The Pennsylvania State University

The Graduate School

College of Engineering

PLANAR ANTENNA ARRAYS FOR CORRELATION

DIRECTION FINDING SYSTEMS FOR USE ON MOBILE

PLATFORMS

A Thesis in

Electrical Engineering

by

Elliot J. Riley

c©2012 Elliot J. Riley

Submitted in Partial Fulfillmentof the Requirements

for the Degree of

Master of Science

December 2012

The thesis of Elliot J. Riley was reviewed and approved* by the following:

Ram M. NarayananProfessor of Electrical EngineeringThesis Advisor

Timothy J. KaneProfessor of Electrical Engineering

Keith A. LysiakARL Mentor

Kultegin AydinProfessor of Electrical EngineeringHead of the Electrical Engineering Department

* Signatures are on file in the Graduate School

ii

Abstract

Radio direction finding systems estimate the direction-of-arrival of electromag-

netic signals. Direction finding systems have used many different processing algo-

rithms since they were first investigated in the beginning of the 20th century. The

processing algorithm that is used to estimate the direction-of-arrival of signals drives

the choice of antenna or antenna array that must be used with the system. The

antenna or antenna array then directly influences the available performance of the

system. This thesis will focus on two planar antenna array designs for use with

a correlation direction finding algorithm. Correlation direction finding algorithms

require precise array manifold data. Array manifold data are comprised of the in-

dividual complex antenna voltage response patterns of each element in the array.

The voltage response patterns of each antenna element are measured over multiple

azimuths, elevations, frequencies, and polarizations. The known array manifold data

are then used to correlate incoming electromagnetic signals to find an estimate of

the direction-of-arrival. The array manifold must have unique response data for all

azimuths of interest to produce unambiguous correlation results. This thesis inves-

tigates the use of two different mechanisms to produce uniqueness or diversity in

array manifold data. One planar antenna array design utilizes equal spaced antenna

elements with the elements providing different response patterns. The other design

utilizes unequally spaced antenna elements with all the elements providing identical

response patterns. The available performance of both antenna arrays for use with a

correlation direction finding algorithm is presented.

iii

Table of Contents

List of Figures vi

List of Tables viii

Acknowledgements ix

1 Introduction 11.1 Direction Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Direction Finding Systems for Mobile Platforms . . . . . . . . . . . . 21.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Background 42.1 Practical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Brief Historical Development . . . . . . . . . . . . . . . . . . . . . . . 52.3 Common DF Considerations . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . 62.3.2 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3.3 Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Practical Correlation Direction Finding Method . . . . . . . . . . . . 102.4.1 Array Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.2 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.3 Characterization of DF Antenna Arrays for Correlation Algorithm 13

2.5 Properties of Direction Finding Antenna Arrays for Correlation DFAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Antenna Design and Modeling 233.1 Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 Size Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.2 Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.3 Array Manifold Diversity . . . . . . . . . . . . . . . . . . . . . 24

3.2 Equally Spaced Pattern Diverse Array . . . . . . . . . . . . . . . . . 253.2.1 Square Spiral Antenna Elements . . . . . . . . . . . . . . . . . 253.2.2 Array Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.3 FEKO Modeling of Square Spiral Array . . . . . . . . . . . . 29

3.3 Unequal Spaced Identical Pattern Array . . . . . . . . . . . . . . . . 383.3.1 E Patch Antenna Elements . . . . . . . . . . . . . . . . . . . . 383.3.2 Array Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3.3 FEKO Modeling of E Patch Array . . . . . . . . . . . . . . . 40

3.4 Modeling Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Antenna Prototyping 494.1 Prototype Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . 494.2 Square Spiral Array Prototype . . . . . . . . . . . . . . . . . . . . . . 504.3 E Patch Array Prototype . . . . . . . . . . . . . . . . . . . . . . . . . 51

iv

4.4 Prototyping Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 56

5 Antenna Testing 625.1 Considerations for Measuring Array Manifolds . . . . . . . . . . . . . 625.2 Anechoic Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2.1 Chamber Properties . . . . . . . . . . . . . . . . . . . . . . . 635.2.2 Antenna Positioning System . . . . . . . . . . . . . . . . . . . 665.2.3 Measurement System . . . . . . . . . . . . . . . . . . . . . . . 67

5.3 Collecting Array Manifold Data in Anechoic Chamber . . . . . . . . . 715.3.1 Prototype Antenna Rotations . . . . . . . . . . . . . . . . . . 715.3.2 Mounting Bracket . . . . . . . . . . . . . . . . . . . . . . . . . 765.3.3 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.4 Testing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.4.1 Square Spiral Prototype Array Testing . . . . . . . . . . . . . 785.4.2 E Patch Prototype Array Testing . . . . . . . . . . . . . . . . 81

5.5 Testing Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6 Conclusions 85

A Adding Normally Distributed Noise to an Array Manifold 87

B Spherical to Planar Wavefront Conversion 91

References 95

v

List of Figures

1 Spherical Coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Modified Coordinate System for Direction Finding Systems. . . . . . 73 Block Diagram of a DF System. . . . . . . . . . . . . . . . . . . . . . 84 Array Manifold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 1D Voltage Array and 2D Array Manifold. . . . . . . . . . . . . . . . 126 Correlation Plot with Strong Peak. . . . . . . . . . . . . . . . . . . . 167 Correlation Plot with Ambiguity. . . . . . . . . . . . . . . . . . . . . 168 Desired Array Manifold Auto-correlation Example. . . . . . . . . . . 189 Ambiguous Array Manifold Auto-correlation Example. . . . . . . . . 1810 Generic DF Array Layout. . . . . . . . . . . . . . . . . . . . . . . . . 2311 Reconfigurable Square Spiral. . . . . . . . . . . . . . . . . . . . . . . 2612 Endfire and Broadside Elements. . . . . . . . . . . . . . . . . . . . . 2713 Endfire and Broadside Element Patterns. . . . . . . . . . . . . . . . . 2714 Square Spiral Array Layout. . . . . . . . . . . . . . . . . . . . . . . . 2815 Square Spiral Array Element Impedances. . . . . . . . . . . . . . . . 3416 FEKO Simulation Coordinate System. . . . . . . . . . . . . . . . . . 3517 Transformed FEKO Coordinates into DF Coordinates. . . . . . . . . 3518 Normalized Complex Patterns of Square Spiral Array Elements. . . . 3719 Square Spiral Array Manifold Characterization. . . . . . . . . . . . . 3720 E Patch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3821 E Patch Pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3922 E Patch Array Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . 4023 E Patch Array Element Impedances. . . . . . . . . . . . . . . . . . . 4524 Normalized Complex Patterns of E Array Elements. . . . . . . . . . . 4625 E Array Manifold Characterization. . . . . . . . . . . . . . . . . . . . 4626 Layers of Prototype Antennas. . . . . . . . . . . . . . . . . . . . . . . 4927 Radome Over All Layers of Antenna Structure. . . . . . . . . . . . . 4928 Underside of Ground Plane with SMA Connectors. . . . . . . . . . . 4929 Square Spiral Array Prototype. . . . . . . . . . . . . . . . . . . . . . 5130 Square Spiral Array Element Impedances. . . . . . . . . . . . . . . . 5531 E Patch Array Prototype. . . . . . . . . . . . . . . . . . . . . . . . . 5632 E Patch Array Element Impedances. . . . . . . . . . . . . . . . . . . 6033 Cross Section of Anechoic Chamber. . . . . . . . . . . . . . . . . . . 6434 Wavefronts in Anechoic Chamber. . . . . . . . . . . . . . . . . . . . . 6535 Antenna Positioning System. . . . . . . . . . . . . . . . . . . . . . . . 6836 Antenna Positioning System Base Features. . . . . . . . . . . . . . . 6937 Roll Head Positioner on Top of Boom. . . . . . . . . . . . . . . . . . 6938 Electronic Motions of Antenna Positioner Looking from Transmit An-

tenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7039 Data Collection System. . . . . . . . . . . . . . . . . . . . . . . . . . 7140 Prototype Antenna Array Coordinates Defined. . . . . . . . . . . . . 7241 Antenna Positioning System Orientation. . . . . . . . . . . . . . . . . 7342 Azimuthal Rotations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

vi

43 Elevation Rotations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7544 Mounting Bracket with Prototype Antenna. . . . . . . . . . . . . . . 7745 Normalized Measured Complex Patterns of Square Spiral Array Ele-

ments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7946 Normalized Modeled Complex Patterns of Square Spiral Array Elements. 7947 Measured and Modeled Square Spiral Array Manifold Characterization. 8048 Normalized Measured Complex Patterns of E Patch Array Elements. 8249 Normalized Modeled Complex Patterns of E Patch Array Elements. . 8250 Measured and Modeled E Patch Array Manifold Characterization. . . 8351 Spherical to Planar Wavefront Diagram. . . . . . . . . . . . . . . . . 91

vii

List of Tables

1 Square Spiral Array Antenna Positions and Pattern Descriptions. . . 282 E Patch Array Antenna Positions and Pattern Descriptions. . . . . . 403 Symbols and Descriptions for Spherical to Planar Wavefront Diagram. 92

viii

Acknowledgements

I would like to first thank The Applied Research Laboratory at Penn State for

providing me with an opportunity to work on a research project. I would also like

to thank a few members of Penn State ARL for their continued help. Thank you

Dr. Keith Lysiak for mentoring me in the theory and operation of direction finding

systems and providing guidance in my research. Thank you Dr. Erik Lenzing for

guiding me in hands on laboratory tasks. Thank you Mr. Dan Brown, Mr. Isaac

Gerg, and Mr. Cale Brownstead for the endless help with MATLAB and document

preparation.

I would also like to thank a few academic members of Penn State University.

Thank you Dr. Ram Narayanan for advising my academic and thesis work and for

introducing me to antenna theory and design in an undergraduate course in the fall of

2010. Thank you Dr. Kane for serving on my committee and for sparking my interest

in electromagnetic theory and applications during an undergraduate electromagnetic

course in the spring of 2010.

ix

1 Introduction

1.1 Direction Finding

The objective of a direction finding system is to estimate the direction-of-arrival

(DOA), angle-of-arrival (AOA), or line-of-bearing (LOB) of a signal. Direction find-

ing may go by the name of radio direction finding (RDF), but in this thesis it will be

simply referred to as direction finding (DF). The DOA, AOA, or LOB estimate may

also be simply referred to as the bearing of the received signal. It should be carefully

noted that by the strictest definition of a DF system that a DF system determines

the DOA of a received signal and does not determine the direction to the transmitter.

However, an estimate of the direction to the transmitter may be what is truly desired

by the system operator. Many factors may alter a signal during its transmission from

the transmitter to the DF system that may cause the DOA estimate to not give the

true great-circle direction to the transmitter.

To give a complete DOA estimate, the system must provide azimuth and ele-

vation angles of the received signal. Azimuth is the angle in the horizontal plane

and elevation is the angle in the vertical plane. An ideal DF system would provide

360 of azimuth coverage, 180 of elevation coverage, operate over a wide frequency

band, work with all modulations, and work with signals that are of all lengths of

time. Most generally the signals received by DF systems in real applications will be

non-cooperative.

DF systems use carefully designed antennas or antenna arrays to exploit as much

information as possible from incoming signals to determine a DOA estimate. Different

algorithms and processing systems require different and precise antenna systems. The

algorithms used to determine the DOA estimate drive the antenna system design while

the antenna system design determines the obtainable accuracy of the overall system.

Prior knowledge of the antenna responses is a vital piece to a DF system. Different

1

algorithms and different antenna systems are used based on the application specific

goals of the system.

DF systems can readily be found in acoustic and electromagnetic applications.

However, this thesis focuses solely on direction finding of electromagnetic signals and

will be assumed throughout the rest of the thesis. Direction finding systems can be

found in commercial, consumer, safety, and military markets.

1.2 Direction Finding Systems for Mobile Platforms

Direction finding systems have widely been used for signals in the HF and VHF

bands. Terrestrial applications have featured stationary and often large antenna ar-

rays. These systems were largely focused on signals in the HF band. Mobile applica-

tions on ships and aircraft have used DF systems for the purposes of radionavigation

using the VHF band.

Newer technologies using the UHF portion of the spectrum have provided the

need for DF systems for smaller mobile platforms to be developed. Mobile platforms

provide certain challenges when designing specific DF systems. In some cases it can

be desired that the antenna array for the DF system be mounted on the side of the

platform. Mounting antennas in this manner requires the antennas to be conformal in

nature. This also restricts the availability of the antennas to receive signals in a full

360 of azimuth. In this case, the DF system requires antenna systems on multiple

sides of the platform to achieve full azimuth coverage. If multiple antenna positions

or a full ranging azimuth antenna structure is not possible, the DF system will be

restricted to a limited range of azimuths. For example, if a vehicle can only allow DF

antennas to be mounted on one side of the vehicle, the DF system will only be able

to operate over the 180 of azimuth available in front of the mounted antenna array.

Mobile platforms also have some undesirable characteristics that may affect the DF

system. The environment surrounding the antenna array can have great operational

2

impacts on the DF system. The environment can introduce unwanted re-radiation

of incoming signals and can affect DOA estimates. While there may be optimal

placements on platforms for DF antennas, the optimal placement may not be possible

due to other constraints and non-ideal placements may have to be used. Challenges

such as this must be met by using DF algorithms that will work accurately with new

antenna array designs and the surrounding platform environment.

1.3 Thesis Overview

The work presented in this thesis deals with two planar antenna array designs suitable

for mobile platform applications using correlation direction finding algorithms. While

the algorithms and processing used in DF systems are vital, the work presented here

will not focus on them. Rather, the work will focus on an investigation of two possible

planar antenna array designs suitable for a correlation style direction finding system.

Specifically, the investigation will look at two different mechanisms to provide array

manifold diversity.

3

2 Background

2.1 Practical Applications

Many practical DF systems have been implemented. One very prevalent use of di-

rection finding systems are for maritime and aircraft navigation. AM radio stations

have been used as well known transmitters and were received by DF systems to help

direct aircraft and ships to their desired location. Another well known system was

LORAN (Long Range Navigation). LORAN utilized fixed land based radio beacons

to provide well known signals for ships and aircraft to utilize for navigation. Au-

tomatic direction finder (ADF) systems were systems that continuously monitored

non-directional beacons to provide aircraft and ships with navigation. The advent of

GPS has greatly diminished the use of these direction finding systems.

The U.S. Coast Guard has used DF systems for search and rescue purposes. These

DF systems are used to monitor emergency radio frequency channels for distress calls.

Systems designed for terrestrial and satellite networks have been used to continuously

monitor for emergency transmissions [1].

DF systems have been used to perform cooperative signal tracking. Examples can

be found in animal tracking. Cooperative transmitters have been placed on animals

so that biologists can study the precise movements of animals. Hobbyists have used

DF systems to locate fallen model rockets with cooperative transmitters on board.

Military applications can also readily be found. DF systems have been used as

homing systems to guide weaponry toward targets. They have been utilized in Elec-

tronic Support Measure (ESM) systems to locate the DOA of hostile radar or homing

systems [1]. DF systems have also found many uses in gathering signal intelligence.

For instance they were used actively by the Allies in WWII to track German sub-

marines [1].

4

2.2 Brief Historical Development

DF systems were first investigated in the early 1900’s. Loop antennas were some of

the first antennas investigated for DF purposes. Loop antennas have nulls in their

response pattern directly in the center of the loop. Therefore, if the loop is rotated

while a signal is being received a minimum signal level will be measured when the

loop is broadside toward the incoming signal. An ambiguity is present because when

the loop is rotated a full 360 a minimum signal will show up 180 apart. The strong

ambiguity present made this an inaccurate DF system.

In 1919 Frank Adcock patented an antenna design that would be used to pro-

vide much better DF performance [1]. Adcock’s design utilized a linear array of two

dipoles. Robert Watson-Watt utilized two orthogonal Adcock arrays to develop an

antenna array with dipoles located in a north, south, east, and west layout. The

antenna elements were combined in a way to provide sinusosoidal and cosinusoidal

response patterns [1]. The sinusoidal and cosinusoidal amplitude responses were then

fed into a system that took the inverse tangent of the signals to generate a bear-

ing. The bearing was then referenced to a sense response that was generated by

coherently combining all of the antenna elements. This system provided an unam-

biguous estimate of the direction of arrival because of the ability to incorporate a

suitable reference channel. These systems were studied and used during the 1930’s

and extensively through WWII.

During WWII the Germans developed another DF technique. The German DF

system utilized a circularly disposed antenna array (CDAA) and was called the Wul-

lenweber. The CDAA utilized a mechanical goniometer that was used to cycle through

all of the antennas in the circular array. The CDAA DF systems were used to beam-

form certain antenna elements into desirable patterns for direction finding, observe

Doppler shifts on different antenna elements to estimate DOA, or to compare phase in-

formation on different elements to determine directional information [2]. Post WWII

5

y

x

z

φ = 0

θ = 90

θ = 0

φ = 90

φ = 180

φ = 270

Figure 1: Spherical Coordinates.

DF research done by the British was heavily focused on wavefront behavior. This

effort lead to interferometric DF techniques [2].

More modern techniques have relied upon digital signal processing. Advanced

correlation algorithms such as the Bartlett, Capon, and Maximum entropy have been

implemented [1]. Advanced Eigen structured algorithms such as Pisarenko, Min-

NORM, and MUSIC have also been explored [1]. Superresolution techniques have

been investigated but have not had much practical success [2].

2.3 Common DF Considerations

2.3.1 Coordinate Systems

Clearly defined coordinate systems are very important in direction finding systems.

The coordinate systems discussed here will ignore all radial distances and will focus

solely on angular positions. A standard spherical coordinate system used in electro-

6

y

x

z

AZ = 0

EL = −90

EL = +90

AZ = 270

AZ = 180

AZ = 90x-y planeEL = 0

North

South

WestEast

Front of Platform

Right of Platform

Rear of Platform

Left of Platform

Figure 2: Modified Coordinate System for Direction Finding Systems.

magnetics is defined in [3]. Fig. 1 shows the angular definitions in this coordinate

system. In direction finding systems, it can be more convenient to slightly modify

these angular definitions. Fig. 2 shows the modifications to these angular values. The

modifications from the spherical coordinates are performed using equations (1) and

(2). AZ is azimuth and EL is elevation.

AZ = −φ (1)

EL = 90− θ (2)

Also note that in Fig. 2 the other designators near the axes on the diagram.

Orienting the axes in such a way to correspond with the geographical directions of

north, south, west, and east can help to make more logical sense of bearing directions.

The same is true about orienting the axes in line with the front, rear, right and left

of the platform that a DF array may be mounted on. These standards are purely

7

Distribution System ADC DF Processor Display

1

2

n

Figure 3: Block Diagram of a DF System.

arbitrary but will be adopted and used here.

Arbitrary symbols can be used to describe azimuth and elevation. Azimuth will

be described by θ and elevation will be described by ψ throughout the rest of this

work.

2.3.2 System Design

Fig. 3 shows a block diagram of a typical DF system layout [1]. First, an antenna

array must be in place to collect signal energy. Then the signals are generally passed

through filters, amplifiers, and cables that make up the distribution system. The

distribution system requires precise phase matching across all channels. More modern

systems then take the signals and digitize them using analog-to-digital converters.

Once the signals are digitized they are fed into a DF processor which is typically

implemented in an FPGA or microprocessor. The speed of modern electronics have

made it possible to implement real-time signal processing that can utilize amplitude

and phase information from the signals to perform DF processing. During the DF

processing stage calibration data may be used to dynamically mitigate system error.

The final stage is to output the processed information to an operator display. While

specific DF systems may have more complex designs, this is the most general high

level view of a DF system.

8

2.3.3 Sources of Error

A major source of error in DF systems can be found in interactions with the DF

antenna systems with the surrounding environment [4]. Surrounding structures of all

types of materials will have electromagnetic characteristics that will influence the ideal

response patterns of the DF antennas. It is required to have an a priori knowledge

of the response of the antennas to incoming radiation for the DF system to work

properly. Distortion of the expected response due to local site interactions can have

extremely negative impacts on a DF system. The interaction of the DF antenna array

with its local environment can be minimized by selecting an operational environment

that is free from other materials. However, this may not be possible especially when

the array may be placed on a mobile platform that will surely have some surrounding

structure. Characterizing an antenna array in its final environment or an environment

closely matched to the final positioning can negate these effects by gaining an a priori

knowledge of how the environment will distort the antenna responses.

The transmission channel will introduce errors into a DF system. As stated pre-

viously, a true DF system will find the DOA of a radio signal at the DF site not

necessarily the direction to a radio transmitter. The propagation channel can intro-

duce multipath effects which may cause the observed DOA to not correspond with

the most direct path to the transmitter. Multipath interference can cause a multi-

component wavefront to be present at the receiving DF system. This multicomponent

wavefront can cause errors in determining the single plane wave front that corresponds

to the desired received signal [4]. Therefore, multipath interference will affect the es-

timate of the DOA and the estimate to the transmitter. The channel may also include

cochannel interference. Cochannel interference is caused by other radio systems that

are operating in the same band of interest as the desired DF signals. The signal-to-

noise-ratio (SNR) achievable at the DF system is directly affected by multipath and

cochannel interference. Other factors influencing achievable SNR include transmitter

9

power, distance of propagation, atmospheric propagation, ionospheric tilting, atmo-

spheric noise, man made noise, and any other electromagnetic disturbance [1]. The

error introduced by the channel is unavoidable and imposes a fundamental limit on

the accuracy of a DF system [4].

Errors may also arise due to system hardware. The distribution block of the

diagram shown in Fig. 3 requires extremely precisely phase matched components.

Phase matched cables and devices are often expensive and can be difficult to install

depending on the orientation of the system. Precise phase matching is important to

ensure that the signals are presented to the DF processor without any distortion in

the phase of the signals. If possible an a priori knowledge of the phase differences

present in any devices can be used as part of the system calibration to help negate

these effects. The internal noise generated by system components can also degrade

the SNR of the receiving system.

2.4 Practical Correlation Direction Finding Method

The DF algorithm explained here will approach DF from a single plane wave sense.

That is while some DF algorithms may focus on resolving multiple signals from mul-

tiple angles, the algorithm discussed here will focus on resolving one received signal

from only one particular angle. This allows for a clear simple understanding of what

the DF algorithm is doing mathematically. Single plane wave direction finding is the

most basic DF process and makes the most sense when looking to investigate a new

DF antenna array design.

2.4.1 Array Manifold

A fundamental piece of many DF systems and algorithms is the array manifold [1].

The array manifold contains the complex voltage responses for each antenna in an

antenna array. It can also be thought of as the individual antenna patterns of each

10

a1(θ0) a1(θ1) a1(θ2) . . . a1(θM )

a2(θ0) a2(θ1) a2(θ2) . . . a2(θM )

a3(θ0) a3(θ1) a3(θ2) . . . a3(θM )

.

.

.

.

.

.

.

.

.

.

.

.

aN (θ0) aN (θ1) aN (θ2) aN (θM ). . .

..

.

A(θ) =

Azimuthal Increments

Antenna Elements.

Frequencies

Figure 4: Array Manifold.

element in the array in a complex form containing both the amplitude and phase in-

formation. The standard array manifold is typically organized as a two dimensional

array where the columns correspond to azimuthal increments and the rows corre-

spond to antenna element numbers. The standard two dimensional array manifold

will be represented by the symbol A(θ). Therefore an antenna array consisting of

N antennas with each element having known complex voltage response data in M

azimuthal increments, will have an array manifold that is an N x M two dimensional

array. Array manifolds can be generated over many frequencies, polarizations, and

elevations. The required number of azimuthal increments, frequencies, polarizations,

and elevations is determined by the specific requirements of the DF system. Fig. 4

shows the standard two dimensional array manifold, A(θ), but also shows how the ar-

ray manifold can have a third dimension representing a discrete number of frequency

measurements. The notation for this array manifold was adapted from [1]. The en-

tries labeled an(θm) are complex values representing the complex antenna response

voltage of each antenna element at discrete azimuthal increments. The development

of array manifolds with discrete numbers of polarization and elevation responses at

11

a1(θ0) a1(θ1) a1(θ2) . . . a1(θM )

a2(θ0) a2(θ1) a2(θ2) . . . a2(θM )

a3(θ0) a3(θ1) a3(θ2) . . . a3(θM )

.

.

.

.

.

.

.

.

.

.

.

.

aN (θ0) aN (θ1) aN (θ2) aN (θM ). . .

..

.

A(θ) =

Azimuthal Increments

Antenna Elements.

v1(θm)

v2(θm)

v3(θm)

.

.

.

vN (θm)

V(θ) =

Figure 5: 1D Voltage Array and 2D Array Manifold.

particular frequencies would make up the fourth and fifth dimensions. These are not

shown on Fig. 4 as these dimensions are purely mathematical in nature.

2.4.2 Correlation

A correlation direction finding method relies on the correlation of a received signal

set with a known response. Let us first utilize the standard two dimensional array

manifold that contains complex voltage responses for a particular frequency, elevation,

and polarization. Let us also assume a signal is received on all N elements that is of

the same frequency, elevation, and polarization as the voltage responses in the array

manifold. A snap shot of the received signal in time must be taken on all antenna

elements. In other words, the received signal must be sampled on all antenna elements

for one specific instant in time. This snap shot will give a vector of signal voltages of

size N x 1 and will be called V(θ). Fig. 5 shows the received voltage vector and the

two dimensional array manifold of interest.

The desired process is to see which column in the array manifold the snap shot

of the received voltages is the most similar to. This will give an estimate of the

most probable azimuth that the signal was received from. This process will now be

explained in its most fundamental and simple form. This process is done mathemati-

cally by taking the conjugate transpose of the voltage vector V(θ) and performing the

12

dot product of this row vector and each column in the array manifold. The conjugate

transpose is required to make the inner dimensions of each array to be the same and

allow for proper matrix operations. This dot product operation will result in a 1 x

M row vector with each entry being the value obtained from from the dot product

operation for each column. These values represent a discrete correlation coefficient.

The entry that has the highest value or correlation coefficient will represent the col-

umn that the received voltage snap shot is most similar to. This can also be thought

of as the estimate for the DOA. This can be represented mathemetically as in eq. (3)

where C(θ) is the 1 x M row vector containing the complex correlation values and †

refers to the conjuate transpose. The highest magnitude value in the complex C(θ)

vector will represent the highest correlation coefficient and will be associated with

the best DOA estimate.

C(θ) = V(θ)†A(θ) (3)

Many other processing operations may be performed. As shown in [1], normaliza-

tion and covariance methods may also be invoked. However, this simple correlation

process explained here is the fundamental process performed in all correlation style

DF techniques and is all that will be discussed. The simple process defined here

focuses on an ideal case when the array manifold being used contained response data

of the same frequency, polarization, and elevation of the incoming signal. However,

in general the received one dimensional voltage snap shot must be correlated with

many different array manifolds with data for different frequencies, polarizations, and

elevations to determine the column that has the best correlation.

2.4.3 Characterization of DF Antenna Arrays for Correlation Algorithm

Closely related to the fundamental correlation algorithm are methods for character-

izing and exploring a DF antenna array for use in a correlation DF system. The

13

characterization process utilizes similar discrete correlation techniques as described

in section 2.4.2.

To start, let us examine the standard two dimensional array manifold that contains

complex voltage response data for a particular frequency, polarization, and elevation.

The first step is to normalize each column in the array manifold. This is done to ensure

that when a column is dotted with the conjugate transpose of itself (correlated with

itself), that the max value to come from the dot product is equal to one. First, the

norm of the column must be found. The norm of a vector is in general defined in

eq. (4) for an arbitrary one dimensional complex vector x.

||x|| =√x†x (4)

The equation shown in eq. (4) shows that for a given column the norm is defined by

the square root of the inner product of the column with the conjugate transpose of

itself. Then each entry in the column must be divided by the norm value. This will

ensure that the inner product of the column with the conjugate transpose of itself

will equal one. Once this is performed for each column, the array manifold will now

be denoted as A′(θ) to show that each entry in each column has been divided by it’s

respective norm value. This will be referred to as the normalized array manifold.

In an ideal DF antenna array, each column in the array manifold would be com-

pletely different from all other columns. In other words, the voltage responses for

each azimuth are completely different from all other azimuths. The words column

and azimuth and can be used interchangeably. If one arbitrary column is taken out

of an ideal array manifold and conjugate transposed and dotted with all columns

in the array manifold (correlated), the correlation coefficient values should be zero

everywhere except for the azimuth corresponding the column that was removed and

used for the correlation. However, this is not easily achieved in reality.

A generic example can be seen in Fig. 6 that shows a strong single correlation

14

peak. This plot shows the results of correlating one column of an array manifold with

all columns in the array manifold. This example shows that the particular column

used for correlation is very different from all other columns in the array manifold

except for itself.

Fig. 7 shows two peaks in the correlation. This example shows that the particular

column used for correlation is very similar to itself and one other column in the array

manifold. Thus, an ambiguity is present and it is unknown which column is correct.

The mathematical operation performed is shown in eq. (5). Let S′(θ) be the N

x 1 arbitrarily removed normalized column vector. Again, C(θ) is the 1 x M row

vector containing the complex correlation values. The vertical axis is shown as the

magnitude of the correlation coefficient squared. This is the adopted standard used

here in the characterization. Note that the values of the correlation coefficients vary

from 0 to 1 as the array manifold in this generic example was normalized.

C(θ) = S′(θ)†A′(θ) (5)

The highest peak corresponds to the column that was used for the correlation and

all other peaks are referred to as sidelobes. The width of the main peak is referred

to as the beamwidth. The beamwidth is defined as the main lobe width at the 0.9

correlation coefficient squared threshold. This standard was adopted through an

empirical means. If additive white Guassian noise is added to the normalized column

that is removed from the array manifold for correlation against all columns to give

a signal-to-noise-ratio (SNR) of 10 dB, the correlation coefficient squared peak tends

to fall to roughly 0.9. Therefore this standard was adopted and will be assumed from

here on.

The next step in characterizing an array manifold is to correlate all columns

with the array manifold. The goal is to observe the main peak beamwidth and max

sidelobe level for each column in the array manifold correlated against the entire array

15

0 20 40 60 80 100 120 140 160 180

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Azimuth (degrees)

|R|2

Figure 6: Correlation Plot with Strong Peak.

0 20 40 60 80 100 120 140 160 180

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Azimuth (degrees)

|R|2

Figure 7: Correlation Plot with Ambiguity.

16

manifold. This process can be shown mathematically in eq. (6). Now C(θ) is a M x

M two dimensional array containing the correlation values. The prime symbols again

refer to the fact that the array has been normalized.

C(θ) = A′(θ)†A′(θ) (6)

This operation can produce plots showing beamwidth and sidelobe levels for all

columns in the array manifold in a two dimensional sense. An ideal array manifold

would produce a plot with a perfect diagonal line across the plot. This would cor-

respond to only one column correlating perfectly with itself and not correlating at

all with all other columns. Again, this is not achievable in reality. Each column has

some associated beamwidth. A generic example of this can be seen in Fig. 8. The

color index corresponds to the correlation coefficients squared. Notice the beamwidth

of the main diagonal as it cuts across all azimuths or columns. The example shown in

Fig. 8 shows a desired array manifold auto-correlation. Fig. 9 shows an undesirable

auto-correlation. Along with the main diagonal, other ambiguous side lobe peaks

are present. These show that this array manifold has columns that are similar to

other columns. This is not desirable because ambiguities will then be present when

performing DF operations on received voltage signals.

From this auto-correlation process of the array manifold, two important quantities

can be obtained. The RMS beamwidth can be calculated by taking the 0.9 beamwidth

for each column and calculating an RMS value. RMS refers to the root mean square

value. A max sidelobe level value can also be obtained by observing all of the sidelobes

present from all column correlations and recording the peak value. The desired results

are to have low RMS beamwidths as sharper correlation peaks will lead to more

accurate DOA estimates. It is also desired to have low maximum sidelobe levels

to reduce the possibilities for ambiguous DOA estimates. These are two important

parameters used to characterize a particular array manifold.

17

Azimuth (degrees)

Ang

le o

f Arr

ival

(de

gree

s)

20 40 60 80 100 120 140 160

20

40

60

80

100

120

140

160

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 8: Desired Array Manifold Auto-correlation Example.

Azimuth (degrees)

Ang

le o

f Arr

ival

(de

gree

s)

0 20 40 60 80 100 120 140 160 180

0

20

40

60

80

100

120

140

160

180 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 9: Ambiguous Array Manifold Auto-correlation Example.

18

The characterization discussed thus far has dealt only with the two dimensional

array manifold at one frequency, polarization, and elevation. It is often desired to

observe how the DF antenna array and associated array manifold will perform over

a range of frequencies. Now, the standard two dimensional array manifold will be

analyzed over a range of frequencies while only dealing with one elevation and polar-

ization. An identical process to that shown in eq. (6) is performed for manifolds at

all frequencies of interest. For each frequency of interest the RMS beamwidth and

max side lobe level is determined. These values of RMS beamwidth and max sidelobe

level can then be plotted versus all frequencies of interest.

All of the analysis thus far has been performed on noise free array manifolds.

Now some noise will be added to make the characterization a better estimate of a real

world scenario. The goal is to now estimate the RMS DF error that is achievable

by the antenna array. The DF error is defined as the difference between the true

DOA and the estimated DOA. This requires the normalized array manifold to be

correlated against a conjugated transposed version of itself that now has additive

white Gaussian noise added to it. The noise can be added to the array manifold to

obtain a desired SNR by the process shown in Appendix A. The noisy array manifold

is now referred to as NA′(θ) where the prime symbol again symbolizes that each

column in the manifold has been normalized. The result of correlating the standard

array manifold, A′(θ), with the noisy array manifold, NA′(θ), will now cause the

expected DOA estimate for a particular azimuth to be shifted in some manner. This

process is shown in eq. (7).

C(θ) = NA′(θ)†A′(θ) (7)

Due to the noise, the correlation peak for a particular column or azimuth may not

align with proper column in the noise free array manifold. Calculating DF error from

this scenario is simply performed by taking the DOA value from the given peaks and

19

subtracting them from the DOA values that the columns should correspond to without

noise. This scenario is performed over many trials in a Monte Carlo type simulation

and then used to calculate an RMS DF error. This approach is a brute force approach

to approximate how an array manifold will perform when correlated under noisy

conditions and for a particular SNR. This process can then be performed with the

array manifolds for each frequency of interest. The results of this approach can then

be plotted to show the estimates of the RMS DF error versus frequency. This process

must be performed separately for all polarizations and elevations of interest. Note

that the Monte Carlo processing does not require beamwidth or sidelobe information.

The characterization process described here will be used for both modeled and

measured antenna response data. Three main plots will be used to present the char-

acterization data of the antenna arrays. The plots will be the RMS beamwidth versus

frequency, max sidelobe level versus frequency, and RMS DF error versus frequency.

The RMS DF error of a particular antenna array and it’s associated array manifold

will be the main metric used to evaluate DF antenna arrays in this thesis while the

other two plots will provide insight into other array parameters.

2.5 Properties of Direction Finding Antenna Arrays for Cor-

relation DF Algorithm

When designing antenna arrays to work with a correlation direction finding technique,

there are certain aspects of the array design that are important in creating a good

performing DF antenna array. A correlation style direction finding algorithm requires

diversity in the array manifold. The diversity is required in the two dimensional sense

of the array manifold where the rows in the array represent the individual antenna

elements and the columns represent azimuthal increments. This diversity can be

achieved in two ways. The first way is to use equally spaced antenna elements but

require that the antenna elements have different response patterns. The second way

20

is to use unequal spacing between the antenna elements and use antenna elements

with identical response patterns.

Simplicity in the individual element design is desirable. This is true for various

reasons. First, simple designs can be more quickly and more accurately prototyped.

Second, it is very important to be able to replace a damaged DF antenna without

requiring that the entire DF system be recalibrated. Simple antenna designs lend well

to repeatable manufacturing processes to allow for easy future maintenance that will

not require system calibration with new hardware. Third, simple antenna designs

can be more easily and more accurately modeled. Modeling DF antenna arrays is

extremely important to the design process and is often the best way of gaining insight

to a DF antenna arrays performance.

Stable and well behaved antenna response patterns are desired for each element in

the DF array. In other words, the antenna response patterns should not vary quickly

as a function of frequency. Array manifolds are typically measured over a range

of frequencies to provide a bandwidth for operation. Within the desired range of

frequencies, a set number of discrete frequencies must be selected to actually generate

the array manifolds. The effect of a having a discrete number of array manifolds can

pose a problem. This problem can arise if the frequency of a received signal is not

the same as one of the frequencies used to generate the array manifolds. Methods of

interpolation may be used to create an accurate estimate of what the array manifold

would be at the desired frequency. Other methods may use the array manifold that

was developed using the closest frequency to the received signal. In either case, some

estimate must be made. This estimate can be more accurate if the array manifold

is stable or changes very slowly over the frequencies of interest. Therefore, antenna

elements that have stable response patterns over the desired frequency range should

be used.

Utilizing antenna elements that do not contain resonances in the operating bands

21

of interest is strongly desired but not an absolute hard requirement of the DF antenna

arrays for use with correlation algorithms. The reasons for this are explained as

follows. One important factor influencing stable antenna response patterns is that

of antenna resonances. Around the point of resonance, the impedance of an antenna

often changes very rapidly. This change also relates directly to rapid changes in the

voltage responses of the antennas which as previously mentioned may cause errors

in frequency interpolation. At resonance, antennas also couple very strongly to their

surroundings which could introduce errors into the antenna response patterns. In

some cases, utilizing an antenna that contains resonances in the band of interest may

be unavoidable. If the desired antenna contains a single resonance point within the

band but also exhibits good impedance match across the rest of the frequency band,

it may be advantageous to ignore the resonance and still use the antenna. This is

a design tradeoff that can only be decided upon based on the exact performance

specifications of a DF system.

22

3 Antenna Design and Modeling

3.1 Design Considerations

3.1.1 Size Constraints

It was preferred that the DF antenna array being designed for use on a mobile platform

adhere to a few constraints. The particular DF array being investigated here had to

fit on a rectangular metal plate of dimensions 545 mm wide by 310 mm in length.

The height of the antenna structure also had constraint. First an initial radome

surrounding the antenna structure and mounting plate was required. However, the

height of this radome was somewhat variable and could be changed if needed. The

hard limiting factor was that the initial radome had to be less than 28 mm from the

rectangular metal plate. Therefore the designed antenna arrays had to fit in a space

545 mm wide by 310 mm in length by 28 mm in height.

Another constraint was that the antenna array be designed to work with an eight

channel receiving system. Therefore eight antenna elements had to be designed to fit

in the available space. A generic two dimensional view of the antenna array can be

seen in Fig. 10.

1 2 3 4

8765

545 mm

310 mm

Figure 10: Generic DF Array Layout.

23

3.1.2 Manufacturing

The manufacturing of the antenna array also provided some additional constraints

on the design. A readily available manufacturing process required that the antenna

structures be designed in a layered configuration. The rectangular metal plate previ-

ously described would serve as the ground plane for the antenna. Above the ground

plane would be a piece of pink foam. The pink foam has a relative permittivity, εr,

very close to one. In other words, the pink foam performs very similar to air; how-

ever it has the ability to provide additional support and vibration resistance to the

antenna structure. Then, on top of this foam would be the substrate with printed

or microstrip style antennas. The substrate used by the manufacturing process was

Rogers RT/duroid R© 5880. This substrate material was readily available for quick

prototyping of the antenna array designs. This material has a dielectric constant of

2.2. On top of the antennas would be another piece of pink foam followed by the

radome. This entire structure could then be mounted to the side of a platform via

connections to the ground plane. SMA connectors for all antenna elements would be

available for connection on the bottom of the ground plane. While it was not an ab-

solute requirement that the antenna arrays be designed to meet these manufacturing

specifications, it was desired because it was an easy and a readily available method

to prototype the antenna array designs.

3.1.3 Array Manifold Diversity

The first step in designing an antenna array for a direction finding system is to design

the individual antenna elements. The antenna elements to be investigated were of the

printed circuit or microstrip style. These antennas are cheap, easy, and reliable to

manufacture. They were also the type of antennas desired by the available prototyping

process. Microstrip antennas are light weight and can be of a planar nature for easy

and efficient mounting on mobile platforms.

24

As previously discussed, antenna arrays for correlation direction finding systems

must have diversity in their array manifolds. This can be achieved in two ways.

If the antenna elements to be used are equally spaced on the planar substrate the

individual antenna response patterns must have some diversity. If the elements are

equally spaced and the individual patterns are different, the columns in the array

manifold will have some associated diversity. Another way to create diversity in the

columns of the array manifold is to use identical antenna elements but vary their

spacing across the planar array. Either of these two approaches and or a combination

of them can be used to increase uniqueness or diversity in the array manifold columns.

The approaches investigated here will be to first design an equally spaced pattern

diverse array and second to design an unequally spaced identical element array.

3.2 Equally Spaced Pattern Diverse Array

3.2.1 Square Spiral Antenna Elements

The first design that was investigated utilized equally spaced elements oriented in

the available space in a manner shown in Fig. 10. The antenna elements used here

were adapted directly from research shown in [5, 6]. The research in [5, 6] uti-

lized a square spiral microstrip antenna that had two microelectromechanical system

(MEMS) switches. The switches allowed different parts of the antenna to be excited

with current to develop reconfigurable response patterns. Through dimensions shown

in [5, 6], the approximate dimensions in terms of free space wavelength were extrap-

olated and can be seen in Fig. 11. The black squares are the positions of the two

MEMS switches that would either open or close to allow current to flow in certain

directions. The two available configurations would allow a broadside or an endfire

pattern to be developed.

While the research utilizing the MEMS switches and reconfigurable patterns offers

an interesting insight into dynamically switching between response patterns, it was

25

0.4395λ0

0.1367λ0 0.1937λ0

0.3874λ0

0.3874λ0

0.3418λ0

0.0223λ0

0.1937λ0

0.2393λ0

Via to Ground Plane

SMA Probe Feed

Figure 11: Reconfigurable Square Spiral.

chosen to look at the characteristics of this antenna structure in a static configuration.

In other words it was chosen to take the ideas presented in [5, 6] and create one static

endfire antenna element and one static broadside element. The static endfire element

that was created can be seen in Fig. 12(a). The static broadside element can be seen

in Fig. 12(b). FEKO was used to create a three dimensional pattern view of the

endfire element in Fig. 13(a) and a three dimensional pattern view of the broadside

element in Fig. 13(b).

3.2.2 Array Layout

With the design of one endfire element and one broadside element, the geometrical

layout of the array had to be investigated. First, the antennas needed to be placed

in an equally spaced configuration. They were chosen to be laid out equally on

the substrate in an two dimensional array configuration with 2 rows and 4 columns.

To improve the diversity in the array manifold, the different antenna elements were

interleaved. In addition to interleaving the elements, the elements were also rotated.

Each element would not provide perfectly symmetrical response patterns. Therefore,

26

0.4395λ0

0.3874λ0

0.3874λ0

0.3418λ0

0.0223λ0

0.1937λ0

SMA Probe Feed

(a) Endfire

0.1367λ0

0.3874λ0

0.3418λ0

0.0223λ0

SMA Probe Feed

(b) Broadside

Figure 12: Endfire and Broadside Elements.

(a) Endfire (b) Broadside

Figure 13: Endfire and Broadside Element Patterns.

if the elements were rotated, they would provide an even more unique response pattern

compared to the other elements in the array. Fig. 14 shows the geometrical layout of

the antenna elements. The feed point of each element was maintained in a constant

position and the elements were rotated around the feed point for positioning. Note

the coordinate axes used to describe the array layout and the values of the azimuth

angle θ. Table 1 describes how the elements were oriented on the array and shows

the positions of the SMA probe feeds in millimeters.

It is important to have the antenna array provide the ability to listen to all az-

imuths of interest. The endfire elements are capable of strongly receiving information

about signals impinging on the array from the front and rear of the platform. The

27

1 2 3 4

8765

x

y

z

Front of Platform

Top of Platform

Bottom of Platform

Rear of Platform

θ = 0

θ = 90

θ = 180

Figure 14: Square Spiral Array Layout.

Table 1: Square Spiral Array Antenna Positions and Pattern Descriptions.

Antenna Number Response Pattern Feed Position (x,y,z) mm1 Endfire (-175,0,-56)2 Broadside (-41,0,-56)3 Endfire (41,0,-56)4 Broadside (175,0,-56)5 Broadside (-175,0,56)6 Endfire (-41,0,56)7 Broadside (41,0,56)8 Endifre (175,0,56)

broadside elements strongly receive signals impinging on the array from the side of

the platform. The use of both the broadside and endfire elements may allow this

array to provide near 180 of azimuth coverage. A more practical and usable range

may be from roughly 20 to 160 of azimuth. Each element provides a signal to a

single channel in a receiver and that information is used to provide a voltage snap

shot. Therefore, it makes sense to think about the total available coverage angles by

thinking about each individual elements response patterns.

28

3.2.3 FEKO Modeling of Square Spiral Array

The square spiral array shown in Fig. 14 needed to be modeled to assess performance.

The numerical modeling program FEKO was utilized. The antenna array needed to

be modeled to estimate the complex far field response patterns and to develop array

manifolds. These estimated array manifolds could then be analyzed to estimate DF

performance in a correlation style direction finding system. The impedance matching

characteristics of the antenna elements for use with a 50 Ω receiving system also

needed to be observed through the numerical models.

The FEKO models were developed utilizing infinite layers. Infinite layer solutions

allowed for simplicity and speed when running the models. The layers were created

according to the desired prototyping process. First, an infinite ground plane layer

was created. Then, an infinite layer was created to model the pink foam that was

to be placed under the antenna substrate. The pink foam layer was created with a

dielectric constant, εr, of 1.005. The thickness of this layer was variable. Initially

the thickness was set to be 10 mm. This layer was left to adjust to find the best

impedance match. The next layer was the substrate material. The substrate layer

was modeled to represent Rogers RT/duroid R© 5880 material. The thickness of this

layer was set at a value of 1.4 mm and the dielectric constant was set as 2.2. The

antenna elements that were created on top of the substrate layer do not have any

associated thickness in the FEKO model. The next layer was another layer of pink

foam of thickness 4.0 mm. The final layer was the radome. This layer was set to a

thickness of 1.4 mm and given a dielectric constant of 2.73. The characteristics of the

foam, substrate, and radome layers were chosen to match the characteristics of the

materials used in the available prototyping process.

With the appropriate layers created, the antenna elements were then created. The

antenna elements for this array were built for use around 1900 MHz. The desired band

for operation was 1710 - 2100 MHz. Using the generic antenna dimensions shown in

29

Fig. 12, the antennas were created with a starting design frequency of 1900 MHz.

They were created on top of the substrate layer and beneath the second foam layer.

With the model of the array created, the first investigation was to optimize the

impedance matching characteristics. FEKO simulations and optimizations were run

to look at the impedance characteristics. The simulations looked at the magnitude

of the input reflection coefficient or |S11|. It was concluded that a design frequency

around 1500 MHz and a thickness of 9.9 mm for the first foam layer gave the best

impedance matching characteristics across the band of interest. The impedance es-

timates for all elements in the array can be seen in Fig. 30. It can be observed

that both the broadside and endfire elements show resonances in the band of inter-

est. As previously stated, in band resonances are typically not desired because the

complex antenna responses will vary rapidly around areas of resonances. However, it

was chosen to allow the in band resonances to further investigate the available DF

performance of this array configuration.

After improving the matching characteristics of the array, FEKO models were run

to develop array manifold data. Some careful steps had to be taken to take modeled

FEKO data into proper array manifold data. FEKO requires that infinite ground

planes be infinite in the x and y directions. Fig. 16 shows how FEKO will compute a

single far field pattern cut using spherical coordinates with φ fixed at 0 and θ varying

from −90 to +90. Note the direction of the unit vectors representing the directions

of θ and φ polarization.

These values must be adjusted to meet the desired DF coordinate system of az-

imuth and elevation. After FEKO generates the data as shown in Fig. 16, MATLAB

routines were used to transform the data into the desired DF coordinate system. The

post processing routines transformed the data into a format shown in Fig. 17. The

single cut was rotated down onto the xy axis and the infinite planes were rotated onto

the xz plane. Fig. 17 shows that the θ data in Fig. 16 was transformed into azimuth

30

1700 1750 1800 1850 1900 1950 2000 2050 2100

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(a) Element 1

1700 1750 1800 1850 1900 1950 2000 2050 2100

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(b) Element 2

31

1700 1750 1800 1850 1900 1950 2000 2050 2100

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(c) Element 3

1700 1750 1800 1850 1900 1950 2000 2050 2100

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(d) Element 4

32

1700 1750 1800 1850 1900 1950 2000 2050 2100

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(e) Element 5

1700 1750 1800 1850 1900 1950 2000 2050 2100

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(f) Element 6

33

1700 1750 1800 1850 1900 1950 2000 2050 2100

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(g) Element 7

1700 1750 1800 1850 1900 1950 2000 2050 2100

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(h) Element 8

Figure 15: Square Spiral Array Element Impedances.

34

y

x

z

θ Polarization

φ Polarization

FEKO Far Field Pattern Cut

φ = 0

θ = −90 to θ = 90

Figure 16: FEKO Simulation Coordinate System.

y

x

z

φ Polarization

θ Polarization

DF Far Field Pattern Cut

AZ = 180 to AZ = 0

EL = 0

Figure 17: Transformed FEKO Coordinates into DF Coordinates.

data. Similarly the φ data was transformed into elevation data. The φ polarization

in Fig. 16 was transformed into θ polarization and θ polarization in Fig. 16 was trans-

formed into φ polarization. Note that the polarization unit vectors shown in Fig. 16

point in different directions depending whether they lie over the positive or negative

portion of the x axis. When the data is transformed negative signs were applied to

the appropriate unit vectors to make them point in the proper directions as shown in

35

Fig. 17. This thesis only deals with information taken in the φ polarization shown in

Fig. 17. This will be designated as vertical polarization.

With the FEKO models and post processing routines developed, complex antenna

response patterns could be analyzed. Fig. 18 shows the complex response patterns

of each element in the square spiral array for vertical polarization and 0 elevation.

These plots show relative pattern responses that have been normalized so that 0 dB

is the maximum value. This plot essentially shows array manifold data in a graphical

form at a frequency of 1920 MHz. Note how the endfire elements (1,3,6,8) have nulls

in their response patterns around 90 azimuth and the broadside elements (2,4,5,7)

have peaks in their response patterns around 90 azimuth.

The complex antenna response patterns were then organized into proper array

manifolds and characterized utilizing MATLAB routines. The analysis was focused

on generating the main three plots as mentioned in section 2.4.3 for the 0 elevation

and vertical polarization case. These plots are RMS beamwidth versus frequency,

max sidelobe level versus frequency, and RMS DF error versus frequency. The results

of this characterization can be seen in Fig. 19.

The top most plot shows RMS beamwidth versus frequency. Note how the beamwidth

tends to decrease as frequency increases. The widest beamwidth value is approxi-

mately 11.

The middle plot shows the max sidelobe level versus frequency. The sidelobe

characteristics stay fairly low across the band except for a large jump in the middle

of the band. These sidelobe levels were not considered to be a major issue because

they were still well under a value of one.

The bottom plot shows the RMS DF error versus frequency. An SNR of 10 dB

and 10 trials in the Monte Carlo simulation were used to generate the estimates. Note

that the Monte Carlo simulation analysis shows RMS DF error across the frequency

range under 2. In other words, across the frequency band of interest this array is

36

0 20 40 60 80 100 120 140 160 180

−40

−30

−20

−10

0

Mag

nitu

de (

dB)

0 20 40 60 80 100 120 140 160 180

−200

−100

0

100

200

Pha

se (

degr

ees)

Azimuth (degrees)

Element 1Element 2Element 3Element 4Element 5Element 6Element 7Element 8

Figure 18: Normalized Complex Patterns of Square Spiral Array Elements.

1700 1750 1800 1850 1900 1950 2000 2050 2100

0

10

20

RM

S B

W (

degr

ees)

1700 1750 1800 1850 1900 1950 2000 2050 2100

0

0.5

1

Max

Sid

elob

e Le

vel

1700 1750 1800 1850 1900 1950 2000 2050 2100

0

2

4

Frequency (MHz)

RM

S D

F E

rror

(de

gree

s)

Figure 19: Square Spiral Array Manifold Characterization.

37

0.1592λ0 0.1592λ0

0.1009λ0

0.0434λ0

0.0434λ0

0.2800λ0

0.3625λ0

0.5059λ0

Figure 20: E Patch.

estimated to provide DOA estimates accurate to within 2. These estimates show that

this array is capable of providing solid DF performance when used with a correlation

algorithm.

3.3 Unequal Spaced Identical Pattern Array

3.3.1 E Patch Antenna Elements

The second design that was investigated utilized identical antenna elements placed at

unequally spaced locations. The antenna elements used are shown in Fig. 20. These

elements are essentially λ2

rectangular patch elements. However these elements have

two rectangular slots in the middle of the elements. The slots allow the antenna

elements to provide a wider bandwidth of operation and make the patch linearly

polarized in the direction of the slots [7]. These elements provide a strong broadside

response pattern. A three dimensional FEKO model of the response pattern can be

seen in Fig. 21.

38

Figure 21: E Patch Pattern.

3.3.2 Array Layout

The E patch antenna elements had to be laid out on the substrate material in an

unequally spaced fashion due to their identical response patterns. The array was

chosen to be laid out on the substrate in a two dimensional array configuration with

2 rows and 4 columns. However, the spacing of the elements in each row was altered.

The spacing in each row was similar to a logarithmic type spacing but was merely

estimated based on the available space on the substrate. The geometrical layout of

the array can be seen in Fig. 22. While the positioning of each element in each row

was altered along the x axis, the feed points were kept at a constant value above and

below the z axis for each row. Table 2 shows the positions of the SMA feeds. Note

the coordinate axes used to describe the array layout are identical to the square spiral

array. Also note that the direction of the slots were oriented in a manner to align

with the previously defined vertical polarization.

As with the square spiral array, it is not anticipated that this array can provide

accurate coverage of 180 of azimuth. The more practical usable range is again roughly

from 20 to 160. Especially with this array consisting of all broadside elements, this

array is more receptive to signals impinging on the array from the side of the platform.

This may make this array have an even slightly less usable range than the square spiral

array.

39

1

x

y

z

Front of Platform

Top of Platform

Bottom of Platform

Rear of Platform

θ = 0

θ = 90

θ = 180

2 3 4

765 8

Figure 22: E Patch Array Layout.

Table 2: E Patch Array Antenna Positions and Pattern Descriptions.

Antenna Number Response Pattern Feed Position (x,y,z) mm1 Broadside (-169,0,-77.433)2 Broadside (-69,0,-77.433)3 Broadside (35,0,-77.433)4 Broadside (143,0,-77.433)5 Broadside (-119,0,42.567)6 Broadside (-15,0,42.567)7 Broadside (81,0,42.567)8 Broadside (169,0,42.567)

3.3.3 FEKO Modeling of E Patch Array

FEKO was again used to analyze matching characteristics for use with a 50 Ω receiving

system and estimate array manifold data for use in a correlation direction finding

system. The layering process used to develop the model for the E patch array was

identical to the process used in the square spiral array. First and infinite ground

layer was created. Then the first foam layer was created with a dielectric constant,

εr, of 1.09 and thickness of 10 mm. This layer was again left to adjust for the best

impedance match. The substrate layer was modeled to represent the same Rogers

RT/duroid R© 5880 substrate material of dielectric constant 2.2. The thickness of the

substrate was set at 1.2 mm. The second foam layer was modeled with a dielectric

40

constant of 1.09 and thickness of 4.0 mm. The final layer was the outermost radome

of thickness 1.4 mm and dielectric constant of 2.79. All of the characteristics of the

layers were selected to closely match the materials used in the prototyping process.

The desired band of interest for this array was 2240 - 2740 MHz. The antennas

were designed at a frequency of 2400 MHz and placed on top of the substrate. Again,

the antennas had no thickness in the model. FEKO simulations and optimizations

were used to optimize the impedance matching characteristics. It was concluded

that a design frequency of 2400 MHz and a thickness of 7.48 mm for the first foam

layer gave the best impedance matching characteristics across the band of interest.

However, an error in the prototyping process made the first foam layer with a thickness

of 10.0 mm. Therefore this model was created with a first foam layer thickness of

10.0 mm. The simulated values for the magnitude of the input reflection coefficient

or |S11| can be seen in Fig. 4.3. A clear resonance can be observed in this band for

these design parameters. However, the resonance appears to vary rather smoothly as

opposed to a very sharp resonant point. Therefore, it was again chosen to deal with

the resonance point in the middle of the band of interest to allow further investigation

of the available DF performance of this antenna array.

An identical process was used to take FEKO simulated antenna response data and

turn it into usable array manifold data for processing in MATLAB scripts. Complex

antenna responses were only analyzed for the vertical polarization and 0 elevation

case. Fig. 24 shows the individual complex antenna response patterns. Similar to

the square spiral patterns, these plots show relative pattern responses that have been

normalized so that 0 dB is the maximum value. Notice how all patterns are nearly

identical and provide a broadside response pattern. The plot shows the patterns for

the antenna elements at 2440 MHz.

The complex antenna responses were then assembled into array manifold data and

analyzed for approximate DF performance. These estimates can be seen in Fig. 25.

41

2200 2300 2400 2500 2600 2700 2800

−35

−30

−25

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0

Frequency (MHz)

|S11

| (dB

)

FEKO

(a) Element 1

2200 2300 2400 2500 2600 2700 2800

−35

−30

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−15

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0

Frequency (MHz)

|S11

| (dB

)

FEKO

(b) Element 2

42

2200 2300 2400 2500 2600 2700 2800

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0

Frequency (MHz)

|S11

| (dB

)

FEKO

(c) Element 3

2200 2300 2400 2500 2600 2700 2800

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0

Frequency (MHz)

|S11

| (dB

)

FEKO

(d) Element 4

43

2200 2300 2400 2500 2600 2700 2800

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0

Frequency (MHz)

|S11

| (dB

)

FEKO

(e) Element 5

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0

Frequency (MHz)

|S11

| (dB

)

FEKO

(f) Element 6

44

2200 2300 2400 2500 2600 2700 2800

−35

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−15

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−5

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(g) Element 7

2200 2300 2400 2500 2600 2700 2800

−35

−30

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

FEKO

(h) Element 8

Figure 23: E Patch Array Element Impedances.

45

0 20 40 60 80 100 120 140 160 180

−40

−30

−20

−10

0

Mag

nitu

de (

dB)

0 20 40 60 80 100 120 140 160 180

−200

−100

0

100

200

Pha

se (

degr

ees)

Azimuth (degrees)

Element 1Element 2Element 3Element 4Element 5Element 6Element 7Element 8

Figure 24: Normalized Complex Patterns of E Array Elements.

2200 2300 2400 2500 2600 2700 2800

0

10

20

RM

S B

W (

degr

ees)

2200 2300 2400 2500 2600 2700 2800

0

0.5

1

Max

Sid

elob

e Le

vel

2200 2300 2400 2500 2600 2700 2800

0

2

4

Frequency (MHz)

RM

S D

F E

rror

(de

gree

s)

Figure 25: E Array Manifold Characterization.

46

The three main plots RMS beamwidth versus frequency, max sidelobe level versus

frequency, and RMS DF error versus frequency are presented.

The top plot shows the RMS beamwidth. The largest beamwidths are found at

the lower end of the band. The maximum beamwidth is just under 14. Note how

the RMS beam width gradually decreases as the frequency increases.

The middle plot shows extremely low maximum sidelobe levels. Across the entire

band it can be seen that the maximum sidelobe levels stay under 0.15. These levels

are well below 1 which means that ambiguous peaks should not be of concern.

The bottom most plot shows the RMS DF error. The Monte Carlo simulation run

with an SNR of 10 dB and 10 trials, shows RMS DF error right around 2 across the

entire band. This array also seems to be capable of providing low DF error.

3.4 Modeling Conclusions

The modeling of both antenna arrays and the subsequent analysis, shows that both

array geometries can provide useful array manifolds for use in a correlation direction

finding system. The E array seems to show lower maximum sidelobe levels. The

square spiral array seems to show better RMS beamwidth performance. The most

important metric of RMS DF error seems to be very comparable for both arrays with

values around 2 across their respective bands.

While the DF performance of each array is fairly similar, the impedance matching

characteristics differ. The E array elements seem to have better matching character-

istics across the entire band compared to both of the square spiral elements as seen in

the modeled |S11| results. Also, the in band resonances seen in the E array elements

seem to be much broader and smoother than square spiral elements.

Based on the modeling of both arrays, it seems as if the unequally spaced identical

pattern array has better overall characteristics. Although it has similar RMS DF error

to the square spiral type array, the better impedance match makes it a more appealing

47

design. Also, the use of only one type of element would be greatly favored for cost,

simplicity, and repeatability in manufacturing. In order to draw further conclusions

on the designs, the arrays were prototyped and tested in an anechoic chamber to

better estimate performance in a real world setting.

48

4 Antenna Prototyping

4.1 Prototype Manufacturing

Both of the array designs were prototyped using the same manufacturing process and

used the same materials. The dimensions of the ground plane and individual layer

thicknesses for each array were given in Chapter 3. A view of the ground plane, first

foam layer, substrate, and second foam layer can be seen in Fig. 26. Fig. 27 shows

the radome placed over all of the layers and attached to the ground plane.

Figure 26: Layers of Prototype Antennas.

Figure 27: Radome Over All Layers of Antenna Structure.

Figure 28: Underside of Ground Plane with SMA Connectors.

Fig. 28 shows the underside of the ground plane with 8 female SMA connectors for

access to all antenna elements. Screw holes were placed in the ground plane. These

49

holes were drilled so that mounting structures could be attached to the ground plane.

These mounting structures could then interface with the side of a mobile platform to

mount the antenna array.

The foam layers have dielectric constants very close to that of free space. There-

fore, their electromagnetic effects are minimal. However, they do provide good struc-

tural stability to the structure. When the radome is fastened to the ground plane, the

entire structure is very rigid. Structural stability is advantageous when considering

placement of these antenna arrays on mobile platforms.

The individual antenna elements sit on top of the Rogers RT/duroid R© 5880 sub-

strate. They were etched out of the substrate using a routing machine. They are

attached to the SMA connectors through a pin feed that passes from the SMA con-

nector through the first foam layer and substrate. The pin feed is then attached to

the antenna elements by a solder joint. The pin feed is surrounded with a dielectric

material as it passes through the first foam layer. However, when passing through

the substrate layer the dielectric is removed and the bare pin is passed through the

substrate up to the antenna. The Rogers RT/duroid R© 5880 substrate is connected

to the ground plane using nylon screws.

4.2 Square Spiral Array Prototype

The square spiral array utilized equally spaced pattern diverse antenna elements. The

details of all antenna elements and placements were discussed in section 3.2. A view

of the prototype can be seen in Fig. 29.

It was desired to see how well the characteristics of the prototype matched that

of the model. To investigate this, impedance measurements were taken across the

same frequency band as examined in the model for the square spiral array. |S11|

measurements were taken using two different pieces of measurement equipment. The

measurements were made with an Agilent E8364B PNA series network analyzer and

50

Figure 29: Square Spiral Array Prototype.

a handheld Agilent N9330A antenna tester. Both pieces of equipment were used to

improve confidence in the accuracy of the measurements.

The acquired measurement data and the modeled data can be seen for each an-

tenna element in Fig. 30. The endfire elements (1,3,6,8) show an extremely good

match between measured and modeled data. The broadside elements (2,4,5,7) also

show an extremely good match between measured and modeled data. However, the

resonance point for both elements is shifted just slightly between measured and mod-

eled data. Also, the measured impedance shows a deeper resonance point. The overall

impedance characteristics match up extremely well.

4.3 E Patch Array Prototype

The E patch array utilized unequally spaced antenna elements that all had the same

response patterns. The details of the antenna elements and placements were discussed

in section 3.3. A view of the prototype antenna can be seen in Fig. 31.

An identical measurement process as the square spiral array was utilized to mea-

sure the impedance characteristics of this array. The modeled data seems to give |S11|

values that show slightly worse matching characteristics than the measured data.

51

1700 1750 1800 1850 1900 1950 2000 2050 2100

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(a) Element 1

1700 1750 1800 1850 1900 1950 2000 2050 2100

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(b) Element 2

52

1700 1750 1800 1850 1900 1950 2000 2050 2100

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(c) Element 3

1700 1750 1800 1850 1900 1950 2000 2050 2100

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(d) Element 4

53

1700 1750 1800 1850 1900 1950 2000 2050 2100

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(e) Element 5

1700 1750 1800 1850 1900 1950 2000 2050 2100

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(f) Element 6

54

1700 1750 1800 1850 1900 1950 2000 2050 2100

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(g) Element 7

1700 1750 1800 1850 1900 1950 2000 2050 2100

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(h) Element 8

Figure 30: Square Spiral Array Element Impedances.

55

Figure 31: E Patch Array Prototype.

However, the resonant frequencies are very close and the overall trend of the data

seems to match well. Similar to the square spiral array, the impedance characteristics

of the measured and modeled array show the same basic trends and point to similar

performance characteristics.

4.4 Prototyping Conclusions

Through the basic impedance performance analysis of both arrays, it can be concluded

that the models for both arrays gave good overall estimates of how the actual arrays

would perform. The E prototype array seems to have better matching characteristics

than predicted by the model. It is not fully understood what made the FEKO model

differ from the actual prototype. This should generally not be considered a problem.

It is preferred that the prototypes have better than predicted performance instead of

the models showing better performance than what can be built.

While the impedance characteristics gave some insight into the prototype arrays

performance, the true goal of the prototype antenna arrays was to observe their

available DF performance for use with a correlation algorithm. This performance

could then be compared to the modeled data to see how well the models would predict

56

2200 2300 2400 2500 2600 2700 2800

−35

−30

−25

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−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(a) Element 1

2200 2300 2400 2500 2600 2700 2800

−35

−30

−25

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−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(b) Element 2

57

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−10

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0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(c) Element 3

2200 2300 2400 2500 2600 2700 2800

−35

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−15

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−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(d) Element 4

58

2200 2300 2400 2500 2600 2700 2800

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0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(e) Element 5

2200 2300 2400 2500 2600 2700 2800

−35

−30

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−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(f) Element 6

59

2200 2300 2400 2500 2600 2700 2800

−35

−30

−25

−20

−15

−10

−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(g) Element 7

2200 2300 2400 2500 2600 2700 2800

−35

−30

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−5

0

Frequency (MHz)

|S11

| (dB

)

Agilent N9330A Antenna TesterAgilent E8364B PNA Network AnalyzerFEKO

(h) Element 8

Figure 32: E Patch Array Element Impedances.

60

the real DF performance of the arrays. To reach this ultimate goal of evaluating DF

performance, a fully equipped anechoic chamber capable of generating array manifold

data was required. This testing is addressed in the following chapter.

61

5 Antenna Testing

5.1 Considerations for Measuring Array Manifolds

Accurate array manifold data for a correlation DF technique directly corresponds

to an accurate DF system. Therefore, measuring array manifold data for direction

finding antenna arrays requires special considerations. Specialized outdoor antenna

ranges or large indoor anechoic chambers capable of working in the desired frequency

range must be utilized. The test facility must have an extremely accurate position-

ing system, minimize all possible reflections, and ensure that plane waves and not

spherical wavefronts are present across the entire antenna array.

Measuring complex voltage response data for each individual antenna element in

an array over multiple azimuths, elevations, and polarizations requires precision when

positioning the antenna array. The rotation mechanisms that orient the antenna array

should be as accurate as possible. The moving mechanisms should produce repeatable

motions with as little mechanical error as possible. Along with rotating to accurate

angle measurements, the rotations by all equipment should rotate very accurately

about a constant axis of rotation. If the rotations do not follow around a constant

axis of rotation there may be a wobble in the rotations that may show up as phase

error in the voltage responses.

Reflections from the surrounding environment should be minimized. Whether the

range is indoor or outdoor all possible sources of reflections should be removed and or

covered with absorber when possible. Reflections will introduce errors into the array

manifold data that will lead directly to incorrect DOA estimates.

With the antenna arrays being designed for single plane wave direction finding,

it is sensible that the test range have pure plane wavefronts impinging upon the

antennas. If the antenna array is positioned in the test environment and is not in the

far field of the transmit antenna, the wavefront impinging on the antenna array will

62

be spherical. Thus large phase differences will be observed across the array.

It should be noted that measuring array manifold data in a clean test environment

simply gives good estimates of the antenna prototypes DF performance. When the DF

antenna array is installed on a platform, the placement on the platform will distort

the measured array manifold data. Fielded DF systems require the measurement

of the array manifold with the DF arrays in their final placement on the platform.

However, measuring the array manifolds of prototype antenna arrays in a controlled

test does provide solid estimates of the potential DF performance.

5.2 Anechoic Chamber

5.2.1 Chamber Properties

With two antenna arrays fully modeled and prototyped, it was desired to take highly

accurate complex array manifold response data. This process required an anechoic

chamber that could support the desired frequency range along with providing the ac-

curacies required for DF antenna measurements outlined in section 5.1. The anechoic

chamber available for use to make these measurements was the anechoic chamber in

Warminster, PA that is operated by the Penn State Applied Research Laboratory.

Information for the chamber has been documented in [8]. A cross sectional view

of the chamber can be seen in Fig. 33. The usable frequency range of this chamber is

100 MHz to 100 GHz. The overall dimensions of the chamber are 100 feet in length,

40 feet in width, and 40 feet in height. The quiet zone around the antenna under

test (AUT) is designed to have a cylindrical shape with a diameter of at least 12 feet

and 56 feet in length. The quiet zone offers a volume where minimal reflections or

interference is anticipated besides the desired transmit signal.

The chamber also has the ability to provide plane wavefronts at the frequencies

of interest to the antenna array. A general rule of thumb presented by [9] is that the

far field region or plane wave region is obtained when the distance from the antenna,

63

StorageRoom

ControlRoom

StagingRoom

100’ - 0”

40’ - 0”

20’ - 0”

56’ - 0”

Transmit AntennaAUT

20’ - 0”

12’ Diameter Cylindrical Quiet Zone

Rail System

56’ - 0”

Figure 33: Cross Section of Anechoic Chamber.

d, is greater than or equal to the value shown in eq. (8).

d =2D2

λ0(8)

D is the largest dimension of the antenna structure and λ0 is the free space wavelength.

This approximation corresponds to an approximate phase error across the antenna

structure of 22.5 [9]. It should be noted that this approximation only holds when

λ0 is on the same order of magnitude as D. For direction finding purposes, it was

desired to have the plane wavefront have phase error across the array structure of less

than 5. This more stringent plane wave approximation was desired to improve the

consistency of the complex voltage responses for the antennas.

To determine the phase error across the antenna arrays when placed in the ane-

choic chamber, the following method was utilized. Fig. 34 shows the transmit antenna

and the flat panel array placed in the anechoic chamber. The diagram is not drawn

64

d

w ≈ 0.5m

dmin ≈ 24m

Transmit Antenna

Planar Antenna Array

Constant Phase Wavefronts

dmax

Figure 34: Wavefronts in Anechoic Chamber.

to scale. Constant phase spherical wavefronts can be seen propagating away from the

transmit antenna toward the planar antenna array. The diagram shows how as the

spherical wavefronts propagate, they begin to appear more like planar wavefronts.

The spherical wavefront impinges upon the planar antenna array with different

phase path distances to the center of the array and to the outer edge of the array.

The shortest phase path is the path to center of the planar array which is roughly

24 m and is labeled in Fig. 34 as dmin. The longest phase path is the path from the

transmitter to the edge of the planar array which is labeled in Fig. 34 as dmax. The

difference between these two paths is labeled in Fig. 34 as 4d. The first step was

calculating the value of dmax using the Pythagorean theorem. This value was found

using eq. (9).

dmax =

√d2min + (

w

2)2 (9)

The value of dmax was then used to find the path length difference as shown in eq. (10).

65

4d = dmax − dmin (10)

The path length difference, 4d, was then changed into a phase path value with units

of radians in eq. (11).

4θrad = 4d2π

λ0(11)

λ0 is the free space wavelength of the frequency of interest. The path length difference

was then converted to units of degrees in eq. (12).

4θdeg = 4θrad180

π(12)

For the lowest frequency of interest, 1710 MHz, this value was found to be ap-

proximately 2.67. For the highest frequency of interest, 2740 MHz , this value was

found to be approximately 4.28. Therefore, it can be seen that the anechoic chamber

provided better than desired 5 of phase error across the array at all frequencies of

interest for both prototype arrays.

Although it was found that the set up utilized in the anechoic chamber provided a

good plane wave incident upon the antennas, a spherical to planar wavefront conver-

sion was investigated in case the anechoic chamber could not provide suitable plane

waves at the frequencies of interest. The conversion is explained in Appendix B and

corrects the phase of a spherical wavefront to a planar wavefront but does not change

the amplitude of the wavefront.

5.2.2 Antenna Positioning System

The antenna positioning system is the structure that holds the AUT in Fig. 33. The

entire antenna positioning system rides on a rail system that allows the structure to

move back and forth in the chamber. An image of the antenna positioning system can

66

be seen in Fig. 35. The antenna positioner system consists of a base, a large white

boom, and a roll head positioner at the top of the boom where the AUT mounts to

the positioning system. The base of the antenna positioning system allows for three

different ways to move the large boom. The base can rotate the boom up and down

so that antennas can be attached to the boom while standing on the ground near the

base. The base can also rotate the boom in a manner as to spin the boom around it’s

vertical axis. This rotation allows the AUT to be rotated from facing the transmit

antenna in a boresight fashion to being spun around so that the back of the antenna

is now directly facing the transmit antenna. The third adjustment that the antenna

positioning system allows is to move the boom back and forth on top of the base by

using a hand crank. These features are pointed out in Fig. 36.

On top of the large boom is the roll head positioner. The roll head positioner will

rotate the AUT around the axis of rotation of the roll head. The roll head positioner

can be seen in Fig. 37 where an arbitrary horn antenna is shown connected to the

roll head positioner.

When looking at the antenna positioning system from the viewpoint of the trans-

mit antenna, the AUT can be moved electronically in two different ways. These

motions are illustrated in Fig. 38. Therefore these two motions must be used in an

appropriate way to facilitate different azimuthal and elevation increments for a set of

frequencies and a given polarization to generate array manifold data.

5.2.3 Measurement System

The data collection system is shown in a block diagram form in Fig. 39. Inside of

the control room is the control computer. The control computer takes in the desired

data as well as controls the movements of the positioning system. First the control

computer positions the antenna positioning system to the desired location. Then the

control computer communicates with the signal generator that serves as the source.

67

Figure 35: Antenna Positioning System.

68

Raise / Lower Boom

Move Boom Back and Forth

Rotate Boom Around Vertical Axis

Figure 36: Antenna Positioning System Base Features.

Roll Head Positioner

Figure 37: Roll Head Positioner on Top of Boom.

69

Figure 38: Electronic Motions of Antenna Positioner Looking from Transmit Antenna.

The source then outputs the desired transmit signal to an RF switch box. The RF

switch box contains RF hardware to work with two separate bands. The low band

electronics operate from 100 MHz to 2 GHz. The high band operates from 2 GHz to 18

GHz. The high band electronics also include an amplifier to boost the signal because

the higher frequencies have greater attenuation across the transmission path. Each

band contains its own respective coupler that allows the source signal to be sent in two

different directions. The source signal is simultaneously sent to the transmit antenna

as well as hard wired to a microwave receiver located in the chamber. The control

computer is then used to select which antenna in the antenna array the receiver will

utilize to receive the transmit signal. A ten way switch allows the system to switch

between ten antenna elements electronically without having to manually disturb the

set up. This is important because manually disturbing the set up could reduce the

consistency of the measurements. Once the signal is received on an antenna element,

it is then routed to the microwave receiver located in the chamber.

The microwave receiver located in the chamber is used to compute S21. S21 is a

parameter that stems from typical microwave network analysis techniques called S

parameters. S21 corresponds to the response at port 2 of a device, a1, due to the

70

Control Room Chamber

SourceMicrowave Receiver

b2

a1

S21 = b2a1

Control Computer

AUTTransmit Antenna 10 Way Switch

RF Switch Box

and Couplers

Figure 39: Data Collection System.

input at port 1 of a device, b2. In this case the input voltage signal is the signal from

the source and the response signal is the signal received by the AUT. Therefore, this

measurement process is identical to taking a typical network analyzer and measuring

the S21 characteristics of a two port device. It should be noted that the received

voltage signals have both an amplitude and a phase. Therefore, in general S21 is

complex. The information is then sent back to the control computer for storage. The

control computer can then reposition the AUT and repeat the measurement for as

many orientations as desired.

5.3 Collecting Array Manifold Data in Anechoic Chamber

5.3.1 Prototype Antenna Rotations

The orientation of the antenna arrays when placed in the chamber was very important.

To keep all of the data consistent with the modeled data, the coordinate system shown

in Fig. 40 was defined. Note that the origin is defined in the center of the array and

is placed at the antenna layer and not on the outer radome. Also note that the front

of the platform corresponds to 0 azimuth. This means that with this orientation the

71

1 2 3 4

8765

x

y

z

Front of Platform

Top of Platform

Bottom of Platform

Rear of Platform

θ = 0

θ = 90

θ = 180

Figure 40: Prototype Antenna Array Coordinates Defined.

antenna array is on the right side of the platform. Antenna elements 4 and 8 are

closest to the front of the platform and antenna elements 1 and 5 are closest to the

rear of the platform.

The two prototype arrays had to be mounted on the antenna positioning system in

such a way that azimuth and elevation information could be obtained. As previously

stated, from the view of the transmit antenna the antenna positioning system can

move in the motions shown in Fig. 38. To properly acquire azimuth and elevation

data, the antenna positioning system and the prototype antennas had to be situated

as shown in Fig. 41. The view in Fig. 41 is the view from the transmit antenna. In the

figure, it can be seen that the roll head positioner synthesizes the azimuthal rotation.

The rotator system contained in the base of the positioner system can synthesize the

elevation rotation. The azimuthal axis of rotation was maintained by the roll head

positioner. The elevation axis of rotation was maintained by using the hand crank to

move the boom so that the center point of the antenna array was in line with the base

72

Elevation Rotation

Azimuthal Rotation

Mounting Bracket

Prototype Array

Elevation Axis of Rotation

Azimuthal Axis of Rotation Roll Head Positioner

Hand Crank

Rotator

y

x

z

5

8

6

7

1

2

3

4

Figure 41: Antenna Positioning System Orientation.

rotator’s axis of rotation. Note that the positioning of the coordinate axes relative to

the array show that the array is oriented at 90 azimuth and 0 elevation in Fig. 41.

It is vital to the testing that the coordinate systems be very carefully noted to

provide correct azimuth and elevation information as described in Fig. 2. The roll

head provides the azimuthal rotation. To observe how the roll head provides the

correct azimuthal rotation, the elevation angle, ψ, will be fixed at 0. Fig. 42 shows

how the roll head can rotate the array to give all desired azimuthal angles between

0 and 180. Note that all of these views are from the transmitter looking toward the

antenna array under test as in Fig. 41. In Fig. 42(a) the antenna elements are facing

in the +y direction toward to the ground of the chamber and antenna elements 4 and

73

8 are the closest to the transmit antenna. This orientation represents 0 azimuth.

The roll head then rolls the panel array so that antenna elements 4 and 8 are now

moving farther from the transmitter and elements 1 and 5 are moving closer towards

to the transmitter. This rotation takes the array from receiving 0 azimuth signals

to 90 azimuth signals. The 90 azimuth position is then shown in Fig. 42(b). At the

azimuth position of 90 all antenna elements are facing in the -x direction broadside

to the transmitter. Then the roll head moves the array so that antenna elements 4

and 8 move farther away from the transmitter and elements 1 and 5 get closer to

the transmitter. This rotation takes the array from receiving 90 azimuth signals to

180 azimuth signals. The 180 azimuth position is then shown in Fig. 42(c). At this

position all antenna elements are facing in the -y direction toward the ceiling of the

chamber.

The rotator in the base of the positioning system provided the elevation rotation.

To observe how the base rotator provides the correct elevation rotation, the azimuth

angle, θ, will be fixed at 90. Fig. 43 shows how the base rotator can rotate the array

to give all desired elevation angels between −90 and 90. Note that all of these

views are from the transmitter looking toward the antenna array under test as in

Fig. 41. Fig. 43(a) shows the antennas facing in the +z direction with the roll head

positioner in between the transmitter and the antenna array. Antenna elements 1,

2, 3, and 4 are the closest to the transmitter in this configuration and the elevation

angle is −90. This is obviously a problem as the roll head will impede the transmit

signal. Therefore, elevation angles cannot be measured at this extreme of an angle.

This figure is used to simply illustrate the motions. The base rotator would then

rotate the array so that the antenna elements 1, 2, 3, and 4 were moved away from

the transmitter and elements 5, 6, 7, and 8 were moved closer to the transmitter.

Fig. 43(b) shows all of the antennas broadside to the transmitter in a position that

represents 0 elevation. The rotator could then rotate the array so that elements 1,

74

Mounting Bracket

Antennas Facing in +y

Roll Head Positioner

y

xz

θ = 0

ψ = 0

(a) Azimuth = 0

Mounting Bracket

Antennas Facing in -x (broadside to transmitter)

Roll Head Positioner

y

x

z

5

8

6

7

1

2

3

4

θ = 90

ψ = 0

(b) Azimuth = 90

Mounting Bracket

Antennas Facing in -y

Roll Head Positioner

y

xz

θ = 180

ψ = 0

(c) Azimuth = 180

Figure 42: Azimuthal Rotations.

Mounting BracketAntennas Facing in +z

Roll Head Positioner

y

xz

θ = 90

ψ = −90

(a) Elevation = -90

Mounting Bracket

Antennas Facing in -x (broadside to transmitter)

Roll Head Positioner

y

x

z

5

8

6

7

1

2

3

4

θ = 90

ψ = 0

(b) Elevation = 0

Mounting Bracket Antennas Facing in -z

Roll Head Positioner

y

xz

θ = 90

ψ = +90

(c) Elevation = 90

Figure 43: Elevation Rotations.

75

2, 3, and 4 continued to move farther away from the transmitter and elements 5, 6, 7,

and 8 moved closer towards the transmitter. Fig. 43(c) shows the antennas facing in

the -z direction with roll head positioner behind the antenna array. Antenna elements

5, 6, 7, and 8 are closest to the transmitter in this configuration and the elevation

angle is 90.

All of the described rotations can be used to acquire complex antenna voltage

responses at specific azimuths and elevations. The elevations were restricted to a

range somewhat smaller than −90 to 90. The exact usable range of elevation data

was not determined for the testing. This thesis uses only 0 elevation measurements

for analysis. Azimuth was varied over the desired range of 0 to 180.

5.3.2 Mounting Bracket

The mount that was designed to hold the prototype antenna arrays and attach to

the roll head positioner was made out of Delrin R© acetal resin. This material is very

strong and rigid. It also had the ability to be machined to very precise tolerances.

The mount needed to be precisely manufactured to ensure that the axes of rotation

provided by the roll head and base rotator were maintained when the antenna was

attached to the positioning system. Delrin R© acetal resin has a dielectric constant,

εr, of roughly 3.5 around room temperature. With this dielectric constant, it was

expected that the mounting structure would have negligible effects on the antenna

responses. Fig. 44 shows one of the prototype antenna arrays in the mounting bracket.

5.3.3 Polarization

The transmit antenna in the anechoic chamber is a traditional horn antenna. The

horn antenna can easily provide vertical or horizontal polarization depending on its

orientation. Horizontal polarization from the horn antenna was actually vertical po-

larization when incident upon the mounted antenna array. This was because the

76

Figure 44: Mounting Bracket with Prototype Antenna.

antenna array was mounted on its side as in Fig. 41. Similarly, vertical polariza-

tion from the horn antenna corresponded to horizontal polarization incident upon

the antenna array.

5.4 Testing Results

Each prototype array was placed in the anechoic chamber and complex array mani-

fold data were collected. All data analyzed in this thesis focuses on vertical polariza-

tion and 0 elevation. Azimuth data for all elements was collected from 0 to 180.

The identical characterization analysis used on the modeled data was used for the

measured data. However, the measured data did not require any transformations to

properly align the data because the antenna arrays were oriented and rotated properly

to acquire the correct azimuth, elevation, and polarization data.

77

5.4.1 Square Spiral Prototype Array Testing

The array consisting of the square spiral elements was tested first. The measured

data simply showed relative magnitude changes based on the reference signal in the

anechoic chamber measurement system. Therefore, the measured and modeled data

were not referenced to the same values. To better compare the sets of data, both the

measured and modeled magnitude data were normalized by the largest magnitude

response in each of the data sets. This forced the maximum magnitude value to

be 0 dB. The true gain of the antennas was not investigated here. Also, the phase

responses were referenced to a common phase position. This allowed the phase data

to align better for both sets of data.

Fig. 45 shows the measured complex response data for all elements in the array

for a frequency of 1920 MHz. Fig. 46 shows the modeled complex response data for

all elements in the array at the same frequency of 1920 MHz. The magnitude values

for all elements track very well for the measured and modeled data. While the peaks

and nulls in the patterns do not line up perfectly, the same overall characteristics can

be observed for all antenna elements.

The antenna elements on the edges of the array seem to have degraded perfor-

mance. These elements include broadside elements 1 and 8 and endfire elements 4

and 5. The broadside elements seem to have a weaker broadside peaks and the endfire

elements seem to have shallower broadside nulls. This is probably due to the rotation

of the individual antenna elements. This degradation in performance compared to

the other antennas may be advantageous in providing more unique responses to all

antenna elements. It can be clearly seen in both the models and the measured data

that all antenna elements provide unique patterns.

It was found that aligning measured and modeled phase information can be a

difficult task. However, a comparison of the measured and modeled data does show

that the trends of each antenna elements phase data do track fairly well. The differ-

78

0 20 40 60 80 100 120 140 160 180

−40

−30

−20

−10

0

Mag

nitu

de (

dB)

0 20 40 60 80 100 120 140 160 180

−200

−100

0

100

200

Pha

se (

degr

ees)

Azimuth (degrees)

Element 1Element 2Element 3Element 4Element 5Element 6Element 7Element 8

Figure 45: Normalized Measured Complex Patterns of Square Spiral Array Elements.

0 20 40 60 80 100 120 140 160 180

−40

−30

−20

−10

0

Mag

nitu

de (

dB)

0 20 40 60 80 100 120 140 160 180

−200

−100

0

100

200

Pha

se (

degr

ees)

Azimuth (degrees)

Element 1Element 2Element 3Element 4Element 5Element 6Element 7Element 8

Figure 46: Normalized Modeled Complex Patterns of Square Spiral Array Elements.

79

1700 1750 1800 1850 1900 1950 2000 2050 2100

0

10

20

RM

S B

W (

degr

ees)

1700 1750 1800 1850 1900 1950 2000 2050 2100

0

0.5

1

Max

Sid

elob

e Le

vel

1700 1750 1800 1850 1900 1950 2000 2050 2100

0

2

4

Frequency (MHz)

RM

S D

F E

rror

(de

gree

s)

ModeledMeasured

Figure 47: Measured and Modeled Square Spiral Array Manifold Characterization.

ences in the phase values can possibly be attributed to anechoic chamber not rotating

the antennas perfectly around the azimuthal rotation axis. It was not expected that

the phase information would align perfectly. These phase results lined up with the

models better than expected.

The complex response data was assembled into proper array manifold data and

analyzed. The three main plots for the measured data overlaid on the modeled data

can be seen in Fig. 47. With the complex response patterns being similar, it was

expected that the DF performance parameters would also align well with the modeled

results.

The measured RMS beamwidth values were extremely similar to those found in

the models. The beamwidth values remain around 10 across the entire band in

both sets of data. The measured data does contain slightly more deviation than the

80

modeled data around 1850 MHz and 2040 MHz.

The maximum sidelobe levels are similar up until roughly 2050 MHz. The mea-

sured data shows much higher levels at the end of the band. The sidelobe levels are

higher but they still remain under a value of 1 which means that no true ambiguities

are present.

The RMS DF error estimates for both sets of data line up extremely well. It can

be seen that the Monte Carlo estimate stays around 1.5 across the entire band for

both sets of data. This is the most important result. It ultimately shows that this

array geometry and design can be used with a correlation algorithm and that the

modeled array manifold data accurately predicted real world performance.

5.4.2 E Patch Prototype Array Testing

An identical measurement and analysis process was performed on the E patch array.

Fig. 48 shows the measured complex response data for all elements in the array at

2440 MHz. Fig. 49 shows the modeled complex response data for all elements in the

array at 2440 MHz. Again, the plots showing the magnitude of the response patterns

were normalized and the phases were referenced to a common value.

The magnitude response of the measured and modeled data match extremely well.

It can be seen that all elements provide nearly identical broadside response patterns.

The only difference between the measured and modeled data is that the measured

data seems to show just a slightly narrower broadside peak.

The most impressive result is how well the phase data line up for the measured and

modeled data. The small errors in the phase measurements are probably attributed

to a slight wobble in the azimuthal axis of rotation in the anechoic chamber. This

wobble may have come from the mount being built slightly imprecise or the roll head

positioner not rotating perfectly about its axis. It should be noted that all phases

are equal at an azimuth of 90. This makes sense when thinking about a plane wave

81

0 20 40 60 80 100 120 140 160 180

−40

−30

−20

−10

0

Mag

nitu

de (

dB)

0 20 40 60 80 100 120 140 160 180

−200

−100

0

100

200

Pha

se (

degr

ees)

Azimuth (degrees)

Element 1Element 2Element 3Element 4Element 5Element 6Element 7Element 8

Figure 48: Normalized Measured Complex Patterns of E Patch Array Elements.

0 20 40 60 80 100 120 140 160 180

−40

−30

−20

−10

0

Mag

nitu

de (

dB)

0 20 40 60 80 100 120 140 160 180

−200

−100

0

100

200

Pha

se (

degr

ees)

Azimuth (degrees)

Element 1Element 2Element 3Element 4Element 5Element 6Element 7Element 8

Figure 49: Normalized Modeled Complex Patterns of E Patch Array Elements.

82

2200 2300 2400 2500 2600 2700 2800

0

10

20

RM

S B

W (

degr

ees)

2200 2300 2400 2500 2600 2700 2800

0

0.5

1

Max

Sid

elob

e Le

vel

2200 2300 2400 2500 2600 2700 2800

0

2

4

Frequency (MHz)

RM

S D

F E

rror

(de

gree

s)

ModeledMeasured

Figure 50: Measured and Modeled E Patch Array Manifold Characterization.

impinging upon all antenna elements at a broadside direction of 90 azimuth. All

antenna elements should be receiving an in phase signal in this case. The measured

and modeled data confirm that this array is operating properly.

The complex response data was then assembled into proper array manifold data

and analyzed. The three main plots can be seen in Fig. 50. With the extremely

similar measured and modeled complex response data, it was expected that the DF

performance would again be very similar to the modeled performance.

The measured RMS beamwidth values follow the same trend as the modeled data.

However, the beamwidths seem to be just slightly lower across the entire band. Also,

the measured data seems to show some small ripple in the data unlike the smooth

curve given by the modeled data.

The maximum sidelobe level shows the most deviation from the modeled results.

83

The measured data are most definitely not as smooth as the modeled. Also, the

measured data shows much higher side lobe levels especially at the end of the band.

Although the sidelobe levels are higher, they are still well below a value of 1 and

should not affect the DF performance estimates.

The RMS DF error estimates using the Monte Carlo analysis are found to be lower

in the measured data set than the modeled data set. The differences are slight and

they both agree that the RMS DF error across the array should be 2 or less. It is

not seen as a problem that the measured data gives even better performance than

the modeled data. It would be cause for questioning if the reverse was true.

5.5 Testing Conclusions

This testing showed that the anechoic chamber utilized is capable of providing ac-

curate complex response data. The magnitude and phase response data for both

arrays matches very well between measured and modeled data. This is required to

investigate array manifold information and to perform subsequent DF performance

analysis.

With accurate complex response data, it was found that the prototype antenna

arrays could provide expected or better than expected DF performance. This shows

the prototypes were manufactured very similar to the manner that they were built in

the numerical models. It also confirms that both the equally spaced pattern diverse

array and the unequally spaced identical pattern array could provide array manifold

diversity for use in a correlation DF algorithm. The testing was a great success

in proving prototype performance as well as building confidence in the numerical

modeling and design methodology.

84

6 Conclusions

The goal of this research was to investigate planar antenna array designs for use on a

mobile platform that could work with a correlation direction finding algorithm. Two

different antenna array designs were proposed. The antenna arrays were modeled,

prototyped, and tested. Analysis was performed to investigate matching characteris-

tics and potential direction finding performance.

The research has proved that both design methodologies can be used with a corre-

lation direction finding algorithm. The equally spaced pattern diverse array and the

unequally spaced identical pattern array provide diverse array manifold data. Anal-

ysis of the antenna arrays showed that they are both capable of under 2 of RMS

DF error. In other words, both arrays have the potential to determine the DOA of a

signal with an error under 2.

When comparing both array designs, the modeled and measured potential DF

performance is very similar. However, the unequally spaced identical pattern array

made out of the E patch elements provides better matching characteristics. The E

patch elements provide S11 values that are much lower across their band of inter-

est than do the broadside and endfire square spiral type elements. Also, the array

made of the E patch elements is overall a simpler design than the array made of the

square spiral elements. The E elements are all identical and oriented in the same

direction unlike the square spiral elements which are not identical and are rotated

to provide different orientations. Therefore, it can be concluded that the unequally

spaced identical pattern array made out of the E patch elements is the better design.

Through the design process it was found that the numerical models developed

using FEKO gave extremely accurate results when compared to measured data.

The measured and modeled complex antenna response data for both antenna arrays

matched up very well. This agreement gave confidence that the models and proto-

types were working as expected. This agreement also shows that numerical modeling

85

can be efficiently used to design and investigate antenna arrays for direction finding

applications.

The testing process showed that magnitude and phase of antenna responses could

be measured in the anechoic chamber that was used. Very often only the magnitude

of an antenna response is desired with antenna measurements. However, the com-

plex response data is required for use with a correlation direction finding algorithm.

The accurate phase results are impressive considering the rotations and mounting

structure that were required to take the measurements.

Future work may be to investigate the use of a combined approach. That is using

different antenna response patterns with unequal spacing. Some form of optimization

may be used to find the best mix of pattern and spacing diversity to further drive

down the potential RMS DF error. Other work may be focused on exploring how an

antenna array such as these may be designed to work with multiple systems. It may

be possible to have these arrays work with communication systems or radar systems

that my share a common frequency band. It is also of interest to investigate how to

make these arrays operate over a wider band. New antenna elements or array designs

may provide a wider frequency range of operation.

86

A Adding Normally Distributed Noise to an Ar-

ray Manifold

Often it is advantageous to add normally distributed noise to an array manifold

for analysis purposes. The goal is to create a desired signal-to-noise ratio (SNR).

The signal in this case refers to the ideal array manifold. Signal-to-noise ratio is by

definition a relation of power quantities in watts. It is shown in eq. (13) in linear

units and in decibel form in eq. (14).

SNR =Psignal [W ]

Pnoise [W ](13)

SNR [dB] = 10log10(SNR) (14)

A(θ) is the symbol used for the array manifold. The array manifold considered here is

simply the two dimensional N x M array where N is the number of antenna elements

and M is the number of azimuthal increments. Each entry in the array manifold

is a complex voltage response an(θm) where n is the antenna element number and

m is the azimuthal increment number of the specific entry. The n corresponds to

the row number and the m corresponds to the column number. A noise array will

be defined as N(θ) and will have the same dimensions as the array manifold. Each

entry in the noise array is of the same form as that of the array manifold and are

designated by nn(θm). The desired process is to modify the noise array to correspond

to the appropriate amount of noise given by the SNR and add the noise to the array

manifold to ultimately create a noisy array manifold that will be represented by

NA(θ) . Since the array manifold and noise array contain voltage values, the SNR

must be given in a voltage form to appropriately modify the amount of additive

noise. The SNR value in decibels shown in eq. (14) can be converted to a linear

87

voltage quantity using eq. (15) and can be referred to as the voltage signal to noise

ratio (VSNR).

VSNR = 10SNR [dB]

20 (15)

With the desired VSNR, the desired process is to modify the noise array by the VSNR

and add the noise to the array manifold. This is shown in eq. (16).

NA(θ) =1

VSNRN(θ) + A(θ) (16)

While eq. (16) shows the desired process, this equation cannot simply be implemented

as shown. Before this process can be implemented properly the array manifold and

noise array must be normalized to the same scale. With both the noise array and

array manifold of the same scaling, the appropriate VSNR can then be applied. Let

us first start with the array manifold A(θ). The objective is to make each column in

the array manifold have a total power of one. The total power in a column is defined

as the inner product of the column with the conjugate transpose of itself. First the

norm of the column must be found. The norm of a vector is in general defined in

eq. (17) for an arbitrary one dimensional complex vector x.

||x|| =√x†x (17)

Equation (17) shows that for a given column the norm is defined by the square root

of the inner product of the column with the conjugate transpose of itself. Then each

entry in the column must be divided by the norm value. This will ensure that the

inner product of the column with the conjugate transpose of itself will equal one.

Thus achieving the goal of making the total power in each column equal to one. This

process must be done to each column in the array manifold. The array manifold

A(θ) will now be rewritten as A′(θ) where now each element in each column has been

88

divided by its respective norm value.

Now a similar process must be performed on the noise array. Each entry in the

noise array is a complex valued voltage. Each entry is defined by nn(θm) where n

is the antenna element number and m is the azimuthal increment number of the

specific entry. The n corresponds to the row number and the m corresponds to the

column number. Each entry is a complex value of the form x+ jy where x and y are

normally distributed real random variables. The norm value obtained by taking the

square root of the inner product of a column with the conjugate transpose of itself

will give on average a value of√

2N . This result is obtained because the complex

values in the column are made up of two real quanties, x and y, of which both are

normally distributed random variables and because there are N entries in the column.

Therefore, to make the average power of each column equal to one, each entry in each

column must be divided by√

2N . This is the same division process as used in the

array manifold except in this case all columns on average will have the same norm of√

2N . This modification of each entry in each column will ensure that each column

has a total power equal to one. The noise array N(θ) will now be rewritten as N′(θ)

to represent that all rows have been appropriately modified.

Now both the array manifold and noise array are of the same scale and can be

appropriately modified to achieve a desired SNR. The desired SNR in decibels is first

modified to a VSNR as in eq. (15). Then the noisy array manifold NA′(θ) can be

made properly using eq. (18). The noisy array manifold has the symbol of NA′(θ) to

show that its constituents are in a normalized form.

NA′(θ) =1

VSNRN′(θ) + A′(θ) (18)

If it is desired the norm values used for division to create the A′(θ) can be used to

un-normalize the noisy array manifold. Un-normalization will give a result with each

entry having a similar magnitude to the original A(θ) but with the correct amount

89

of additive noise.

90

B Spherical to Planar Wavefront Conversion

y

x

TX

Planar Wavefront

Spherical Wavefront

xpath

R1r

R

y

r cosφ

φ

R

Figure 51: Spherical to Planar Wavefront Diagram.

A simple technique was investigated to take perfectly spherical wavefronts and turn

them into perfectly planar wavefronts. The technique was developed to transform

the phase path of a spherical wavefront to the phase path of a planar wavefront. The

setup is shown in Fig. 51. Table 3 describes all variables in Fig. 51.

The main goal is to develop an equation for 4R. A general equation for 4R

would allow the path length difference from any point on the spherical wavefront to

the planar wavefront to be determined. To start the derivation a few terms can be

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Table 3: Symbols and Descriptions for Spherical to Planar Wavefront Diagram.

Symbol Description Unitsxpath path length of spherical wavefront from transmitter meters (m)R distance of transmitter from origin meters (m)R1 distance from transmitter to point on planar wavefront meters (m)4R difference in distance from planar wavefront to spherical wavefront in straight line from transmitter meters (m)r radial distance from origin to point of interest on planar wavefront meters (m)y perpendicular distance from x axis to point of interest on plane wavefront meters (m)φ angle from x axis to radial distance line degrees ()

further defined by using information from the diagram in Fig 51. First x can be

defined as in eq. (19).

x = R− r cos θ (19)

Then y can be defined.

y = R− r cos θ (20)

R1 can be defined.

R1 =√x2 + y2 (21)

From the diagram in Fig. 51, 4R can be defined.

4R = R1 − x (22)

Now substituting eqs. (19) and (21) into eq. (22) gives the following.

4R =√x2 + y2 −R− r cosφ (23)

This can further be rewritten by substituting eqs. (19) and (20) into eq. (23).

4R =√

(R− r cosφ)2 + r2 sin2 φ−R− r cosφ (24)

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The final equation for 4R shown in eq. (24) is the final phase correction for the

phase path difference for any point on a spherical wavefront to a planar wavefront.

The phase path distance is now converted to a phase difference in radians, 4θrad, in

the following equations. f represents frequency in units of Hz and c is the speed of

light in units of ms

.

4θrad =2π4Rλ

(25)

4θrad =2π4Rf

c(26)

The phase path difference can be written in degrees, 4θdeg, as well.

4θdeg =2π4R180

λπ(27)

4θdeg =2π4Rf180

cπ(28)

With the phase correction factor in units of radians as shown in eqs. (25) and (26),

eq. (29) shows the process to correct an array manifold, Aspherical(θ) containing spher-

ical wavefront phase information to an array manifold containing planar wavefront

phase information Aplanar(θ). Both Aspherical(θ) and Aplanar(θ) are considered here

to be N x M arrays where N corresponds to antenna element number and M corre-

sponds to azimuthal increments. Each entry in the arrays is a complex valued voltage

response. It should be noted here that no correction is being performed for amplitude

of the wavefronts. For the situation considered here, it was assumed that the differ-

ences in amplitude between the wavefronts would be negligible and therefore was not

addressed.

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Aplanar(θ) = ej4θradAspherical(θ) (29)

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References

[1] Antenna engineering handbook. New York: McGraw-Hill, 2007.

[2] P. J. D. Gething, Radio direction finding and superresolution / P.J.D. Gething,

2nd ed. Peter Peregrinus, London, 1991.

[3] M. Zahn, Electromagnetic field theory : a problem solving approach. Malabar,

Fla: R.F. Krieger, 1987.

[4] Encyclopedia of RF and microwave engineering. Hoboken, N.J: Wiley-

Interscience, 2005.

[5] G. Huff, J. Feng, S. Zhang, and J. Bernhard, “A novel radiation pattern and

frequency reconfigurable single turn square spiral microstrip antenna,” IEEE Mi-

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[6] G. Huff and J. Bernhard, “Integration of packaged rf mems switches with radiation

pattern reconfigurable square spiral microstrip antennas,” IEEE Transactions on

Antennas and Propagation, vol. 54, no. 2, pp. 464 – 469, Feb. 2006.

[7] F. Yang, X.-X. Zhang, X. Ye, and Y. Rahmat-Samii, “Wide-band e-shaped patch

antennas for wireless communications,” IEEE Transactions on Antennas and

Propagation, vol. 49, no. 7, pp. 1094 –1100, Jul. 2001.

[8] R. Soerens, J. Aubin, M. Winebrand, L. Foged, and J. Miller, “Methods for ane-

choic chamber certification at vhf/uhf frequencies,” in 2011 IEEE International

Symposium on Antennas and Propagation (APSURSI), Jul. 2011, pp. 3117 –3120.

[9] C. A. Balanis, Antenna Theory: Analysis and Design. Hoboken, NJ: John Wiley

& Sons, Inc., 2005.

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