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 Fulfillment of 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. Narayanan Professor of Electrical Engineering Thesis Advisor

Timothy J. Kane Professor of Electrical Engineering

Keith A. Lysiak ARL Mentor

Kultegin Aydin Professor of Electrical Engineering Head 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 1 1.1 Direction Finding ...... 1 1.2 Direction Finding Systems for Mobile Platforms ...... 2 1.3 Thesis Overview ...... 3

2 Background 4 2.1 Practical Applications ...... 4 2.2 Brief Historical Development ...... 5 2.3 Common DF Considerations ...... 6 2.3.1 Coordinate Systems ...... 6 2.3.2 System Design ...... 8 2.3.3 Sources of Error ...... 9 2.4 Practical Correlation Direction Finding Method ...... 10 2.4.1 Array Manifold ...... 10 2.4.2 Correlation ...... 12 2.4.3 Characterization of DF Antenna Arrays for Correlation Algorithm 13 2.5 Properties of Direction Finding Antenna Arrays for Correlation DF Algorithm ...... 20

3 Antenna Design and Modeling 23 3.1 Design Considerations ...... 23 3.1.1 Size Constraints ...... 23 3.1.2 Manufacturing ...... 24 3.1.3 Array Manifold Diversity ...... 24 3.2 Equally Spaced Pattern Diverse Array ...... 25 3.2.1 Square Spiral Antenna Elements ...... 25 3.2.2 Array Layout ...... 26 3.2.3 FEKO Modeling of Square Spiral Array ...... 29 3.3 Unequal Spaced Identical Pattern Array ...... 38 3.3.1 E Patch Antenna Elements ...... 38 3.3.2 Array Layout ...... 39 3.3.3 FEKO Modeling of E Patch Array ...... 40 3.4 Modeling Conclusions ...... 47

4 Antenna Prototyping 49 4.1 Prototype Manufacturing ...... 49 4.2 Square Spiral Array Prototype ...... 50 4.3 E Patch Array Prototype ...... 51

iv 4.4 Prototyping Conclusions ...... 56

5 Antenna Testing 62 5.1 Considerations for Measuring Array Manifolds ...... 62 5.2 Anechoic Chamber ...... 63 5.2.1 Chamber Properties ...... 63 5.2.2 Antenna Positioning System ...... 66 5.2.3 Measurement System ...... 67 5.3 Collecting Array Manifold Data in Anechoic Chamber ...... 71 5.3.1 Prototype Antenna Rotations ...... 71 5.3.2 Mounting Bracket ...... 76 5.3.3 Polarization ...... 76 5.4 Testing Results ...... 77 5.4.1 Square Spiral Prototype Array Testing ...... 78 5.4.2 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...... 6 2 Modified Coordinate System for Direction Finding Systems...... 7 3 Block Diagram of a DF System...... 8 4 Array Manifold...... 11 5 1D Voltage Array and 2D Array Manifold...... 12 6 Correlation Plot with Strong Peak...... 16 7 Correlation Plot with Ambiguity...... 16 8 Desired Array Manifold Auto-correlation Example...... 18 9 Ambiguous Array Manifold Auto-correlation Example...... 18 10 Generic DF Array Layout...... 23 11 Reconfigurable Square Spiral...... 26 12 Endfire and Broadside Elements...... 27 13 Endfire and Broadside Element Patterns...... 27 14 Square Spiral Array Layout...... 28 15 Square Spiral Array Element Impedances...... 34 16 FEKO Simulation Coordinate System...... 35 17 Transformed FEKO Coordinates into DF Coordinates...... 35 18 Normalized Complex Patterns of Square Spiral Array Elements. . . . 37 19 Square Spiral Array Manifold Characterization...... 37 20 E Patch...... 38 21 E Patch Pattern...... 39 22 E Patch Array Layout...... 40 23 E Patch Array Element Impedances...... 45 24 Normalized Complex Patterns of E Array Elements...... 46 25 E Array Manifold Characterization...... 46 26 Layers of Prototype Antennas...... 49 27 Radome Over All Layers of Antenna Structure...... 49 28 Underside of Ground Plane with SMA Connectors...... 49 29 Square Spiral Array Prototype...... 51 30 Square Spiral Array Element Impedances...... 55 31 E Patch Array Prototype...... 56 32 E Patch Array Element Impedances...... 60 33 Cross Section of Anechoic Chamber...... 64 34 Wavefronts in Anechoic Chamber...... 65 35 Antenna Positioning System...... 68 36 Antenna Positioning System Base Features...... 69 37 Roll Head Positioner on Top of Boom...... 69 38 Electronic Motions of Antenna Positioner Looking from Transmit An- tenna...... 70 39 Data Collection System...... 71 40 Prototype Antenna Array Coordinates Defined...... 72 41 Antenna Positioning System Orientation...... 73 42 Azimuthal Rotations...... 75

vi 43 Elevation Rotations...... 75 44 Mounting Bracket with Prototype Antenna...... 77 45 Normalized Measured Complex Patterns of Square Spiral Array Ele- ments...... 79 46 Normalized Modeled Complex Patterns of Square Spiral Array Elements. 79 47 Measured and Modeled Square Spiral Array Manifold Characterization. 80 48 Normalized Measured Complex Patterns of E Patch Array Elements. 82 49 Normalized Modeled Complex Patterns of E Patch Array Elements. . 82 50 Measured and Modeled E Patch Array Manifold Characterization. . . 83 51 Spherical to Planar Wavefront Diagram...... 91

vii List of Tables

1 Square Spiral Array Antenna Positions and Pattern Descriptions. . . 28 2 E Patch Array Antenna Positions and Pattern Descriptions...... 40 3 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 z

θ = 0◦

φ = 180◦

φ = 270◦ φ = 90◦ y

x φ = 0◦

θ = 90◦

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 z

EL = +90◦

AZ = 180◦ South Rear of Platform

AZ = 90◦ AZ = 270◦ East x-y plane y West Right of Platform EL = 0◦ Left of Platform

x AZ = 0◦ North Front of Platform

EL = 90◦ − 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 1

2

Distribution System ADC DF Processor Display

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 Frequencies

Azimuthal Increments

a1(θ0) a1(θ1) a1(θ2) ... a1(θM )

a2(θ0) a2(θ1) a2(θ2) ... a2(θM )

a3(θ0) a3(θ1) a3(θ2) ... a3(θM ) A(θ) = . . . . . Antenna Elements ......

aN (θ0) aN (θ1) aN (θ2) ... aN (θM )

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 Azimuthal Increments

v1(θm) a1(θ0) a1(θ1) a1(θ2) ... a1(θM )

v2(θm) a2(θ0) a2(θ1) a2(θ2) ... a2(θM )

v3(θm) a3(θ0) a3(θ1) a3(θ2) ... a3(θM ) V(θ) = . A(θ) = . . . . . Antenna Elements ......

vN (θm) aN (θ0) aN (θ1) aN (θ2) ... aN (θM )

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 A0(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 S0(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) = S0(θ)†A0(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 1

0.9

0.8

0.7

0.6

2 0.5 |R|

0.4

0.3

0.2

0.1

0 0 20 40 60 80 100 120 140 160 180 Azimuth (degrees) Figure 6: Correlation Plot with Strong Peak.

1

0.9

0.8

0.7

0.6

2 0.5 |R|

0.4

0.3

0.2

0.1

0 0 20 40 60 80 100 120 140 160 180 Azimuth (degrees) 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) = A0(θ)†A0(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 1

20 0.9

0.8 40

0.7 60

0.6 80 0.5

100 0.4 Angle of Arrival (degrees) 120 0.3

140 0.2

160 0.1

0 20 40 60 80 100 120 140 160 Azimuth (degrees) Figure 8: Desired Array Manifold Auto-correlation Example.

0 1

20 0.9

0.8 40

0.7 60

0.6 80 0.5 100 0.4

Angle of Arrival (degrees) 120 0.3

140 0.2

160 0.1

180 0 0 20 40 60 80 100 120 140 160 180 Azimuth (degrees) 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 NA0(θ) where the prime symbol again symbolizes that each column in the manifold has been normalized. The result of correlating the standard array manifold, A0(θ), with the noisy array manifold, NA0(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) = NA0(θ)†A0(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.

545 mm

5 6 7 8

310 mm

1 2 3 4

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, r, 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 0.2393λ0

0.1937λ0

Via to Ground Plane

SMA Probe Feed

0.3418λ0

0.4395λ0 0.3874λ0

0.0223λ0

0.1367λ0 0.1937λ0

0.3874λ0 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 0.1937λ0

SMA Probe Feed

0.3418λ0 SMA Probe Feed

0.3418λ0 0.4395λ0 0.3874λ0

0.3874λ0

0.0223λ0

0.0223λ0

0.3874λ0

0.1367λ0 (a) Endfire (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 z Top of Platform y

5 6 7 8

θ = 180 θ = 0 ◦ x ◦ Rear of Platform Front of Platform

1 2 3 4

Bottom of Platform θ = 90◦ 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) mm 1 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, r, 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 0 FEKO

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Figure 15: Square Spiral Array Element Impedances.

34 FEKO Far Field Pattern Cut z

φ = 0◦

θ = 90◦ to θ = 90◦ −

y

φ Polarization

x θ Polarization

Figure 16: FEKO Simulation Coordinate System.

DF Far Field Pattern Cut z

AZ = 180◦ to AZ = 0◦

EL = 0◦

y

x θ Polarization

φ Polarization

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

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0 20 40 60 80 100 120 140 160 180

200 Element 1 Element 2 100 Element 3 Element 4 Element 5 0 Element 6 Element 7 Element 8

Phase (degrees) −100

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20

10

RMS BW (degrees) 0 1700 1750 1800 1850 1900 1950 2000 2050 2100

1

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37 0.5059λ0

0.1009λ0

0.2800λ0 0.3625λ0

0.0434λ0

0.0434λ0

0.1592λ0 0.1592λ0 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

λ elements are essentially 2 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 z Top of Platform y

5 6 7 8

θ = 180 θ = 0 ◦ x ◦ Rear of Platform 1 2 3 4 Front of Platform

Bottom of Platform θ = 90◦ 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) mm 1 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,

r, 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 0 FEKO

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45 0

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0 20 40 60 80 100 120 140 160 180

200 Element 1 Element 2 100 Element 3 Element 4 Element 5 0 Element 6 Element 7 Element 8

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20

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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.

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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 0 Agilent N9330A Antenna Tester Agilent E8364B PNA Network Analyzer FEKO −5

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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 20’ - 0” 100’ - 0”

Storage Room

56’ - 0”

12’ Diameter Cylindrical Quiet Zone Control Room 40’ - 0” Transmit Antenna AUT Staging 20’ - 0” Room

Rail System 56’ - 0”

Figure 33: Cross Section of Anechoic Chamber. d, is greater than or equal to the value shown in eq. (8).

2D2 d = (8) λ0

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 △ Constant Phase Wavefronts

dmax

w 0.5m ≈

Transmit Antenna

Planar Antenna Array

d 24m min ≈ 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 d. The first step was 4 calculating the value of dmax using the Pythagorean theorem. This value was found using eq. (9).

r w d = d2 + ( )2 (9) max min 2

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

65 d = dmax dmin (10) 4 −

The path length difference, d, was then changed into a phase path value with units 4 of radians in eq. (11).

2π θrad = d (11) 4 4 λ0

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).

180 θdeg = θrad (12) 4 4 π

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 Move Boom Back and Forth

Rotate Boom Around Vertical Axis Raise / Lower Boom

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

Control Computer

Transmit Antenna AUT 10 Way Switch

b2 RF Switch Box Source and Couplers Microwave Receiver S = b2 21 a1

a1

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 z

Top of Platform y

5 6 7 8

θ = 180 θ = 0 ◦ x ◦ Rear of Platform 1 2 3 4 Front of Platform

Bottom of Platform θ = 90◦

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 Axis of Rotation

Prototype Array

Mounting Bracket 8 4 7 x 3 Azimuthal Axis of Rotation Roll Head Positioner z 6 2 5 1

y Azimuthal Rotation

Elevation Rotation

Hand Crank Rotator

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 θ = 0◦ θ = 90◦

ψ = 0◦ ψ = 0◦ Antennas Facing in -x (broadside to transmitter)

Mounting Bracket Mounting Bracket 8 4 x z Roll Head Positioner 7 x 3 Roll Head Positioner z 6 2 5 1

y y Antennas Facing in +y

(a) Azimuth = 0◦ (b) Azimuth = 90◦

θ = 180◦ Antennas Facing in -y

ψ = 0◦

Mounting Bracket

x z Roll Head Positioner

y

(c) Azimuth = 180◦

Figure 42: Azimuthal Rotations.

θ = 90◦

ψ = 90◦ −

θ = 90◦

ψ = 0◦ Antennas Facing in -x (broadside to transmitter) Antennas Facing in +z Mounting Bracket

x Mounting Bracket 8 4 z Roll Head Positioner 7 x 3 Roll Head Positioner z 6 2 5 1 y y

(a) Elevation = -90◦ (b) Elevation = 0◦

θ = 90◦

ψ = +90◦

Mounting Bracket Antennas Facing in -z

x z Roll Head Positioner

y

(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,

r, 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

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79 20

10

RMS BW (degrees) 0 1700 1750 1800 1850 1900 1950 2000 2050 2100

1

0.5

Max Sidelobe Level 0 1700 1750 1800 1850 1900 1950 2000 2050 2100

4 Modeled Measured 2

0 RMS DF Error (degrees) 1700 1750 1800 1850 1900 1950 2000 2050 2100 Frequency (MHz) 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

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−30 Magnitude (dB)

−40

0 20 40 60 80 100 120 140 160 180

200 Element 1 Element 2 100 Element 3 Element 4 Element 5 0 Element 6 Element 7 Element 8

Phase (degrees) −100

−200 0 20 40 60 80 100 120 140 160 180 Azimuth (degrees) Figure 48: Normalized Measured Complex Patterns of E Patch Array Elements.

0

−10

−20

−30 Magnitude (dB)

−40

0 20 40 60 80 100 120 140 160 180

200 Element 1 Element 2 100 Element 3 Element 4 Element 5 0 Element 6 Element 7 Element 8

Phase (degrees) −100

−200 0 20 40 60 80 100 120 140 160 180 Azimuth (degrees) Figure 49: Normalized Modeled Complex Patterns of E Patch Array Elements.

82 20

10

RMS BW (degrees) 0 2200 2300 2400 2500 2600 2700 2800

1

0.5

Max Sidelobe Level 0 2200 2300 2400 2500 2600 2700 2800

4 Modeled Measured 2

0 RMS DF Error (degrees) 2200 2300 2400 2500 2600 2700 2800 Frequency (MHz) 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).

P [W ] SNR = signal (13) Pnoise [W ]

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).

SNR [dB] VSNR = 10 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).

1 NA(θ) = N(θ) + A(θ) (16) VSNR

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 A0(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 N0(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 NA0(θ) can be made properly using eq. (18). The noisy array manifold has the symbol of NA0(θ) to show that its constituents are in a normalized form.

1 NA0(θ) = N0(θ) + A0(θ) (18) VSNR

If it is desired the norm values used for division to create the A0(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 Planar Wavefront

Spherical Wavefront

xpath

TX r cos φ R

φ x

y

r R1

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 R. A general equation for R 4 4 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

91 Table 3: Symbols and Descriptions for Spherical to Planar Wavefront Diagram.

Symbol Description Units xpath 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) R difference in distance from planar wavefront to spherical wavefront in straight line from transmitter meters (m) 4 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.

p 2 2 R1 = x + y (21)

From the diagram in Fig. 51, R can be defined. 4

R = R1 x (22) 4 −

Now substituting eqs. (19) and (21) into eq. (22) gives the following.

p R = x2 + y2 R r cos φ (23) 4 − −

This can further be rewritten by substituting eqs. (19) and (20) into eq. (23).

q R = (R r cos φ)2 + r2 sin2 φ R r cos φ (24) 4 − − −

92 The final equation for R shown in eq. (24) is the final phase correction for the 4 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, θrad, in 4 the following equations. f represents frequency in units of Hz and c is the speed of

m light in units of s .

2π R θrad = 4 (25) 4 λ

2π Rf θrad = 4 (26) 4 c

The phase path difference can be written in degrees, θdeg, as well. 4

2π R180 θdeg = 4 (27) 4 λπ

2π Rf180 θdeg = 4 (28) 4 cπ

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.

93 j4θrad Aplanar(θ) = e Aspherical(θ) (29)

94 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- crowave and Wireless Components Letters, vol. 13, no. 2, pp. 57 –59, Feb. 2003.

[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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