source and compare the phase difference could determine the

AOA [2].

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When track a target, tracking radar must first acquire the targets initial AOA.

Most tracking radars adopt pencil beam to get high accuracy in angle resolution but it

become difficult to search huge amount of volume in space. The beamwidth of the pencil

beam is approximately less than a few degrees in both azimuth and elevation plane.

Because of its narrow beamwidth shape, pencil beam is popular used in tracking

operation. To design a practical system, we could use DF to get a rough AOA then pass

the scan angle to the tracker to do the tracking job [1].

B. PREVIOUS WORK

This thesis is a portion of the ongoing project began by Bartee [3] in 2002. Gezer

[4] followed the project and designed a digital phased array to track UAVs with the use

of Commercial-of-the-shelf (COTS) hardware to lower cost. The design of tracking

system was also verified through the simulations.

Eng [5] built up a calibration station that could automate calculate the DC offset

form the LabView program. It provided an easy way to measure the DC offset from the

modulation boards and it also gave more accuracy than before. The components of the

calibration system were easy to disassemble so it made the upgrade works more easily to

accomplish. By changing different Analog to Digital Converter (ADC) could give better

resolution in the future.

Jessica [6] implemented a single channel Robust Symmetrical Number System

(RSNS) to do the DF measurement. Several of moduli sets were used and run through

MATLAB simulations. Results showed at low SNR there were large angle resolution

errors. In addition, large dynamic range moduli sets could yield high angle resolutions

errors if compared to small dynamic range moduli sets. The bench top hardware with low

noise amplifier (LNA) and demodulator boards were built and tested. The system was

connected to National Instruments (NI) PXI-5112 cards and LabView software with

calibration function was also run and tested.

Tan and Pandya [7] carried out the design of a UAV tracking system with the use

of RSNS DF and monopulse Digital Beamforming (DBF). Three different LabView

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Modules were also developed. They were monopulse beamforming and tracking, NTSC

decoding and Frequency Modulation (FM) Demodulation. The beamforming and tracking

module used RSNS and combined with monopulse DBF to acquire and track a UAV

using the six-element antenna array. The FM demodulation module was tested

successfully for a single channel condition. The NTSC decoding module was able to

decode video signals and display on the LabView console.

C. SCOPE OF RESEARCH

The purpose of this thesis is to design, build and test a single channel RSNS with

monopulse DBF to accurately acquire the AOA from the signal source. Hardware would

be mainly come from COTS components to lower cost. Simulations would be

implemented on Matlab and hardware operate and monitor software would be built up on

LabView.

The first part of my research would illustrate the RSNS algorithms used on DF

and the concern issues when design a DF system. Folding waveforms and ambiguity

would be explained. Followed by the theory explanations, hardware operation would be

implemented. Besides, calibration of the modulation boards would be described shortly.

RSNS DF method would be used to measure AOA and then do comparisons between the

measured value and the true value. Further, analyze the calculated AOA values with the

true AOA values. More, use the derived measured data and put it in different SNRs to see

the effects. Try to find out which SNR values are acceptable for the DF job.

The second part of my research would illustrate the angle tracking techniques and

different types of tracking radar system. Tracking accuracy would also be explained to

better understand the noise effect on the tracking system design. Then a single channel

RSNS with monopulse DBF tracking system would be constructed. The six-element

phased array would be used for the tracker. Measurement would be in the anechoic

chamber to reduce interference and the layout of the anechoic chamber would be

mentioned. The tracking system would use RSNS DF first to find the rough AOA and

then pass the scan angle to the monopulse DBF module to do a better tracking job.

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System performance would be tested and also use Matlab programs to do the

simulations. Measure values would be compared to the theoretical values to tell the

difference and further more do the analysis. Conclusions would be made to make

following improvement works successful.

D. THESIS OUTLINE

Chapter II illustrates the basic idea of DF and explains the folding waveforms and

ambiguity situation. Furthermore, explains the quadrature demodulation and fundamental

RSNS theory.

Chapter III reviews different types of tracking radar system and include the angle

tracking techniques and tracking accuracy considerations.

Chapter IV provides the single channel RSNS system design set up and includes

Matlab simulations in different SNRs to see the cost and effects. Moreover, covers the

modulation boards calibration and LabView demonstrations.

Chapter V contains single channel RSNS with monopulse digital beamforming

hardware set up and LabView tracking programs design. Also illustrates the anechoic

chamber layout and compares the results.

Chapter VI contains conclusions and recommendations for future study.

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II. DIRECTION FINDING AND ROBUST SYMMETRIC

NUMERIC SYSTEM

A. DIRECTION FINDING

Radio DF systems use linear phase arrays to measure AOA from the incident

planar EM wave. There are three categories of DF methods: amplitude comparison, phase

delay and time delay [8].

In order to fulfill the comparison works at least two antenna elements are

required, however multiple elements could be used. The antenna is assumed to be

operated in the far field and arrival EM wave is restricted to narrowband frequency.

Amplitude comparison method converts the amplitude response received from

antennas into voltages and then interprets to the AOA. Phase and time delay use the

phase and time difference between the antenna elements to derive AOA.

Distance between elements is already determined by the required resolution.

Figure 1 displays a planar wave incident to a phase array with two linear elements

separate by a distance d, which is referred as the baseline distance. The antenna field of

view (FOV) ranges from -90 degrees to +90 degrees. The planar EM wave first arrive

antenna 2 then keeps traveling another sin( )d distance to antenna 1 [6].

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Figure 1. Incident Plane Wave Arrive to Two Element Antennas (After [6])

The received signal out of the antenna element is

( )cosi c i iV V t = + +

where i indicate the antenna element number ( i = 1,2,.etc), c is defined as the carrier

frequency, i is the phase delay comes from cables and i is the path difference

compare to the reference, in this case antenna 2 is the reference.

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The received iV signals pass to the quadrature demodulator to do mixing and LPF

processing which would be elaborated more detailed in the quadrature demodulator

section. Signals come out of the demodulator are , ,I Q I and Q and they belong to

antenna 1 and antenna 2 respectively. In addition, iI (in-phase) and iQ (quadrature-phase)

could be expressed as

( )cosi i iI A =

( )sini i iQ A =

( ) ( )

i i iA I Q= +

tan iii

Q

I

=

where iA is the amplitude and i is the phase [9]. Figure 2 shows a more intuitive I/Qplane relations.

Figure 2. I/Q Signal Diagram (From [10])

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On the other hand, if define the origin is in the middle of two antenna elements,

the phase value of each element could be given as 1 sin2

kd = and 2 sin

2

kd =

where2k

= . The phase difference could be calculated as

( )2 1 sin .kd = =

Once derived , then phase folding waveforms out of the quadrature

demodulator could be obtained and are equal to

( ) ( )2

cos .2

outV

V = +

comes from the cables are neglected because the cable length are already known andassumed to be equal. Output voltages, 2 / 2,V are normalized to unity for simplified

purpose. Finally, combine Equations and , the phase folding waveform could besimplified as

( ) ( )cos sin .outV kd =

Equation shows AOA could be directly calculated because k, d and are

already known. What is the reason to create the phase folding waveform? A signal

processing method called RSNS could achieve a high resolution without large baseline

distance. To get higher resolution, increase baseline distance is necessary. When baselinedistance is increased, there would create ambiguity which would cause multiple AOAs

and detail reasons would explain in the following RSNS section.

B. AMBIGUITY AND FOLDING WAVEFORMS

To get higher resolution, increase the distance between elements is necessary.

However, if baseline distance is increased over half wavelength, ambiguity problem will

be arisen. This could result in more than one AOA then the true AOA could not be

indicated.

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1. Ambiguity

From Equation, is related to wavelength, distance and AOA. However,

frequency is also related to wavelength. In this section, demonstrations will show not

only baseline distance but also frequency cause ambiguities.

When antenna element spacing is equal to / 2 , we get ( )sin . = Figure 3

clearly shows the relation between phase difference and AOA and one phase difference

could map to one AOA. The mapping relation is unique.

-100 -80 -60 -40 -20 0 20 40 60 80 100-200

-150

-100

-50

0

50

100

150

200

(degrees)

(degrees)

d/=0.5

Figure 3. Phase difference vs. AOA at d= / 2 (After [6])

However, if element distance increases to , ( )2 sin . = Figure 4 displays

the relation between phase difference and AOA and one phase difference could map to

two AOAs. When phase difference equals to -100 degrees, both -18 and +47 degrees

could be the AOA. The mapping relation is multiple and this phenomenon is called

ambiguity.

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Figure 4. Phase difference vs. AOA at d= (After [6])

Next, the frequency parameter is also a variable that would cause ambiguity. This

time keeps element distance fixed and equals to 0.5m. By changing frequency to inspect

if there is ambiguity. As figure 5 shows, when frequency equals to 300MHz, there is no

ambiguity arisen.

-100 -80 -60 -40 -20 0 20 40 60 80 100-200

-150

-100

-50

0

50

100

150

200f=300MHz, d=0.5m (baseline spacing)

(degrees)

(degrees)

Figure 5. Phase difference vs. AOA at frequency=300MHz

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Adjusting frequency from 300MHz to 900MHz, as figure 6 illustrated, there is

ambiguity. When phase difference equal to -100 degrees, there could be three possible

AOAs.

Figure 6. Phase difference vs. AOA at frequency=900MHz

When design a single channel DF system, distance between elements, wavelength

and frequency should all take into considerations to avoid ambiguity phenomenon. After

illustrate the ambiguity problem, the folding waveforms are similar to ambiguity.

2. Folding Waveforms

The folding waveform is periodic between / 2 and folding waveform number

could be summarized as

2.

dn

=

Figure 7 shows when / 2d = , there is only one folding waveform. This could be

easily verified by using equation and another property is folding waveform is

symmetrical.

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-100 -80 -60 -40 -20 0 20 40 60 80 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1d/=0.5

Angle of Arrival (degrees)

V

out(Normalized)

Figure 7. Output Voltage vs. AOA at / 2d = (After [6])

Next, increase the baseline distance to see the effect. In figure 8, there are two

folding waveforms whend = .

-100 -80 -60 -40 -20 0 20 40 60 80 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1d/=1


V

out(Normalized)

Figure 8. Output Voltage vs. AOA at d = (After [6])

Finally, increase the baseline distance equals to 2 . Figure 9 shows there are four

folding waveforms.

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-100 -80 -60 -40 -20 0 20 40 60 80 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1d/=2


V

out(Normalize

d)

Figure 9. Output Voltage vs. AOA at 2d = (After [6])

To sum up, increase the baseline distance will also increase the folding

waveforms. When folding waveform is greater than one, ambiguity would arise

simultaneously.

C. QUADRATURE DEMODULATION

1. Signal Modulation

Modulation and Demodulation techniques are commonly used in the

communication system such as radio station, wireless network and telecommunication.

By modulating a sinusoid, carrier frequency c , with the message signal, ( )s t , can

convert the message signal to a certain transmitting frequency and in figure 10 displays a

basic modulation block diagram. There are three main reasons could explain why use

modulating and demodulating process.

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Figure 10. ( )s t modulates with a sinusoid carrier frequency c

First, baseband signals do not propagate far. For example, voice signals could

only be heard in a short range. However, if a voice signal modulates with a higher carrier

frequency, it could be converted to EM waves and transmitted far away such as AM/FM

applications [11].

Second, a single channel could be divided into several bandlimited sub-channels

if each sub-channel modulates with different carrier frequency. This method is also called

Frequency-Division Multiplexing (FDM) because spectrum is not unlimited resource so

this technique is used quite often in the real world.

Third, transmitting frequency should adapt to the physical size of the antenna.

Low frequency signals have long wavelength and large diameter antennas are required.

However, if the physical size of the antenna is too large, it becomes unpractical to use

[7].

2. Quadrature Demodulation

The process of recovering the original signal ( )s t is called demodulation. The

radar signal ( )s t at carrier frequency c cf = could be represented as

( ) ( ) ( ) ( ) ( ) ( ) ( )cos[ ] cos sin .c c cs t A t f t t I t f t Q t f t = + =

In equation shows the signal ( )s t is divided into ( )I t and ( )Q t components which

are derived by using the quadrature demodulation technique. In figure 11 shows the

quadrature demodulation processing diagram and figure 12 displays an analog quadrature

demodulator which has an LO input frequency range from 0.8GHz to 2.7 GHz.

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Figure 11. Quadrature Demodulation Process (After [10])

Figure 12. AD8347 Quadrature Demodulator Made by Analog Devices, Inc. (From [10])

Define a complex envelop signal ( )u t and given as

( ) ( ) ( ) .u t I t jQ t = +

The signal ( )s t could be substituted to

( ) ( ){ } ( ) ( )Re .2c c

c

j t j t

j t u t e u t es t u t e

+ = =

To divide signal ( )s t into ( )I t and ( )Q t , first mix ( )s t with LO signal, ( )cos .LOt As

the upper part of figure 11, the in-phase channel could be mathematically represented as

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( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

1cos

4

4 4 4 4

Re Re .2 2

c c LO LO

c LO c LO c LO c LO

c LO c LO

j t j t j t j t LO

j t j t j t j t

j t j t

s t t u t e u t e e e

u t u t u t u t e e e e

u t u t e e

+ +

+

= + +

= + + +

= +

Next, pass the mix signal through LPF and LO frequency ( LO ) equals to c . Then the

first term in equation could be eliminated by using a LPF and the second term could be

derived and equal to( ) ( )

Re .2 2

u t I t =

On the other hand, the quadrature channel of the lower part of figure 11 could be given as

( ) ( )( ) ( ) ( ) ( )

sin Im Im .2 2

c LO c LOj t j t LO

u t u t s t e e

+ =

Using the same method through LPF, and the second part is filtered out. The first term is

left and equal to( ) ( )

Im .2 2

u t Q t =

D. ROBUST SYMMETRIC NUMERIC SYSTEM THEORY

The concept of RSNS process is used to reconstruct the folding waveforms out of

the antenna and it could obtain high AOA resolutions without long baseline distance. In

this section, RSNS parameters would be defined first then follows the interferometry

design steps.

1. Parameters Define

The fundamental elements of the RSNS algorithm are the moduli ( )im and they

should be greater than zero and relatively primed. The number of moduli depends on the

number of antenna elements and is denoted as N. For example, as figure 1 shows a two

element antenna should have two moduli so N equals to 2.

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A row vector is defined as

[0,1,2,..., 1, , 1,..., 2,1].i i im m m

A sequence used to represent the folding waveform is constructed by repeating each

element N times in the row vector. For the ith sequence ( )1,2,...,i N= , it should look like[0, 0,..., 0,0 ,1,1,...,1,1,..., , ,..., , ,...,1,1,...,1,1].

im i i i i

N N N N

X m m m m=1 4 2 43 14 2 43 14 2 431 4 4 2 4 43

After sequence sets are generated, align them vertically and shift one column per sub-

sequence. Next, define Mas the dynamic range which means the maximum column pair

of the shifted sequence set has no repetitions. Table 1 display a more clearly explanation

for 1 3m = and 2 4.m = In this case, there is no column pair duplicated from column

number 6 to 20 and its also the maximum column pairs.

Table 1. RSNS Sequence for moduli set [3,4] (From [6])

Previous works in [5, 6, 7, 8] found out for some specific two elements cases, dynamicrange could be summarized and calculated as follows:

( )

3 1,1 2 1

3 61 2

for m and m m

M m m

= +

= +

( )

5 2,1 2 1

3 71 2

for m and m m

M m m

= +

= +

( )5 3 ,1 2 1 4 2 2.1 2

for m and m m C C

M m m

= +

= +

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2. Interferometer Design

Before proceed to the interferometer design, there is one thing has to be clarified.RSNS algorithm is used to reconstruct the virtual folding waveform of each channel soeverything inside the RSNS block is virtual. There are several steps needed to implement

a RSNS interferometer system.The first one is to calculate the number of folds for each moduli which are givenas

.

2

Mni

Nmi=

With the ni information, then the corresponding virtual element baseline distance could

be derived. By substitute equation into equation, a new equation could be given as

.2 4

i ii

Md n

Nm

= =

Another issue need to be concerned is the received signals from antennas degrade

at wide FOV angles. Therefore a rescale processing is adopted to alleviate the angledistortion. Only part of the FOV angles is used instead of the whole FOV angles. From

equation, a new relation of ( ) ( )sin 'sin 'd d = could be derived and define the scaling

factor( ) as

( )

( )

sin'

sin '

d

d

= =

where 'd is the scaled baseline distance. To verify the rescale effect, a smaller ' is usedin equation and derived a longer 'd . As mentioned in the beginning of this section, a longbaseline distance means a better AOA resolution. Further, combining equation with, a

new relation could be given as'

4i i

i

Md d

m N

= =

where 'id is the virtual scaled baseline distance [6].

Next, encode the folding waveforms from equation into virtual folding waveformsby comparing to the threshold given as

,0.5

cos , 1 .i

ij m i

i

m jV j m

m

+=

Figure 13 shows a virtual folding waveform example of moduli 1 3m = and 2 4m = .

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Figure 13. RSNS Folding Waveforms for 1 3m = and 2 4m = (From [12])

Finally, calculate the phase adjustment ( )i and align the center of the dynamic

range to the folding waveforms at broadside ( )0 = [12]. Therefore, after add phaseadjustment, equation would become

( ) ( )cos sin .outV kd = +

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III. TRACKING RADARS AND TECHNIQUES

In Section A, different types of tracking radars will be introduced. In Section B,

several angle tracking techniques would be explained and focus will be on the monopulse

tracking. In Section C, lots of factors affect tracking accuracy will be discussed.

A. TYPES OF TRACKING RADAR SYSTEM

The purpose of tracking radar is to track a designated target with continuous

measurement of the target coordinates, range and velocity. In chapter V, the simulation is

interested in target arrival angle not the speed. There are many applications use tracking

radars for either civilian or military purposes. In civilian area, airports are one of the mostimportant places where air traffic control (ATC) plays an important role. Radars are

employed to safely control air traffic in the vicinity of airports are called Air Surveillance

Radar (ASR). In military area, tracking radar tracks target trajectory and computes best

intercept path then guide missiles to the target. Figure 14 shows an AN/MPQ-53 radar

which is used on search, target detection, track and identification.

Figure 14. AN/MPQ-53 (After [13])

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1. Single-Target Tracker (STT)

The single-target Tracker (STT) continuously tracks a target with a high data rate

of observation frequency. Data rate depends on the how many times radar observes the

target and typically 10 observations per second are enough for the guided missile

weapon-control radar. The STT with closed-loop servo system obtained the angle-error

signal and keep adjusting the tracker to minimize the angle-error. Lots of military

weapon-control system deploys STT to track airplanes or missiles. Figure 15 shows

tracking radar (AN/FPQ-6) with 29-ft reflector antenna. It has 0.1 mil tracking accuracy

and is specialized in long-range, small-target tracking.

Figure 15. AN/FPQ-6 (From [14])

2. Automatic Detection and Track (ADT)

The observation rate (renew rate) of Automatic Detection and Track (ADT) is

lower than STT because it deploys an open-looped servo system. Data rate is proportional

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to the rotation rate of the servo. However, ADT could track large amounts of targets at

the same time but STT could only track one.

3. Phased Array Radar Tracking

Phased array radar could track large amounts of targets by steering the beams

electronically. Computers use different time frames to control beams point to the desired

direction. It has high target renew rate of STT and multiple targets tracking ability of

ADT. The structure of phase array is more complicated than STT and ADT because each

array element should contain individual phase shifter, LNA and TX/RX module.

Figure 16. AN/SPY-1D (From [15])

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4. Track While Scan (TWS)

B. ANGLE TRACKING TECHNIQUES

1. Conical Scan

Sample text.

Sample text.

2. Sequential Lobing

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3. Monopulse Tracking

a. Amplitude Comparison Monopulse

b. Phase Comparison Monopulse

C. TRACKING ACCURACY

1. Theoretical Angular Accuracy

Sample text.

Sample text.

2. Limitations to Tracking Accuracy

a. Glint

b. Receiver Noise

c. Amplitude Fluctuations

d. Servo Noise

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IV. SINGLE CHANNEL RSNS COMPUTER SIMULATION AND

HARDWARE TESTING RESULTS

A. SINGLE CHANNEL RSNS DESIGN

B. CALIBRATION

C. HARDWARE SETUP

D. RSNS IN LABVIEW

E. MATLAB SIMULATION

-80 -60 -40 -20 0 20 40 60 80

-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degre

es)

Difference between Ideal AOA, Estimated AOA and Measured AOA at SNR = 10

Ideal AOA

Estimated AOA @ SNR = 10

Measured AOA

Figure 17. Difference between Ideal AOA, Estimated AOA and Measured AOA at SNR = 10

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-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degrees)


Ideal AOA


Measured AOA


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-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degrees)


Ideal AOA


Measured AOA


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-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degrees)


Ideal AOA


Measured AOA


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-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degrees)


Ideal AOA


Measured AOA


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-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degrees)


Ideal AOA


Measured AOA


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-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degrees)


Ideal AOA


Measured AOA


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-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degrees)


Ideal AOA


Measured AOA


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-80 -60 -40 -20 0 20 40 60 80-100

-80

-60

-40

-20

0

20

40

60

80

100

AOA (Degrees)

Error(Degrees)


Ideal AOA


Measured AOA


F. COMPARISON AND RESULTS

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V. TRACKING WITH SINGLE CHANNEL RSNS AND

MONOPULSE DIGITAL BEAMFORMING TESTING RESULTS

A. ANECHOIC CHAMBER

B. HARDWARE SETUP

C. TRACKING PROGRAM IN LABVIEW

D. COMPARISON AND RESULTS

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VI. CONCLUSIONS AND RECOMMENDATIONS

A. CONCLUSIONS

B. RECOMMENDATIONS FOR FUTURE WORK

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LIST OF REFERENCES

[1] Merrill I. Skolnik, Introduction to Radar Systems 3rd Edition, pp. 248266,McGraw-Hill, New York, NY, 2001.

[2] Toby Haynes, A primer on digital beamforming, Spectrum Signal Processing,1998

[3] John A. Bartee, Genetic algorithms as a tool for phased array radar design,Masters Thesis, Naval Postgraduate School, Monterey, California, June 2002.

[4] Berat Levent Gezer, "Multi-Beam Digital Antenna for Radar, Communications,and UAV Tracking Based on Off-The-Shelf Wireless Technologies," MastersThesis, Naval Postgraduate School, Monterey, California, September 2006.

[5] Eng, Chun Heong, "Design and Development of an Automated DemodulatorCalibration Station," Masters Thesis, Naval Postgraduate School, Monterey,California, December 2009.

[6] Jessica A. Benveniste, "Design and Development of a Single Channel RSNSDirection Finder," Masters Thesis, Naval Postgraduate School, Monterey,California, March 2009.

[7] Tan and Devieash James Pandya, UAV Digital Tracking Array Design,Development and Testing, Masters Thesis, Naval Postgraduate School,Monterey, California, December 2009.

[8] Anthony Lee, Variable Resolution Direction Finding Using the RobustSymmetrical Number System, Masters Thesis, Naval Postgraduate School,Monterey, California, December 2006.

[9] David C. Jenn, "RSNS Processing Using A Single Channel," Naval PostgraduateSchool, Monterey California, 2006 (unpublished notes).

[10] David C. Jenn, "Digital Antennas," Naval Postgraduate School, MontereyCalifornia, 2006 (unpublished notes).

[11] James H. Mcclellan, Ronald W. Schafer and Mark A. Yoder, Signal ProcessingFirst, 1st edition, Pearson Prentice Hall, Upper Saddle River, NJ, 2003.

[12] Jui-Chun Chen, "A Virtual RSNS Direction Finding Antenna System," MastersThesis, Naval Postgraduate School, Monterey, California, December 2004.

[13] Anonymous, AN/MPQ-53, Available:http://www.mobileradar.org/picts/radar_sets/mpq_53/mpq_53.html, accessedOctober 14, 2010.

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[14] Anonymous, The FPQ-6 Skin-tracking Radar, Available:http://www.honeysucklecreek.net/other_stations/carnarvon/fpq6.html, accessedOctober 14, 2010.

[15] Anonymous, AN/SPY-1D, Available: http://pl.wikipedia.org/wiki/AN/SPY-1,

accessed October 14, 2010.

[16] Kazimierz Siwiak and Yasaman Bahreini,Radiowave Propagation and Antennasfor Personal Communications, 3rd edition, Artech House, Norwood, MA, 2007.

[17] David M. Pozar, Microwave Engineering, 3rd edition, John Wiley & Sons,Hoboken, NJ, 2005.

[18] Warren L. Stutzman and Gary A. Thiele,Antenna Theory and Design, 2ndedition, John Wiley & Sons, Hoboken, NJ, 1998.

[19]

[20] Merrill I. Skolnik,Introduction to Radar Systems, 3rd edition, McGraw-Hill, NewYork, NY, 2001.

[21] Fawwaz T. Ulaby,Fundamentals of Applied Electromagnetics, 5th edition,Pearson Prentice Hall, Upper Saddle River, NJ, 2007.

[22] David C. Jenn,Radar and Laser Cross Section Engineering, 2nd edition,American Institute of Aeronautics and Astronautics, Reston, Virginia, 2005.

[23] Simon Haykin and Michael Moher,Introduction to Analog & DigitalCommunications, 2nd edition, John Wiley & Sons, Hoboken, NJ, 2007.

[24] Roberto Cristi, Modern Digital Signal Processing, 1st edition, ThomsonLearning, Pacific Grove, CA, 2004.

[25] Adel S. Sedra and Kenneth C. Smith, Microelectronic Circuits, 5th edition,Oxford University Press, New York, NY, 2004.

[26]

[27]

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INITIAL DISTRIBUTION LIST

1. Defense Technical Information CenterFt. Belvoir, Virginia

2. Dudley Knox LibraryNaval Postgraduate SchoolMonterey, California

3. Chairman, Code ECNaval Postgraduate SchoolMonterey, California

4. Professor David C. JennDepartment of Electrical and Computer Engineering

Naval Postgraduate SchoolMonterey, California

5. Professor Roberto CristiDepartment of Electrical and Computer EngineeringNaval Postgraduate SchoolMonterey, California

6. Robert D. BroadstonDepartment of Electrical and Computer EngineeringNaval Postgraduate School

Monterey, California

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