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© Copyrighted by
Matthew N. Barr
2017
Abstract
Digitally scanned arrays are highly beneficial for use in passive radar systems due to their adaptive beam- and null-steering capabilities, critical for reliable wide area surveillance as well as multi-target tracking. Furthermore, the lack of moving components needed to perform scanning operations reduces long term maintenance costs.
A large, low-cost overlapped subarray architecture was designed, assembled, and characterized using commercial off the shelf antennas. The subarray architecture reduces the number of ADCs required without compromising gain or beamwidth, but limits the maximum achievable scan angle due to grating lobes. To combat this the subarrays are overlapped, thus suppressing grating lobes and sidelobe levels; the increased system scan angle results in wider area surveillance and tracking but also increases resilience to direct signal interference, generally the limiting factor for passive radar performance.
Furthermore, the two-dimensional array enables three-dimensional target localization with azimuth and elevation steering. The final design and mutual coupling analysis is shown here, both which include FEKO® simulations and compact range measurements made at the ElectroScience Laboratory. The final array design exhibits 20.5-22.2 dBi of gain at boresight, a HPBW of 5.5-6.9°, and a maximum scan angle of ± 15-17° in azimuth across its 150 MHz bandwidth.
ii Dedication
For Mom, Dad, and Michael – and their perpetual love and support
iii Acknowledgments
My time at the ElectroScience Laboratory has been one of the most rewarding experiences of my life. I would like to offer a special thanks to my advisors: Chris Baker, for ushering me into graduate school, and Graeme Smith, for providing me with outstanding direction once I arrived there. Furthermore, my first and last electromagnetics professor, Kubilay
Sertel, who introduced me to – and answered countless questions on – the world of electromagnetics has my upmost appreciation. I would also like to thank Eric Martin and
Václav Navrátil for the hours they spent helping me in – and on the roof of – the lab assembling the array.
Most of all, I extend the deepest and sincerest thank you to Landon Garry. For everything.
I could not have asked for a better mentor.
iv Vita
2015 ………………………………………………. Bachelor of Science Electrical and Computer Engineering The Ohio State University
2017 ………………………………………………. Student Research Assistant The Ohio State University ElectroScience Laboratory
Fields of Study
Major Field: Electrical and Computer Engineering
Studies: Electromagnetics Antenna Array Design
v Table of Contents
Page
Abstract ...... ii Dedication ...... iii Acknowledgments...... iv Vita ...... v Table of Contents ...... vi List of Tables ...... viii List of Figures ...... ix Chapter 1: Introduction ...... 1 1.1 Bistatic / Passive Radar ...... 3 1.2 Radar Antenna Arrays ...... 5 1.3 Thesis Layout ...... 8 Chapter 2: Array Theory ...... 9 2.1 Fundamental Principles & Array Factor Development ...... 9 2.2 Characteristics of Arrays ...... 15 Chapter 3: MuTeRa Subarray Design Considerations ...... 19 3.1 Subarray Terminology and Pattern Synthesis ...... 21 3.2 Subarray Pattern Interactions ...... 26 3.3 Subarray Architectures ...... 31 3.3.1 Random and Non-identical Subarray Geometries ...... 33 3.3.2 Non-uniform and Overlapped Subarray Architectures ...... 36 3.3.3 Amplitude Tapering...... 38
vi Chapter 4: Array Design Analysis and Selection ...... 43 4.1 Element Selection & Modeling ...... 44 4.2 Subarray Metrics Analysis ...... 48 4.2.1 Number of Subarray Elements ...... 51 4.2.2 Subarray Spacing ...... 57 4.2.3 Frequency of Operation ...... 64 4.2.4 Amplitude Tapering...... 67 4.3 Final Design Selection ...... 70 Chapter 5: Assembly, Testing & Performance Evaluation ...... 72 5.1 Subarray RF Design ...... 75 5.2 Mechanical Considerations ...... 77 5.3 Mutual Coupling Analysis ...... 81 5.3.1 First Array Level Mutual Coupling ...... 83 5.3.2 Second Array Level Mutual Coupling ...... 86 5.4 Final Array Specifications ...... 87 Chapter 6: Concluding Remarks ...... 90 Bibliography ...... 93
vii List of Tables
Table Page
2.1 Project coordinate system details ...... 11
4.1 DB2e antenna specifications ...... 46
4.2 Final subarray design specifications ...... 71
5.1 RF component specifications ...... 76
5.2 Final assembled array specifications ...... 89
viii List of Figures
Figure Page
2.1 Phase fronts of a plane wave ...... 10
2.2 Project coordinate system ...... 11
2.3 Basic array factor characteristics ...... 15
3.1 Defining the maximum scan angle ...... 21
3.2 Basic subarray architecture ...... 22
3.3 Array level diagrams and pattern multiplication ...... 24
3.4 Final array level diagram for a contiguous subarray ...... 25
3.5 Contiguous subarray patterns with multi-level scanning ...... 27
3.6 Basic subarray architecture excluding phase shifters ...... 29
3.7 Contiguous subarray patterns with single-level scanning ...... 30
3.8 Subarray architecture MSA pattern dependencies ...... 32
3.9 RLA grating lobe suppression analysis...... 34
3.10 Overlapped subarray architecture ...... 36
3.11 ULA windowing analysis ...... 39
ix 3.12 Kaiser window ULA analysis ...... 40
3.13 Subarray windowing analysis ...... 41
4.1 Illustrated DB2e and directional gain data...... 47
4.2 Staggered overlap subarray geometry ...... 50
4.3 Subarray metrics for N=1 DB2e antenna ...... 52
4.4 Subarray metrics for N=2 DB2e antennas ...... 53
4.5 Subarray metrics for N=3 DB2e antennas ...... 53
4.6 N elements per subarray metrics analysis – decreasing MSA case ...... 54
4.7 N elements per subarray metrics analysis – increasing MSA case ...... 55
4.8 Illustration of a single subarray containing two DB2e antennas ...... 56
4.9 Subarray spacing metrics ...... 57
4.10 Subarray spacing metrics analysis ...... 58
4.11 Analysis of the MSA curve peaks from Figure 4.9 – case 1...... 59
4.12 Analysis of the MSA curve peaks from Figure 4.9 – case 2...... 60
4.13 Subarray spacing pattern analysis – increased grating lobe cancellation ...... 61
4.14 Subarray spacing pattern analysis – decreased grating lobe cancellation ...... 62
4.15 Subarray spacing pattern analysis – effects of increasing 훥푁 on the MSA ...... 63
4.16 Subarray metrics at 533 MHz ...... 65
4.17 Subarray metrics at 677 MHz ...... 65
4.18 MSA pattern analysis vs. frequency ...... 66
4.19 Subarray amplitude tapering metrics, where 훥푀=0.75 m ...... 68
x 4.20 Subarray amplitude tapering metrics, where 훥푀=1.0 m ...... 68
4.21 Subarray metrics for M=7 subarrays containing N=2 DB2e antennas ...... 70
5.1 Fully assembled array ...... 73
5.2 Single subarray RF component block diagram ...... 76
5.3 Unistrut® material cross sections utilized in array assembly ...... 79
5.4 Four simulated DB2e antennas – mutual coupling and S-Parameter data ...... 82
5.5 Compact range measurement setups ...... 84
5.6 Azimuth/H-plane single subarray (AF1) pattern comparison ...... 85
5.7 Azimuth/H-plane final array pattern comparison ...... 86
5.8 Principle azimuth final array patterns...... 88
xi Chapter 1: Introduction
The goal of this thesis is to thoroughly present the design and fabrication process of a large electronically scannable subarray antenna for use in a preexisting passive radar system. Currently at The Ohio State University ElectroScience Laboratory (ESL), research is being conducted with the objective of improving passive radar detection and localization techniques. For reasons that will become apparent in the sections that follow, an array is an advantageous choice of antenna for such objectives. The previous array used by the system was a simple uniform linear array (ULA) of bowtie antennas, which has been used to produce robust direction of arrival (DOA) results in azimuth. However, there is a desire to test the performance of a large, reconfigurable planar array to extend detection ranges and enable 3D target localization. Such is the motivation for this project: creating an improved antenna array which can be utilized to enhance the passive radar capabilities and research conducted at the ESL.
Creating an improved antenna array was achieved through the use of a subarray architecture, which allowed the number of elements to be increased without the addition of costly digitization channels. Increasing the number of array elements leads to a higher gain, resulting in an increased target detection range. Control over the radiating characteristics
1 of the array was achieved by manipulating the spacing between each of the subarrays and the elements within them. This allowed the half power beamwidth of the array to be decreased and the array’s scanning capabilities to be maximized, leading to a finer angular localization performance and an increased angular detection range.
Optimizing an array’s radiation pattern can be achieved through the use of amplitude tapers, random and non-identical subarray architectures; it will be shown however, that each of these techniques requires a large number of elements to be effective. Instead, utilizing overlapped subarrays that are staggered in two dimensions increases the area over which the elements can be placed, allowing for greater control over the radiating pattern of the array. Furthermore, staggering the subarrays provides two dimensional scanning that allows for three dimensional target localization.
Utilizing 14 commercial off the shelf antennas1 and an overlapped subarray architecture, an array measuring 4.1 m long and 1.8 m tall was designed and assembled at a cost not exceeding $6,500. The array was then tested and characterized using a combination of anechoic chamber measurements and advanced computational electromagnetic software.
1 Each of the 14 antennas contains 2 bowtie elements – 28 elements in total 2 1.1 Bistatic / Passive Radar
A bistatic radar can be defined as a radar system whose transmitter and receiver are separated by an appreciable distance. While there are several different definitions that attempt to explicitly classify what constitutes an “appreciable distance,” it is generally considered to be one that is large enough to cause the system’s properties to significantly differ from a co-located / monostatic radar system. There are two main classes of bistatic radar systems. The first being those using cooperative transmitters, which are controlled or designed by the system user. The second are those which utilize, or hitchhike off of, a second party transmitter known as a non-cooperative transmitter.
A passive bistatic radar is a system that utilizes preexisting electromagnetic broadcasts that have not been specifically designed for radar applications as the system’s (non- cooperative) transmitter. These transmitters are often referred to as illuminators of opportunity, and are often radio, television, or cellular broadcasts.
Like so many other novel engineering ideas, the origins of bistatic radar can be traced to Nikola Tesla and his ideas on electromagnetic scattering. The earliest bistatic radar measurements were taken in the 1920s by American naval engineers interested in tracking enemy vessels, and in the UK to measure the height of the ionosphere. The technology then rapidly developed over the course of World War II, being utilized in maritime and airborne target detection, notably by the German Klein Heidelberg radar that utilized a British system as its transmitter. The Klein Heidelberg system is considered to be the first use of a radar with a true non-corporative transmitter. It wasn’t until the 1980s and 90s however, that passive bistatic radar utilizing FM and Analog TV transmissions as illuminators of opportunity began to be rigorously investigated. Passive radar research continues to be a 3 subject of interest, with the generally low cost associated with non-corporative hitchhiking and lack of need for a spectrum license making passive radar investigation an ideal topic for university research [1][2].
A basic passive radar consists of two receive components: the reference and surveillance antennas. The reference antenna is directed towards a desired illuminator of opportunity to capture a copy of the transmitted signal, while the surveillance antenna is directed towards a target or region of interest to capture the transmitted signal after it has reflected off of a target. The bistatic radar geometry can then be exploited to estimate a target’s range, Doppler, and/or DOA.
Direction of arrival estimation – and subsequently localization – can be accomplished by carrying out successive bistatic range or Doppler measurements and estimating the receiver look angle and range [2][3], or by utilizing multiple transmitters/receivers through the use of trilateration [4]. An alternative method of DOA estimation and target localization presented in [5] combines elements from the previous two methods through digital signal processing and the use of a single antenna array receiver.
Among the many characteristics that make antenna arrays ideal for radar systems, the null steering capability of an array is one method for combating direct signal interference within a passive radar system. Because target echoes are received while the transmitter is simultaneously broadcasting, the strength of the direct transmitted signal will overwhelm the receiver and severely limit the radars ability to detect the reflected target echoes, which are frequently up to 90 dB weaker than the direct signal transmission [6]. Steering a null in the direction of the transmitter greatly enhances the signal to interference noise ratio, allowing the targets DOA to be estimated from the signal outputs of the individual array
4 elements. The beamforming and null steering capabilities of an electronically steerable array offer the opportunity to improve direct signal interference suppression while maintaining the ability to perform accurate DOA estimation with a single antenna array
[6].
1.2 Radar Antenna Arrays
How a radar interfaces with its surroundings is primarily a function of its antenna performance. One of the most fundamental characteristics of any antenna is how it distributes/collects energy in angular space. Highly directive antennas that concentrate the majority of their energy in one direction are desirable for radar applications, due to the fact that they provide superior angular resolving power. However, if that energy can be pointed in only one general direction, the radar will not be able to effectively perform target detection and tracking, the primary function of many radar systems. Thus, the quality of a radar antenna can be measured by its ability to dynamically direct/collect narrow beams of energy into/from its surrounding environment.
A reflector antenna mounted on a mechanical rotator is a type of antenna configuration that can meet the high directivity and scanning requirements of a radar. Typically a feed horn will radiate towards a large reflector (commonly in the shape of a parabolic dish), which will align the phase fronts of the incident spherical radiation into collimated beams that resemble a plane wave when viewed across the aperture of the reflector. Because the
Fourier transform of a plane wave produces a delta function, it follows that taking the
Fourier transform of the plane wavelike aperture currents of a reflector antenna will result 5 in a highly directive far field pattern. While this is an ideal feature for a radar antenna, the mechanical rotators required for scanning are typically bulky and suffer from relatively slow scanning speeds. In addition, this architecture prohibits persistent surveillance and limits capability due to the prescribed dwell times and constant revisit rates. Furthermore, increasing the size of the antenna to improve its directivity can quickly lead to mechanical problems [7].
An array offers a solution to the mechanical problems that are associated with increasing the electrical length of an antenna to improve its directivity. By combining a series of antenna elements, a discretely sampled version of a much larger antenna can be created. This results in increased directivity without an increase in the physical size of the antenna elements. In general, arrays offer a high bandwidth, extreme scanning/beam agility, and have the largest versatility and level of control of any antenna configuration
[8][7][9]. Furthermore, the absence of moving components and active elements make passive arrays extremely reliable with generally long operational lifetimes [9].
The extreme beam agility of an array is one of its most attractive features for radar applications. Arrays that are scanned electronically can change their direction of maximum radiation roughly six orders of magnitude faster than a mechanically steered system. This allows for “tracking to be established the instant a target is detected”, “single-target tracking accuracies to be obtained against multiple targets”, “dwell times and waveforms to be individually optimized to meet detection and tracking needs”, and enables “sequential detection techniques to be used, significantly increasing detection range” ([9], pg. 129).
Additionally, an array’s capability of digital beamforming is highly beneficial for use in radar systems. Digital beamforming allows for the synthesis of multiple simultaneous
6 beams, which can be used to perform multi-target tracking and increase search speeds over a given area. Furthermore, implementing time delays digitally increases the bandwidth and accuracy of a system by eliminating mispointing that arises from phase shifters and other temperature sensitive analog devices ([9], Ch. 9).
While arrays have many characteristics that are desirable for radar systems, there are several distinct design challenges that cannot be overlooked. These include the formation of grating lobes, electronic scanning induced gain reduction, and the high cost of digitization channels. While the first two of these challenges require specific design attention, the high cost of analog to digital converters (ADCs) can be mitigated through the use of a subarray architecture. A subarray architecture utilizes analog combiners to amalgamate the responses of several elements prior to entering the receiver, effectively reducing the required ratio of ADCs to number of elements. This is a practical way to reduce the cost of an array without suffering any major performance degradation, and is specifically useful when working with preexisting radar systems where the addition of digitization channels is not possible.
7 1.3 Thesis Layout
An overview of the work presented in this thesis, an introduction to bistatic/passive radar and radar antenna arrays, was presented in the preceding sections. Chapter 2 provides the basic array theory relevant to this project. It is in this chapter that a global coordinate system is defined and a mathematical development of the array factor presented. The chapter concludes with the prevalent terminology and characteristics used in the analysis of arrays.
Chapter 3 begins with the project’s specific design goals and relevant information on the radar system for which the array is being designed. Then the theory and associated terminology of subarrays are presented. The chapter finishes with a description of several subarray optimization techniques and an analysis of their applicability to this project.
Chapter 4 provides details on the antenna selected for use as the array’s radiating elements. A description of the metrics used to optimize the array’s characteristics is then presented, followed by in depth analysis of the metrics and where their effects manifest themselves. An array design is then selected based on the presented metrics.
Chapter 5 describes the assembly of the array, including its mechanical attributes, selected materials and RF components. An analysis of mutual coupling and the array’s performance is then presented, which includes a comparison of simulated and anechoic measurement data.
Chapter 6 concludes the thesis with final remarks and discussion of the project results.
8 Chapter 2: Array Theory
2.1 Fundamental Principles & Array Factor Development
A linear arrangement of elements with uniform amplitude, spacing, and constant progressive phase shift is known as a uniform linear array (ULA). In an array, each element contributes to the overall radiation pattern, which can be calculated with a vector sum of the E-field contributions to each element in the far-field. When a plane wave is normally incident on an array of perfectly isolated isotropic radiators, as seen in Figure 2.1 (a), each element will receive the same magnitude and phase excitation. When this is the case (and no phase shift is applied) the currents produced by each element will add coherently and produce the maximum achievable response of the array. When the elements are not uniformly excited in phase, the induced currents typically will not add constructively, thereby reducing the measured response of the incoming signal ([8], pg. 311). This occurs when a signal arrives from an off normal direction to the broadside of the array. When an array is illuminated by a plane wave that arrives at some angle, ϕ, off of the array’s broadside direction, as seen in Figure 2.1 (b), the elements positioned towards the direction of incidence will receive the signal before the other elements. The signal time delay
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Every element in any arbitrary array will have some amplitude and phase component that is only dependent on its position relative to the phase center (defined as the origin) of the array. The summation of these amplitudes and phase components is defined as the array factor (AF) and is given for an array steered to broadside by (2.1) below.
′ 푁 푗풌•풓푛 푨푭 = ∑푛=1 퐴푛푒 (2.1)
풌 = 푘0[cos(휃) cos(휙) 풙̂ + cos(휃) sin(휙) 풚̂ + sin(휃) 풛̂] (2.2)
′ ′ ′ ′ 풓푛 = 푥 풙̂ + y 풚̂ + z 풛̂ (2.3)
2휋 푘 = 0 휆 (2.4)
Where 푁 is the total number of elements in the array, 푛 is the antenna index, 퐴푛 is a purely real valued amplitude weight, 푘0 is the wavenumber, and 풌 is the wave vector, which is a function of the direction of the incoming/outgoing signal. The position of the 푛th element
′ is given by 풓푛, whose dot product with the wave vector yields the phase distance, Ψ푛, of the antenna to the reference plane. It should be noted that the orientation of the phase distance is defined from the receiving direction [10]. Using the speed of light, 푐, and the phase distance, the time delay of an individual element can be found via (2.5) [8]:
′ 풌∙풓푛 Ψ푛 Δ푡푛 = = (2.5) 푐(푘0) 푐(푘0)
Steering the main lobe of a narrowband signal in an arbitrary direction can be achieved by manipulating the phase delay of each element, such that element responses add coherently at some angle off of the broadside direction of the array. This is achieved by adding an exponential phase term to the response of each element whose wave vector, 풌풔 is a function of the desired scan angle, as seen in (2.6).
12 풌풔 = 푘0[cos(휃푠) cos(휙푠) 풙̂ + cos(휃푠) sin(휙푠) 풚̂ + sin(휃푠) 풛̂] (2.6)
The scanning phase factor is then given a negative value in order to counteract the phase offset caused by the incoming signal. This results in the maximum signal response occurring when the main lobe is scanned in the direction of the incoming/outgoing signal, due to the phase components cancelling each other out. The array factor can thus be rewritten as:
′ ′ 푁 푗풌•풓푛 −푗풌풔•풓푛 푨푭 = ∑푛=1 퐴푛푒 푒 (2.7)
Null steering can be achieved in a similar manner to main lobe steering by instead finding the phase offset that minimizes the array factor in a specific direction.
Assuming that the array is made up of identical elements and mutual coupling can be neglected, the final far field pattern of the array can be produced by multiplying the radiation pattern of a single antenna by the array factor, and is known as pattern multiplication. The final radiation pattern of the array can then be expressed as:
′ ′ 푁 푗풌•풓푛 −푗풌풔•풓푛 푬푻(휙, 휃) = 푬(휙, 휃) ∑푛=1 퐴푛푒 푒 (2.8)
푬(휙, 휃) = 푬휙(휙, 휃)휙̂ + 푬휃(휙, 휃)휃̂ (2.9)
Where 푬푻 is the total electric field produced by the array, and 푬 is the radiation pattern of a single element which includes the 휙̂ and 휃̂ polarization components 푬휙 and 푬휃 [10]. The directivity of the array can then be calculated using (2.10), where 퐴 is the physical area of the array. The gain can then be found by multiplying (2.10) by any losses present within the array [11].
4휋 퐷 = 퐴 휆2 (2.10)
13 There are several assumptions being made in this version of the array factor that are critical to determining the scope in which this version of the array factor is valid, and therefore useful. First is that the far field criterion seen below is satisfied. The distance, 푅, from the antenna to the boundary between its near and far fields is given by:
2퐷2 푅 = (2.11) 휆
Where 퐷 is the largest dimension of the aperture [12], or the length of the array in this case.
The second assumption is that the elements share a uniform pointing direction. In order to account for any arbitrarily oriented elements, a rotational matrix would have to be applied to each of the elements that aligns the array geometry and the polarization of the individual elements to a global coordinate system [10]. The final, and most crucial, assumption to be aware of is that the array factor does not take into account mutual coupling between the elements. Mutual coupling can severely degrade the performance of an array by lowering the antennas overall gain, potentially causing scan blindness and changing the general pattern in which the array radiates [10]. Therefore, mutual coupling must be taken into account separately in the design and analysis process. Nevertheless, the array factor remains paramount in the understanding of array theory. The array factor presented above can be used to effectively analyze a planar array with non-uniform element positions and amplitude excitations, and it will serve as the mathematical foundation for the array analysis carried out within this project.
14 2.2 Characteristics of Arrays
Antennas are the interface between a radar and the outside world. Therefore, the performance of a radar system is closely related to the kind of information its antenna can provide, which can be partially quantified by analyzing the array factor, an example of which can be seen in Figure 2.3 below.
휆 Figure 2.3: Basic array factor characteristics. Showing a N=11 element ULA spaced at 훥 = 푁 2 at a frequency of 677 MHz, with peak sidelobe levels ≈ -13 dB
The -3 dB beamwidth is the angular distance between the points on the main beam where the amplitude of the array factor has been reduced by half (or 3 dB), and is often referred to as the half power beamwidth (HPBW). The HPBW is a measure of how “directional” an antenna is, and is therefore closely tied to a radar’s angular localization performance, which can be calculated using (2.12), [5][8].
15 휙 훿 = 3푑푏 휙 √2(푆푁푅) (2.12)
2 푃푟 푃푡퐺푡퐺푟휆 휎 푆푁푅 = = 3 2 2 (2.13) 푃푛 (4휋) 푅푡 푅푟 푘푇퐹퐵퐿
Where (2.13) is the standard bistatic radar range equation with the following terms:
훿휙 = azimuth resolution 휎 = radar cross section (RCS)
휙3푑푏 = azimuth beamwidth 푅푡 = transmitter to target range
푆푁푅 = signal to noise ratio 푅푟 = target to receiver range
푃푟 = received power 푘 = Boltzmann’s constant
푃푛 = noise power 푇 = temperature
푃푡 = transmit power 퐹 = system noise figure
퐺푡 = transmitter gain 퐵 = equivalent noise bandwidth
퐺푟 = receiver gain 퐿 = system losses
The same expression for calculating angular localization performance can be applied in elevation as well.
A narrow beamwidth is ideal for tracking applications because the radar can isolate targets of interest more precisely by further mitigating clutter, extraneous scatterers and nearby targets. Conversely, larger beamwidths are ideal for persistent surveillance, as a larger area can be covered by the main beam without scanning [8]. The beamwidth of an antenna is primarily determined by the length of its aperture compared to its operating wavelength, with larger apertures leading to more narrow beamwidths.
The aperture of an array can be enlarged by increasing the number of elements and/or the spacing between them. While the addition of elements in an array is primarily limited by cost constraints and the ability of the radar to process increased amounts of data, the
16 distance that the elements of an array can be spaced suffers from a more fundamental limitation. If the elements of an array are spaced too far apart, additional lobes, known as grating lobes, whose energy is equivalent to the main beam, will be produced. Grating lobes are generally undesirable due to the fact that they siphon energy from the main beam.
Furthermore, grating lobes produce responses that are ambiguous with those produced with the main beam, making it difficult to accurately calculate a target’s DOA [9].
The production of grating lobes is also a function of the phase shift applied to the elements to induce scanning. Any applied phase shift between the elements will reduce the element spacing required for the currents produced by an incident wave to combine in phase [9]. Therefore, the maximum distance that the elements can be spaced without inducing grating lobes is related to the maximum desired scan angle of the array and vice versa. For a ULA, this relationship between the element spacing, 푑푚푎푥, and the maximum scan angle, 휙푚푎푥, is given by:
휆 휆 푑푚푎푥 = ≤ (2.14) 1+|sin(휙푚푎푥)| 2
It can therefore be concluded that the maximum scan angle – scannable field of view– of an array is inversely proportional to its achievable angular resolution, which is a function of an array’s element spacing. It should be noted that from the above equation it can be seen that if the elements of an array are spaced less than half a wavelength apart, the array can scan to any angle without grating lobes [8].
Similar to grating lobes, an antenna’s sidelobes rob power from the main lobe, and can potentially produce ambiguous returns. For radar purposes, if a target is sitting in the direction of a large sidelobe and produces a return that is large enough to cross the detection
17 threshold of the system, unwanted ghost targets will be detected, resulting in increased system tracking strain [9]. This is specifically an issue with the peak sidelobes, which for a ULA sit directly next to the main beam at a level of approximately -13.5 dB. Therefore, the reduction of an array’s sidelobe levels is highly advantageous for radar applications.
In summary: by adding the response of multiple antenna elements, an array can create a large effective aperture without increasing the size of its radiating elements. This produces a larger and more directional radiation pattern that can be controlled and scanned by adjusting the phase responses of the individual elements. The array factor and element pattern can be used to analyze the radiation characteristics of an array, most notably the
HPBW, maximum scan angle, and the sidelobe levels. It is these characteristics that played the dominant role in the design analysis used in this project.
18 Chapter 3: MuTeRa Subarray Design Considerations
The Multistatic digital Television passive Radar (MuTeRa) testbed at The Ohio State
University ElectroScience Laboratory is a wideband UHF system for passive radar research. The system is designed to utilize digital Advanced Television System Committee
(ATSC) transmissions in the 470-700 MHz band, chosen due to the high transmit powers and moderate 6 MHz channel bandwidth [13]. Furthermore, the digital modulation provides higher ambiguity performance stability and range resolving capabilities compared with analog FM broadcasts. The passive radar system has an RF passband of 530-680 MHz and 8 receive channels, one of which is reserved for a high gain Yagi-Uda reference antenna that is used to capture a “clean copy” of the transmitted DTV signal. There are eight 6 MHz DTV illuminators in the greater Columbus area that operate inside of the of the radar’s passband, each broadcasting with horizontally polarized antennas [14].
The design goal of this project is the creation of a robust, low cost digitally scannable array, which will serve as the surveillance antenna of the aforementioned passive radar system. The array should balance a narrow half power beamwidth with a large maximum scan angle, while maintaining low sidelobe levels across the 530-680 MHz band. It should be noted that although MuTeRa has a passband of 150 MHz, the 6 MHz transmissions are
19 digitally processed individually; therefore, conventional narrowband array theory is applicable to the analysis.
The desire to create an antenna with a higher gain than the ULA which this project is replacing, could be achieved by designing a new radar system with a larger number of receive channels to accommodate an increase in the number of elements that could be utilized within an array. The additional elements would allow the length of the array (and the effective aperture) to be increased without the formation of grating lobes. This would lead to an increase in the gain of the array and create additional degrees of freedom that could be utilized for radar processing. Increasing the number of receive channels would lead to the highest performance; however the large cost required to achieve this renders this option impractical. Alternatively, configuring higher gain elements in a subarray architecture provides a practical solution that allows for an increased number of elements, without the costs associated with increasing the number of RF and digitization channels.
In order to effectively analyze and design a usable subarray antenna, the maximum scan angle described in (2.14) requires a more practical definition. Because radar systems are generally hindered by large sidelobe levels leading to ambiguous responses before grating lobes arise, it is more appropriate to define the maximum scan angle by a system’s allowable reduction in gain or increase in sidelobe levels caused by scanning. A gain reduction of 6 dB was chosen as the maximum allowable drop in system gain, as seen in
Figure 3.1 (a) and a -10 dB threshold was set as the maximum allowable peak sidelobe level, as seen in Figure 3.1 (b). These thresholds were selected to be within 3 dB of the
HPBW and the -13 dB peak sidelobe levels of a ULA radiating at broadside.
20
(a) Maximum gain reduction of -6 dB at 휙푠=19.2° (b) Peak sidelobe level of -10 dB at 휙푠=14.3°
Figure 3.1: Defining the maximum scan angle based upon (a) the maximum gain reduction and (b) the peak sidelobe level, for an arbitrary NxM subarrays shown at 677 MHz
Thus the maximum scan angle for this design can explicitly be defined as the minimum angle relative to broadside which causes the main beam gain to drop 6 dB, or causes a sidelobe to move within 10 dB of the scanned main-beam gain.
3.1 Subarray Terminology and Pattern Synthesis
A subarray consists of several antenna elements whose individual responses are passed into a combiner network, where in-phase combining steers each subarray to broadside.
Each subarray response is then passed into a RF downconverter and then digitized such that digital beamforming may take place. The general structure of a subarray antenna can be seen in Figure 3.2.
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The nomenclature is built from the “ground up,” beginning with a single individual element and ending with the final radiation pattern of the array. Each summation site in between is denoted as an array level; the first summation site after the element pattern would thus be referred to as “array level 1,” and continue through “array level N.” In the same vein, the array factors that are representative of the structure of each array level are
th denoted as “AFN,” the N level array factor.
The multiplication of the element pattern with all of the subsequent array level patterns will produce the final array pattern. The construction of the final radiation pattern for 4 subarrays consisting of 3 isotropic antennas is presented on the following page, in Figure
3.3.
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3.2 Subarray Pattern Interactions
When a contiguous subarray is steered to broadside, the grating lobes of the higher order array levels will be canceled by the nulls of the previous levels [16]. This phenomena can be seen in Figure 3.5 (a) and (b); the grating lobes of AF2 sit in the same angular locations (approximately ± 40°) as the nulls of AF1. If a phase shift is applied to all levels of a contiguous array (AF1 and AF2), complete grating lobe cancellation will continue to occur until grating lobes appear in the lowest array level, at which point grating lobes will appear in the final array pattern. This process is illustrated on the following page in Figure
3.5, which shows the array patterns for 4 contiguous subarrays consisting of 3 isotropic elements.
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In practice, implementing a time delay unit (TDU) behind each element is expensive and, in many cases, impractical. Therefore, many subarrays typically use narrowband phase shifters behind each element and then employ TDUs or digital beamforming at the second array level [17]. This is one of the primary advantages of subarray architectures: the reduction of cost resulting from replacing TDUs with narrowband phase shifters. Due to the narrowband nature of the phase shifters, this style of subarray architecture does however come at the cost of mispointing if the array is being operated over a wideband [9].
The severity of the mispointing in a contiguous array (or ULA) is given by:
Δ푓 Δ휙 = − tan(휙푠) (3.2) 푓0
Where Δ푓 is the bandwidth of the signal, 푓0 is the signal’s center frequency, and 휙푠 is the scan angle of the array. In addition to angular mispointing, phase shifters are limited by the fact that they are not infinitely sensitive. As a result, the accuracy of the array will be limited by the finite number of phase shifts that each phase shifter can apply [8].
Furthermore, most phase shifters are active devices, meaning they require power in order to operate, an issue if the array is required to operate in a location with limited power sources [18]. While phase shifters are less costly than TDUs, they still result in additional costs and can contribute significantly to the overall weight of an array [9]. These items were not reconcilable within the time, complexity and cost constraints of this project.
Therefore, phase shifters were excluded from the final design of this project
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Because of the high sensitivity of most radar systems, it is possible that in the situation where only one array level is being scanned, that a grating lobe of AF2 moving into a sidelobe of AF1 will produce a response strong enough to cross the detection thresholds set to determine the maximum scan angle of the array. This will result in further degradation of the array’s scanning performance. If the pattern interactions of the different subarray levels can be controlled, then the final radiation pattern of the array can be tailored to meet different scanning (and resolving) requirements. Therefore, striking the optimal balance between a subarray’s maximum scan angle and HPBW must begin with an optimization of the subarray’s pattern interactions.
3.3 Subarray Architectures
Several architectures for subarray pattern optimization were investigated as a part of this project, with emphasis on how each affected the maximum scan angle (MSA) and half power beamwidth (HPBW) of the array. In Section 3.2 it was shown that the MSA of a subarray is primarily limited by a grating lobe of the second array level moving into the main beam of the first. Therefore a reduced MSA will occur if the grating lobes of AF2 are spaced tightly together as seen in Figure 3.8 (b) and (e), or if the main beam of AF1 widens as seen in Figure 3.8 (c) and (f).
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3.3.1 Random and Non-identical Subarray Geometries
Redistributing the radiated energy of an array can be achieved by orienting the elements in an aperiodic arrangement. Due to the periodic nature of electromagnetic signals, when the elements of an array are spaced beyond half of a wavelength apart, grating lobes will appear, which poses a particular problem for wideband operation [19]. Breaking up the periodicity of the array elements prevents the phase fronts of an incoming signal from adding up constructively, thereby suppressing sidelobe levels and mitigating grating lobe formation [20].
Because the energy present in undesirable side/grating lobes is redistributed among the elements of the array, the amount of side/grating lobe suppression that can be achieved is highly dependent on the number of array elements [21]. This can easily be seen in the array patterns in Figure 3.9, which show three ULAs and three random linear arrays (RLAs) with an equivalent number of elements and array length. The spacing of the elements within each RLA was selected at random between 휆/2 and 2휆.
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quickly limits utilizing periodic subarrays with randomly distributed elements as a viable approach to this project.
An alternative approach to implementing aperiodicity in a subarray involves varying the number of elements inside of each subarray. This can also be achieved by randomly thinning the array, in which case the spacing of the array will be non-uniform. In either case, the signal combination will be aperiodic which will lead to the suppression of grating lobes. The degree of suppression will again be dependent on the number of elements within the array. Similar to random arrays, this would require a large number of subarrays, or a large number of elements per subarray to adequately suppress grating lobes. Furthermore,
“practical implementation of randomly divided arrays is more complicated than that of a uniformly divided array; it requires non-identical beamforming networks” ([20], pg. 820).
The added complexities of analyzing, selecting and fabricating an array design, along with the requirement for a large number of elements necessitates an alternative approach to dealing with grating lobes and the complexities of wideband operation.
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This is a far simpler combining configuration which eliminates the need to split the signal response of each element, which will in turn reduce the overall signal attenuation.
However, care must be taken when choosing the second-level array factor spacing to avoid mechanical conflicts. In addition, closely spaced elements can result in high levels of mutual coupling – investigated in Section 5.3.
Because the MSA and HPBW of a subarray is determined by the pattern interactions of the different array levels, it follows that manipulating the spacing of the elements within each subarray can be used to increase the MSA of the array. This can be achieved by adding an additional summation point (an additional array level), whose spacing can then be similarly optimized to produce an increased MSA. The result of this is a non-uniform arrangement of the radiating elements within the subarray.
Allowing the radiating elements to be arranged non-uniformly and the subarrays to be overlapped greatly increases the level of control over the different patterns within the subarray. The ability to systematically manipulate the subarray patterns makes utilizing overlapped subarrays and a non-uniform element distribution an ideal optimization technique for this project.
37 3.3.3 Amplitude Tapering
For an array of uniform amplitude, the real valued amplitude coefficients, 퐴푛, within the array factor, shown in (2.7), are consistent throughout the summation. Often the coefficients are given a value of unity and the array factor is divided by the total number of elements to normalize the maximum value to zero decibels. As such, the normalized array factor can be written as:
1 ′ ′ 푨푭 = ∑푁 퐴 푒푗풌•풓푛 푒−푗풌풔•풓푛 , 퐴 = 1 N 푛=1 푛 푛 (3.3)
A uniform amplitude distribution across the elements will produce the largest directivity and therefore the narrowest beamwidth the array can achieve [7]. However, a uniform amplitude distribution also has the highest sidelobe levels. These can be reduced through the use of non-uniform amplitude excitations, also known as a taper or window.
As described in Section 2.1, sidelobes are generated by the summation of the received signals with phase shifts between the array elements, which occur due to a signal’s angle of incidence upon an array. Because the far field radiation pattern of any antenna can be found by taking the Fourier transform of the current distribution across the aperture, sidelobe levels will be reduced if the response of the outer array elements is deemphasized, or similarly if the response of the center elements is maximized in comparison to the rest of the array [8].
When an amplitude taper is applied to an array, the sidelobes will diminish and the main beam will broaden. It can be seen in Figure 3.11 that the application of a Kaiser window, seen in Figure 3.11 (b), to the ULA response seen in Figure 3.11 (a) will push the
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EURDGVLGHGLUHFWLRQRIIHUVWKHEHDPZLGWKVFDQQLQJVLGHOREHOHYHODQGFRVWFKDUDFWHULVWLFV that are required for this project. The pattern interactions of each subarray level determine the maximum achievable scan angle and the HPBW of the final array pattern, which can be optimized through the use of amplitude tapering, overlapped subarrays, and non- uniformly spaced elements.
42 Chapter 4: Array Design Analysis and Selection
The concept of pattern multiplication as it is applied to subarray design inherently increases the number of parameters that must be analyzed to optimize the final array configuration. The primary design considerations for ULAs, including the number of elements, their spacing and frequency of operation must be assessed separately within every array level of a subarray in order to build an understanding of the pattern interactions that lead to the array’s final radiating pattern.
All of the pattern analysis up until this point has utilized isotropic radiators, which is ideal for conceptual analysis; however, in order to perform any practical subarray analysis the radiation pattern of the individual elements must be considered. The selection and modeling of the individual antennas selected for this project is discussed in Section 4.1, the results of which were incorporated into the parametric analysis, presented in Section 4.2, and used to select the final subarray design.
43 4.1 Element Selection & Modeling
The radiating elements used within the array will not only contribute to the final radiation pattern via its electric field distribution, but will also set practical constraints on the positioning of the subarray components. There are several important features to consider when selecting the elements of an array which include:
1. gain pattern
2. bandwidth
3. polarization
4. physical size and weight
5. environmental durability
6. cost
The gain pattern of the individual elements largely determines the backlobe of the array, which should ideally be as small as possible to reduce the contributions from signals scattering off of the array’s support structure. Furthermore, the gain pattern of the individual elements should not interfere with the subarray patterns, which are predominantly responsible for the scanning and beamwidth characteristics of the subarray’s final radiation pattern. The gain pattern of the antennas should essentially form an “envelope” around the main beam of the first-level array factor, as to not interfere with these operations.
The bandwidth and polarization of the radiators are both well-defined within the scope of this project. The antennas must span the 530-680 MHz band in accordance with the portion of the ATSC broadcast band utilized by the MuTeRa system. Initially the selected radiators were required to be vertically polarized, in an attempt to minimize direct signal 44 interference which can degrade the signal to interference and noise ratio of passive radar performance.
In order to support research pertaining to the effects of antenna polarization on passive radar performance, the selected mechanical mounting configuration should permit re- orientation of the antennas to change the array’s primary polarization. To aid in this process, the elements should be compact and light-weight with maximum flexibility.
Furthermore, the antennas must be able to withstand year-round exposure to the elements, as they will be stowed outdoors due to the large size of the array. The elements and mounting structure should also be resilient to wind-loading in order to minimize vibrations that could lead to anomalous Doppler shifts of the received data.
The cost and time constraints of this project dictated that commercial off the shelf
(COTS) antennas be utilized versus fabricating the individual radiators. Bowtie, Yagi-Uda, and log-periodic antennas were each considered as potential radiators for this project. After considering the aforementioned requirements and project cost constraints, a dual bowtie antenna designed as a “long range indoor/outdoor HDTV antenna” was selected as the radiating element. The relevant technical data provided by the manufacturer is provided in
Table 4.1.
45 Table 4.1: DB2e antenna specifications [25] Technical Data Sheet: Antennas Direct DB2e Antenna Physical Data: Dimensions: Width = 23 in. Height = 16.25 in. Depth = 7 in. Weight: TBD Turning Radius: 12.5 in. Electrical Data: Band: UHF 470 MHz to 698 MHz Channels 14 - 51 Impedance: 75 ohm Connector: F - Female Performance Data: Peak Gain: 11.8 dBi @ 698 MHz VSWR: 3.0 Max 470 MHz to 698 MHz
Using the method of moments (MoM) FEKO® solver, the DB2e antenna was modeled and the principle H and E plane patterns, seen in Figure 4.1 (b) and (d), were compared to those provided by the manufacturer, shown in Figure 4.1 (c) and (e). It should be noted that the bowties of the DB2e antenna seen in Figure 4.1 (a) are separated by 25.5 cm at their centers.
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The simulated data shown in Figure 4.1 (b) and (d) was generated at the center frequencies utilized by the MuTeRa system, which span from 533-677 MHz for the total band of 530-680 MHz. Specifically 533, 587, 605, 617, 653, 665, and 677 MHz were modeled. The gain pattern data provided by the manufacturer is presented in Figure 4.1 (c) and (e), which shows the gain response at 475, 550, 625, and 700 MHz. While the frequencies presented in the above figures are not one to one, the pattern data simulated for this project matches well with the mid band specifications provided by the manufacturer and was therefore incorporated into the subarray design analysis. It should be noted that the data provided by the manufacturer was also generated using a computational solver and is not measured data. Furthermore, the data was generated without the inclusion of the antenna’s balun.
4.2 Subarray Metrics Analysis
As explained in Chapter 3, subarray design involves a significant number of parameters that must be determined in the design of the array. As such, the optimization process began with an investigation of these degrees of freedom along with their impact on standard array metrics – predominantly the MSA, HPBW, and main-beam gain of the array. Noting that the number of RF receive channels (7) and the frequency range of operation (530-680
MHZ) were set by the MuTeRa system specifications, the degrees of freedom are:
48 1. the spacing between each element
2. the spacing between each subarray
3. the number of elements per subarray
4. the subarray’s amplitude taper.
The spacing between the elements and the spacing between each subarray were the main focus of this investigation, as these items have the largest room for variability. In contrast, selecting the number of subarrays was straightforward, with a larger number of digitized responses maximizing MuTeRa’s processing freedom and providing greater control over the array response. Therefore, the array was designed to utilize seven subarrays, the largest number available.
It will be shown that there can be significant variations in the MSA with subtle changes in the spacing characteristics of the array. Therefore, a staggered overlap subarray geometry was selected, where the individual subarrays are staggered in elevation as seen in Figure 4.2. This configuration allows for more freedom when selecting the subarray positions than an interlaced overlap geometry, as seen in Figure 3.10, due to the fact that there is less opportunity for multiple elements to occupy the same space. In the far field the array structure will appear linear, and assuming there is no significant mutual coupling, will produce the same radiation pattern that would be present if the subarrays were all to be placed in the same plane. Furthermore, this subarray configuration can be classified as a planar array, and therefore can be scanned not just laterally, but vertically as well; this is highly advantageous for radar processing. It should be noted that in Figure 4.2, the “DB2e
Phase Center” refers to the center point between the two “DB2e Bowtie Elements,” which are spaced 25.5 cm apart and illustrated in Figure 4.1 (a).
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Where:
Δ푀 = subarray spacing
푁 = number of DB2e antennas per subarray
푊 = width of the DB2e antenna, 32.21 cm
Δ푁 = the DB2e center spacing
4.2.1 Number of Subarray Elements
The metrics presented in this section were generated at 677 MHz for an array consisting of seven subarrays. Due to cost and space limitations, this project was limited to a maximum of up to three DB2e antennas per subarray. Results were therefore analyzed for subarrays consisting of one, two and three antennas per subarray. The MSA of the array was calculated using the method outlined in Chapter 3.
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4.2.3 Frequency of Operation
As was outlined in Chapter 2, the behavior of an array’s radiation pattern is dependent on its electrical length (spacing of its elements), and therefore the exact frequency of operation. As can be seen in (2.5), the phase delay across an array’s surface is a function of the element positions (or array length) with respect to wavelength. In the case of a ULA,
(2.5) can be rearranged (and simplified) to find the azimuth phase variation across the surface of the array, which can be written as:
2휋퐿 sin(휙) Δ = (4.2) 휙 휆
It can be seen in (4.2) that by increasing either the length of the array, L, or increasing the frequency of operation will increase the phase variation across the array; as a consequence the main beam of the array will become narrower. In contrast, if the frequency of operation is decreased, the main beam will become broader [8].
The metrics presented in Figure 4.16 and Figure 4.17 were generated at the center frequencies of the 6 MHz ATSC channels at the band edges, 533 and 677 MHz, for M=7 subarrays. Each of which contain two DB2e antenna elements for a total of four bowtie radiators per subarray. It should be noted that this is the same structure seen in Figure 4.8 used to generate the metrics presented in Section 4.2.2.
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Due to the fact that the HPBW is primarily dependent on the spacing between the individual subarrays and not the DB2e center spacing, the primary challenge of the design analysis resided in optimizing the MSA of the array, which is limited by the upper frequency bound of the bandwidth. Therefore the primary optimization analysis of the array was carried out at 677 MHz, so that a minimum MSA could be selected across the bandwidth, with the understanding that a larger subarray spacing would lead to a “better”
(narrower) HPBW.
4.2.4 Amplitude Tapering
As outlined in Section 3.3.3, effectively implementing an amplitude taper within a subarray architecture requires utilizing a large number of elements within each subarray and a system that can tolerate the signal attenuation associated with creating the taper. If such an architecture is selected, then amplitude tapering can be highly beneficial for use within a subarray antenna. Not only does amplitude tapering provide a general reduction in the sidelobe levels of an array, but it can also provide flexibility in the array design as seen in Figure 4.19 and Figure 4.20. These metrics were generated at 605 MHz for an array consisting of seven subarrays, each containing five isotropic elements. The responses of the subarray elements were tapered with a Kaiser distribution, where the beta value indicates the intensity of the taper. It should be noted that when beta is set to zero, no taper is applied.
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increasing the spacing of AF1 will lead to a narrower HPBW, offsetting the widening caused by the taper and leading to similar MSA characteristics as the non-tapered case.
This can be useful if an array design is limited by mutual coupling, because the elements can be spaced further apart with very little loss to the MSA.
At least three elements are required in order to implement an amplitude taper, with control over the taper’s effect on the radiating pattern increasing as the number of elements increases. This is due to the fact that the taper can be implemented more gradually over a wider range of elements. While two DB2e elements consist of four bowtie elements, each
DB2e antenna combines the response of its two bowties through a balun to a single port.
Applying an amplitude taper to the bowties individually would require removing the balun or manipulating the antenna’s wiring; either case would require accounting for the resulting change in impedance that would occur. As was stated in Section 4.2.1, manipulating the
DB2e antenna structure was outside the scope of this project. Because of this, the first- level of the array only consists of N=2 ports to which a taper could be applied. Therefore an amplitude taper is not compatible with the first array level for the selected subarray design of this project.
Amplitude tapering could, however, be applied to the second array level after digitization has taken place. As outlined in Section 3.3.3, the application of a taper will cause a widening of the main lobe; this is particularly problematic for the second array level, as it is AF2 that is primarily responsible for the HPBW of the final array pattern. It is for these reasons that amplitude tapering was omitted from the design of this project.
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design’s respective directivity pattern, the final design was selected for this project, the specifications of which are listed in Table 4.2 below:
Table 4.2: Final subarray design specifications Number of Bowties per DB2e Antenna 2 Individual DB2e Bowtie Spacing 25.5 cm Number of DB2e Elements per Subarray 2 AF1: DB2e Center Spacing 36 cm Number of Subarrays 7 AF2: Subarray Spacing 58 cm Vertical Subarray Spacing 57 cm Total Number of DB2e Elements 14 Total Number of Array Elements 28 Total Array Length 4.1 m (13.45 ft.)
Based upon the above metrics, the selected array design is expected to have an azimuth
MSA ranging from 19.6 – 15.5° and a HPBW ranging from 6.9 – 5.5° across the 530 – 680
MHz band.
71 Chapter 5: Assembly, Testing & Performance Evaluation
This chapter addresses the practical considerations and physical assembly of the array design presented in the previous chapter. Furthermore, the performance of the array is evaluated in the presence of RF component losses and mutual coupling, and is compared to the expected/designed array specifications presented in Section 4.3.
The completed array can be seen in two different configurations on the following page in Figure 5.1. The array was mounted on six caster wheels so that it can be adjusted in the azimuth direction, and a levering action allows the elevation tilt of the array to be varied from 0-90°.
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As the electrical properties of the array were the focus of this project, assembly began with the RF component selection, where emphasis was placed on selecting low loss components with high levels of isolation. Because the response of each subarray (AF2) is digitized, any phase or power mismatch that results from components at this array level can be calibrated out. This is not the case however at the first-level of the array, which consists of only analog components. Therefore, any component loss or phase mismatch that occurs within the first array level will directly lead to AF1 pattern deterioration, a reduced detection range, and/or angular uncertainty in the pointing direction of the array.
After the RF components had been selected, a mechanical structure was then designed that is capable of supporting the selected RF components. The primary concern when selecting the array’s mounting structure was its overall rigidity; any movement or misalignment of the structure will cause a change in the element positions, resulting in phase discontinuities that will again result in angular uncertainty in the pointing direction of the array. Furthermore, all of the array components, both mechanical and electrical, must be able to withstand permanent outdoor storage and meet a budget of $10,000.
74 5.1 Subarray RF Design
The component tree seen in Figure 5.2 outlines the necessary RF components for a single subarray. Each subarray contains two DB2e antennas, each of which are connected to a 75 ohm F-type to 50 ohm SMA adapter to account for the impedance mismatch between the antennas and MuTeRa’s RF front end. While applying an adapter on each antenna, opposed to after the combination stage, doubles the required number of adapters, it reduces loss within the system, because the number of components that reflections from the impedance change can propagate through is reduced.
Three feet of phased matched cabling is then used to carry the response from each of the antennas to a two way combiner. Again, the cable is phased matched due to the fact that any phase discontinuities between the signals being combined cannot be digitally accounted for and will therefore lead to mispointing within the array. After the signal combination, 70 ft. of low loss cable carries the response to the passive radar. It should be noted that phased matched cabling is not used after the signal combination step, because the responses from each of the seven subarrays can be calibrated digitally. Furthermore, the long cable length was selected to increase the number of rooftop positions that the array can be placed in.
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All of the losses presented in Table 5.1 were specified by the component’s manufacture.
It is important to note that the compact range measurements taken of a single subarray, the results of which are presented in Section 5.3, include the losses present from all of the RF components, excluding the long cable assembly.
Weather proofing the RF components was accomplished by selecting COTS antennas whose radiating elements were constructed of aluminum and intended for outdoor use, purchasing cabling that has water resistant and ultraviolet/RF shielded jackets, and by wrapping all of the electrical connections in silicone sealing tape. The cost of all of the RF materials utilized for this project was just under $4,500.
5.2 Mechanical Considerations
The rooftop site for the array implies that both the selected RF and mechanical/structural components of the array require withstanding the year round weather conditions common to Columbus, Ohio, which can include heavy wind and rain, light hail, and an annual temperature variation of roughly -10 to 90 °F. In addition, the array should be light weight as to not damage the roof, with a mechanism for securing it in place, both during measurements and in the stowed configuration. Furthermore, in order to provide flexibility in the experiments that can be carried out using the array, it is advantageous for the array to be adjustable/reconfigurable in structure with mechanical mobility in the azimuth and elevation directions. The primary mechanical design considerations for the array can be summarized as follows:
77 1. Weatherproof
2. Light weight, sturdy, and securable
3. Mechanically reconfigurable
a. Azimuth and elevation pointing
b. Subarray spacing
c. Polarization
Dictated by the selected RF components and array design, the support structure needs to be capable of supporting approximately 60 lbs. of components over a roughly 25 ft2 area, while maintaining the ability to be mechanically adjustable and reconfigurable.
Furthermore, the structure is required to weigh less than 400 lbs. (including the 60 lbs. of
RF components), be generally weather proof, and cost less than $5,500 to meet the project budget.
Meeting the aforementioned design requirements was accomplished utilizing
UNISTRUT® metal framing and channel. The hollow steel tubing depicted in Figure 5.3
(a) was utilized for the supporting frame of the array structure. It has uniform perforations that allowed for easy alignment of the different sections used to construct the array.
Additionally, the fact that the tubing is hollow reduces the overall weight of the array structure.
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that can be achieved by sliding each subarray into the desired position on the track.
Adjusting the subarrays vertically can be achieved by separating the track and securing them into new positions on the mounting frame. If more height or length is required, the appropriate sections can be replaced with longer supports. Furthermore, the polarization of the array can easily be changed by simply rotating the subarrays 90° and re-securing them using the perforations in the supporting frame.
The final assembled array is 14 ft. long and 6 ft. high in its tallest configuration. The six casters evenly distribute the approximately 315 lbs. of weight onto two sheets of plywood, preventing damage to the roof of the building. Including all of the mechanical and RF components, the total cost of this array was approximately $6,500.
80 5.3 Mutual Coupling Analysis
In order to evaluate the performance of the array, a single subarray was measured in the ElectroScience Laboratory’s compact range. A single subarray was measured for practicality; the full length of the array would have exceeded the size of the range’s quiet zone where gain patterns can be reliably calibrated. These measurements were then compared to results produced using a combination of FEKO® simulations (specifically the
MoM solver) and generic pattern multiplication. The goal of this evaluation was to characterize the radiating pattern of the array in the presence of any mutual coupling and the integrated system losses present within the array.
In order to evaluate if mutual coupling significantly affects the radiating pattern of the array, a FEKO® simulation was conducted consisting of two subarrays, each containing two DB2e antennas, as seen in Figure 5.4 (a). In order to handle the increased computational requirements of this simulation, the DB2e elements were simplified; care was taken to ensure that the radiation characteristics of the DB2e antennas did not deviate substantially from the original simulation results presented in Section 4.1.
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The S-parameters presented in Figure 5.4 (b) suggest that the mutual coupling between the elements that are staggered in elevation is relatively low, measuring between -36 dB and -50 dB across the array’s bandwidth. It can be seen in Figure 5.4 (b) that the largest source of mutual coupling occurs in S12 and is a result of the DB2e placement within the first array level. This is to be expected, as the radiating elements of the antennas are in close proximity and run parallel to each other. Bowtie antennas are similar to dipole antennas in that they radiate outward in the broadside – opposed to the endfire – directions.
Therefore, when the two bowtie elements are placed in parallel with each other, the amount of mutual coupling will increase, due to the fact that the antennas are radiating directly into each other.
5.3.1 First Array Level Mutual Coupling
The assessment of mutual coupling cannot be left solely to an assessment of the S- parameters but requires further analysis of the radiating pattern of the array. To supplement the FEKO® analysis, compact range measurements were taken, the setup of which can be seen in Figure 5.5 on the following page.
83
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(b)
Figure 5.5: Compact range E-plane (a) and H-plane (b) measurement setups
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The patterns seen in Figure 5.7 show a high level of agreement both in their directional patterns and their calculated gain values. The gain of the 2 DB2e simulation was normalized using the chamber measured gain and the maximum amount of cable loss specified in Table 5.1. If mutual coupling is negligible between the subarrays, the total gain of the array can be found by multiplying the linear gain over the total number of subarrays
[10]. The gain of the 14 DB2e simulation was taken directly from the FEKO® model, which fully accounts for any scattering and mutual coupling present at the second array level.
Because of the high level of agreement between the directional – and maximum – gain of the two models, as well as the low S-parameter – specifically the S13, S14, S23, and S24 – values presented in Figure 5.4 (b), it can be concluded that the effects of mutual coupling are negligible on AF2, and that the response of the array can be accurately characterized by simulating the response of two DB2e elements, as seen in Figure 4.8, and multiplying it by a seven element isotropic second-level array factor.
5.4 Final Array Specifications
The final array patterns were generated by multiplying the first-level array pattern
(generated from a two DB2e antenna FEKO® simulation) with a seven element isotropic second-level array factor. The resulting final patterns were then normalized to the proper gain, as outlined in Section 5.3.2, and can be seen in Figure 5.8. For both the 533 and 677
MHz cases, the grating lobes of AF2 sit within the peak sidelobes of AF1, resulting in slightly elevated sidelobes at broadside. In either case however, when AF2 is scanned, the
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GHVLJQHGWREH DQG WKH06$RIWKHDVVHPEOHGDUUD\UDQJHVIURP± The roughly 2.5 – 0.5° reduction in MSA from the design goal is acceptable within the confines of this project. It should be noted that the far field distances shown in Table 5.2 were calculated using (2.11).
Table 5.2: Final assembled array specifications
Far Field Maximum Scan Angle HPBW Frequency Gain Distance Azimuth Elevation Azimuth Elevation 533 MHz 59.78 m ± 17.16° ± 0° 6.94° 25.4° 20.5 dBi 677 MHz 75.93 m ± 14.96° ± 0° 5.48° 20.0° 22.2 dBi
In the array’s current configuration, little scanning can be carried out in elevation without the presence of significant sidelobe levels. At broadside, however, the sidelobes are sufficiently low to perform the azimuth scanning operations that have been described in this work. As the primary focus of this array’s design has been in its azimuth characteristics, a full description of the array’s elevation characteristics have been left to future work.
89 Chapter 6: Concluding Remarks
A large electronically scannable array was designed, assembled, and tested in order to support the passive radar research being carried out at The Ohio State University. A subarray architecture was selected in order to increase the array’s gain and scannable depth of field, without increasing the number of digitization channels within the radar system. A variety of different subarray optimization techniques, including amplitude tapering, random arrays, and overlapped subarray architectures were assessed in conjunction with the design goals of this project: creating a low cost large array with a narrow half power beamwidth (HPBW) that maintains a large maximum scan angle (MSA). It was determined that the constraints of the project – primarily the number of subarrays – would not support a random subarray architecture, and that an overlapped subarray architecture consisting of non-uniformly spaced elements would best meet the project goals.
Due to the considerable number of design freedoms, subarray optimization cannot be carried out in closed form. Each subarray design must be examined and optimized independently, while taking into account the effects of mutual coupling, the individual element patterns, and the sensitivity of the system for which the array is being designed.
After selecting a commercial off the shelf (COTS) antenna that met the electrical and
90 mechanical requirements of this project, MSA and HPBW metrics were analyzed as a function of overlapped subarray spacing, amplitude tapering, the number of elements per subarray, and the spacing between each of the elements within each subarray. The number of subarrays and their spacing determine the width of AF2, which is the primary factor in determining the overall HPBW of the array. The number of elements and their spacing within each subarray controls the width and sidelobe positions of AF1, whose interactions with the peaks and nulls of AF2 determine the MSA of the array. Non-uniform element placement and windowing at the first array level reduces the average sidelobe level with little to no increase in the HPBW of the array. Furthermore, windowing can be used to refine the width of AF1 and thus manipulate the scanning characteristics of the array, which provides freedom in selecting the element spacing within each subarray.
Ultimately, a 4.1 m array design was selected that utilizes seven subarrays consisting of two COTS antennas, each of which contain two bowtie elements. The choice to use two
COTS antennas per subarray eliminated the option of amplitude tapering, as it requires the presence of at least three element ports. Instead, the first-level array pattern was optimized by selecting a non-uniform spacing between the four elements within each subarray.
Using a combination of anechoic chamber measurements and computational EM software, it was concluded that mutual coupling was negligible at the second array level, but could not be neglected at the first. It was concluded, however, that while the effects of mutual coupling could not be ignored within each subarray, the effects were limited to a
MSA reduction of no more than 2.5°, effects not strong enough to warrant a design change.
The final assembled array operates at a bandwidth of 530 – 680 MHz, with an average gain of 21.4 dBi, a maximum scan angle ranging from ±15.0 – 17.2°, and a half power
91 beamwidth ranging from 6.9 – 5.5°. Utilizing steel framing, low loss RF components, and
COTS antennas, a 28 element array was assembled that is both adjustable in the azimuth and elevation directions and easily reconfigurable, at a total cost of approximately $6,500.
The calibration of the array and its use in collecting passive radar data will be left to future works.
92 Bibliography
[1] W. Melvin and J. Scheer, Principles of Modern Radar, Volume III: Radar Applications. Edison, NJ: SciTech Publishing, 2014. [2] N. J. Willis, Bistatic Radar. SciTech Publishing, 2005. [3] P. E. Howland, D. Maksimiuk, and G. Reitsma, “FM radio based bistatic radar,” IEEE Proc. - Radar, Sonar Navig., vol. 152, no. 3, pp. 107–115, 2005. [4] M. Daun, U. Nickel, and W. Koch, “Tracking in multistatic passive radar systems using DAB/DVB-T illumination,” Signal Processing, pp. 1365–1386, 2011. [5] J. H. Huang, J. L. Garry, G. E. Smith, and C. J. Baker, “Array Based Passive Radar Target Localization,” in 2016 IEEE Radar Conference (RadarConf), 2016, pp. 1–6. [6] J. H. Huang, M. N. Barr, J. L. Garry, and G. E. Smith, “Subarray Processing for Passive Radar Localization,” in 2017 IEEE Radar Conference (RadarConf), 2017, pp. 0248–0252. [7] C. Balanis, Antenna Theory: Analysis and Design, 3rd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005. [8] M. A. Richards, J. A. Scheer, and W. A. Holm, Principles of Modern Radar, Vol. I: Basic Principles. Raleigh, NC: SciTech Publishing, 2010. [9] G. Stimson, H. Griffithis, C. Baker, and D. Adamy, Introduction to Airborne Radar, 3rd ed. Edison, NJ: SciTech Publishing, 2014. [10] T. A. Milligan, Modern Antenna Design, 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005. [11] B. A. Munk, Finite Antenna Arrays and FSS. Hoboken, NJ: John Wiley & Sons, Inc., 2003. [12] R. C. Johnson, Antenna Engineering Handbook, 3rd ed. United States of America: McGraw-Hill, Inc., 1993. [13] “ATSC Digital Television Standard.” Advanced Television Systems Committee, Inc., Washington, D.C., 2007.
93 [14] J. L. Garry, G. E. Smith, and C. J. Baker, “Wideband DTV passive ISAR system design,” in Radar Conference (RadarCon), 2015 IEEE, 2015, pp. 834–839. [15] T. J. Brockett and Y. Rahmat-Samii, “Subarray Design Diagnostics for the Suppression of Undesirable Grating Lobes,” IEEE Trans. Antennas Propag., vol. 60, no. 3, pp. 1373–1380, 2012. [16] W. S. Lee, S. T. Khang, K. S. Oh, and J. W. Yu, “Design methodology for phased subarray antennas with optimized element phase control,” in 2013 European Microwave Conference, 2013, pp. 1659–1662. [17] D. H. Sinnott and G. R. Hlaack, “The Use of Overlapped Subarray Techniques in Simultaneous Receive Beam Linear Arrays,” RADC Proc. Antenna Appl. Symp., vol. 2, pp. 21–37, 1984. [18] R. Tang and R. Burns, “Phased Arrays,” in Antenna Engineering Handbook, 3rd ed., R. Johnson, Ed. United States of America: McGraw-Hill, 1993. [19] Kiersten C. Kerby and Jennifer T. Bernhard, “Sidelobe Level and Wideband Behavior of Arrays of Random Subarrays,” IEEE Trans. Antennas Propag., vol. 54, no. 8, pp. 2253–2262, 2006. [20] Amit P. Goffer, Moshe Kam, and Peter R. Herczfeld, “Design of Phased Arrays in Terms of Random Subarrays,” IEEE Trans. Antennas Propag., vol. 42, no. 6, pp. 820–826, 1994. [21] Y. Lo, “A Mathematical Theory of Antenna Arrays with Randomly Spaced Elements,” IEEE Trans. Antennas Propag., vol. 12, no. 3, pp. 257–268, 1966. [22] C. T. Lin and L. Hung, “Sidelobe reduction through subarray overlapping for wideband arrays,” in Proceedings of the 2001 IEEE Radar Conference, 2001, pp. 228–233. [23] J. S. Herd, S. M. Duffy, and H. Steyskal, “Design considerations and results for an overlapped subarray radar antenna,” in 2005 IEEE Aerospace Conference, 2005, pp. 1087–1092. [24] Tony Azar, “Overlapped Subarrays: Review and Update,” IEEE Antennas Propag. Mag., vol. 55, no. 2, pp. 228–234, 2013. [25] Antennas Direct®, “Technical Data Sheet: Antennas Direct DB2E Antenna.” Antennas Direct, Inc., 2011. [26] Unistrut® and Atkore International®, “Unistrut®, General Engineering Catalog - NO. 17A.” Harvey, IL, 2016.
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