SMART ANTENNA SYSTEM
BY
AHMED MOHAMED ELMURTADA ELAMEEN
INDEX NO: 074005
Supervisor
Ostaz : Mohamed Gaafer Elnurani
A REPORT SUBMITTED TO
University of Khartoum
In partial fulfillment of the requirement for the degree of
B.Sc. (HONS) Electrical and Electronic Engineering
(COMMUNICATION ENGINEERING)
Faculty of Engineering
Department of Electrical and Electronic Engineering
September 2012
DECLARATION OF ORIGINALITY
I declare that this report entitled―SMART ANTENNA SYSTEM‖
is my own work except as cited in the references. The report has not been
accepted for any degree and is not being submitted concurrently in
candidature for any degree or other award.
Signature: _________________________
Name: ____________________________
Date: _____________________________
II
ACKNOWLEDGMENT
As the end of my days as under graduate student draws nigh, I have the
occasion to reflectupon the many long days, and the even longer nights,
that all too quickly lengthened intoyears, that finally culminated with a
B.Sc. in Electrical Engineering. Whatthis reflection has revealed is that
the splendor of thisachievement is possible only as a result of the support
of others. And while my nameshall be the only one on the diploma, these
others deserve similar or equal recognition.
First of all, Thanks to Allah for giving us faith and health, to My Parents,
Brother and Sister for their huge support.
Special gratitude is extended to all gratitude to all those who gave me the
possibility to complete this project.The research thesis was done under
the supervision of Ustaz Mohamed Gaafer Elnoraniin the department of
Electrical and Electronic Engineering . I am deeplywould like to thank
him, for his continuous support and encouragement, supervision and
useful suggestions throughout this project. It was him , who provided an
aim and direction to this project and constantly pushed us to work harder
on it.
I wish to express my appreciation to my project partner, Yasir Nizar, for
his hard work,team spirit and the impressive Great times we spent.
At last, I declare special thanks for my friends and colleagues in 07
batch.
III
ABSTRACT
Rapidly and Emerging trends of mobile communication and ever growing demand of
mobile users created the need for new technologies that could satisfy this need under
limited bandwidth provided to telecom companies .Smart antenna systems are one of
these technologies which could provide directed radiation pattern towards desired
direction , better capacity and reduce interference .which affects used bandwidth
antennas are not smart; it is the overall system that tell them what to do is smart.
Smart antenna Systems had two main parts Beam forming, which the radiation pattern
is shaped and directed through it, and Direction of Arrival (DOA) algorithm that
detects the user‘s location and uses it to direct the pattern. The antennas in the array
interact constructively in the desired direction and destructively in other directions.
In this thesis, Overview of smart antenna System concepts,how they work,
Performance and Benefits had been chosen to study. By modelling a communication
system contains a smart antenna system to show the improvement in Received Power,
SNR and BER. Creating Array Factor and Directed the Pattern for both Linear and
Planar Arrays. Generate the Signal, modulation and transmit it through channel
expose with added Noise.
Simulation and resultsobtained Using MATLAB
toindicated Preference of using smart antenna over conventional single element
antennaand it Provide a way better performance.
IV
‫المستخلص‬
‫ظهور تقنيات متجددة يف جماالت االتصاالت الالسلكية و الطلب املتزايد الالمتناىي للمستخدمني ‪ ,‬خلق حاجة‬
‫ماسة لتقنيات جديدة ميكنها تلبية ىذه االحتياجات حتت ظل توفر عرض نطاق حمدود لشركات االتصاالت ‪ .‬تعترب‬
‫انظمة اهلوائيات الذكية احد ىذه التقنيات حيث تنشئ "منط اشعاعي " حنو التجاه معني الرسال االشارة حنوه ‪ ,‬و‬
‫لتوفري سعــة افضل ‪ .‬كما تقلل التداخل اذ تؤثر ىذه االشياء على عرض النطاق املستخدم ‪.‬‬
‫اهلوائية حبد ذاهتا ليست "ذكية" ‪ ,‬لكنو النظام الذي جيعلها تعمل بذكاء ‪ .‬تتكون اهلوائيات الذكية من جزئني اساسيني‬
‫‪ " :‬مولد الشعاع"‪ ,‬حيث يتم توجيو و حتديد شكل النمط االشعاعي عربه ‪ ,‬باالضافة للوغرمثية اجتاه السقوط اليت حتدد‬
‫موقع املستخدم(اهلدف) و يتم استخداىا لتوجيو النمط حنو ىذا االجتاه ‪ .‬اهلوائيات داخل املصفوفة تعمل بشكل بناء‬
‫يف االجتاه املطلوب و بشكل ىدام لتقليل التداخل يف االجتاىات االخرى الغري مرغوبة ‪.‬‬
‫يف ىذه االطروحة ‪ ,‬سيتم دراسة مفاىيم انظمة اهلوائيات الذكية ‪ ,‬الكيفية اليت تعمل هبا ىذه االنظمة ‪ ,‬ادائها و‬
‫فوائدىا ‪ .‬بأخذ نظام اتصاالت حيوي ىوائيات ذكية كمثال لتوضيح التحسن يف القدرة املستقبلة ‪ ,‬نسبة االشارة‬
‫للضجيج و معدل اخلطأ يف الثنائيات‪ .‬انشاء معامل مصفوفة للهوائية و توجيو النمط االشعاعي للهوائيات املصفوفية‬
‫اخلطية و للثنائية االبعاد باستخدام توليد النمط االشعاعي ‪ .‬يتم تكوين االشارة ‪ ,‬و تعديل و ارساهلا عرب القناة يف‬
‫وجود ضجيج مضاف ‪ .‬مع استخالص نتائج احملاكاة باستعمال برنامج ‪ MATLAB‬لتوفري حتليل يوضح افضلية‬
‫استخدام اهلوائيات الذكية على اهلوائيات االعتيادية املستخدمة ‪ .‬و اثبات ان اهلوائيات الذكية تعطي اداء افضل ‪.‬‬
‫‪V‬‬
TABLE OF CONTENTS
DECLARATION OF ORIGINALITY
II
ACKNOWLEDGMENT
III
ABSTARCT
IV
‫المستخلص‬V
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
VI
XI
XIII
LIST OF SYMBOLS AND ABBREVIATIONS
XIV
CHAPTER ONE INTRODUCTION1
1.1
Problem Statement ................................................................................. 1
1.2
Background and Motivation .................................................................. 2
1.3
Objectives .............................................................................................. 2
1.4
Methodologies and Tools ...................................................................... 3
1.5
Report layout ......................................................................................... 3
CHAPTER TWO LITERATURE REVIEW1
2.1
ANTENNA Fundmentals ...................................................................... 1
2.1.1
Introduction ............................................................................................. 1
2.1.2
Radiation pattern: .................................................................................... 1
2.1.3
Beamwidth .............................................................................................. 2
2.1.4
Radiation Intensity .................................................................................. 2
2.1.5
Directivity ............................................................................................... 2
2.1.6
Lobe ........................................................................................................ 2
2.1.7
beam (of an antenna) ............................................................................... 3
2.1.8
Gain ......................................................................................................... 3
2.2
HALF WAVE DIPOLE ANTENNA .................................................... 3
2.3
ARRAYS ANTENNA ........................................................................... 4
2.3.1
Introduction ............................................................................................. 4
VI
2.3.2
Arrays Performance ................................................................................ 5
2.3.3
Array element.......................................................................................... 5
2.3.4
Two Element Array................................................................................. 5
2.3.5
Array Factor ............................................................................................ 7
2.3.6
N-ELEMENT LINEAR ARRAY: UNIFORM AMPLITUDE AND
SPACING ............................................................................................................... 8
2.3.6.1
Introduction ....................................................................................... 8
2.3.6.2
Array Factor for Linear Array ........................................................... 9
2.3.6.3
Phased (Scanning) Array ................................................................. 11
2.3.7
PLANAR ARRAY................................................................................ 11
2.3.7.1
Introduction ..................................................................................... 11
2.3.7.2
Array Factor ..................................................................................... 13
2.4
SMART ANTENNA ........................................................................... 15
2.4.1
INTRODUCTUON ............................................................................... 15
2.4.2
Switched beams systems: ...................................................................... 15
2.4.3
Adaptive array systems ......................................................................... 17
2.4.4
Switched beams versus adaptive systems ............................................. 18
2.4.5
Spatial Division Multiple Access (SDMA) .......................................... 20
2.4.6
Smart Antennas Benefits....................................................................... 20
2.4.7
Smart Antennas Drawbacks .................................................................. 21
2.4.8
Design considerations ........................................................................... 21
2.4.9
DSP ....................................................................................................... 22
2.4.10
Beamforming ........................................................................................ 22
2.4.11
Adaptive Beamforming ......................................................................... 22
2.4.12
Mutual Coupling ................................................................................... 22
2.4.13
Optimal Beamforming Techniques ....................................................... 23
2.4.14
DOA ...................................................................................................... 23
CHAPTER THREE METHODOLOGY AND TOOLS25
3.1
Introduction.......................................................................................... 25
3.2
Project Requirements ........................................................................... 26
3.3
Project Strategy.................................................................................... 27
VII
3.4
Matlab tools: ........................................................................................ 27
3.4.1
Introduction ........................................................................................... 27
3.4.2
Key Features ......................................................................................... 28
3.4.3
Computer Performance ......................................................................... 28
3.5
System Architecture ............................................................................ 29
3.6
Simulation story: .................................................................................. 29
3.7
Input parameters: ................................................................................. 30
3.7.1
Carrier Frequency: ................................................................................ 30
3.7.2
The location of the user: ....................................................................... 30
3.7.3
The number of elements in the array: ................................................... 30
3.8
System parameters and Assumptions: ................................................. 30
3.9
Simulation steps: .................................................................................. 32
3.9.1
Code Inputs ........................................................................................... 33
3.9.2
Simulating a user................................................................................... 33
3.9.3
DOA ...................................................................................................... 33
3.9.4
Signal generation .................................................................................. 33
3.9.5
Modulation ............................................................................................ 33
3.9.6
Beamforming ........................................................................................ 34
3.9.7
Transmission: ........................................................................................ 36
3.9.8
Reception: ............................................................................................. 36
3.9.9
Channel ................................................................................................. 36
3.9.10
Demodulation ........................................................................................ 36
3.9.11
Sampling ............................................................................................... 36
3.9.12
BER ....................................................................................................... 36
3.10
Measurements and outputs: ................................................................. 37
3.11
simulation Outputs ............................................................................... 37
3.11.1
Signal Track Line .................................................................................. 38
3.11.2
Array Factor .......................................................................................... 38
3.11.3
DOA For Multiple User/Target Locations ............................................ 38
3.11.4
SIGNAL TO NOISE RATION ............................................................. 38
3.11.5
BER:...................................................................................................... 39
3.11.5.1
Linear array - BER .......................................................................... 39
VIII
3.11.5.2
Planar array - BER ........................................................................... 39
CHAPTER FOUR RESULTS AND DISCUSSION41
4.1
Overview.............................................................................................. 41
4.2
Signal Track Line Test ........................................................................ 41
4.2.1
10 bits Binary Signal Message .............................................................. 41
4.2.2
Modulated Signal .................................................................................. 41
4.2.3
Received Signal .................................................................................... 42
4.2.4
Demodulated Signal .............................................................................. 43
4.2.5
Sampled Signal ..................................................................................... 44
4.3
Array Radiation Pattern ....................................................................... 44
4.4
Array Factor ......................................................................................... 46
4.4.1
Ten Elements Array Factor ................................................................... 46
4.4.2
Five Elements Array Factor .................................................................. 46
4.4.3
Single Element Array Factor ................................................................ 47
4.4.4
Planar Array Factor ............................................................................... 48
4.5
DOA For Multiple User/Target Locations .......................................... 49
4.6
SIGNAL TO NOISE RATIO .............................................................. 49
4.7
BER...................................................................................................... 50
4.7.1
Linear Antenna BER ............................................................................. 51
4.7.1.1
Using Single elements in the array ................................................. 51
4.7.1.2
Using 5 elements in the array .......................................................... 52
4.7.1.3
Using 10 elements in the array ....................................................... 53
4.7.2
Planar Antenna BER ............................................................................. 55
4.7.2.1
Array Factor ..................................................................................... 55
CHAPTER FIVECONCLUSIONS and RECOMMENDATIONS58
5.1
Project review ...................................................................................... 58
5.2
Future Works ....................................................................................... 59
IX
REFRENCES ........................................................................................................... 60
APPENDIX A : MATLAB CODESA-1
APPENDIX B : IEEE DEFINITION STANDARD
X
B-1
LIST OF FIGURES
Figure‎2.1 Radiation Lobs and Beamwidth of an antenna pattern
3
Figure‎2.2 Linear plot of power pattern and its associated lobes and
beamwidth
3
Figure‎2.3 Three dimensional pattern of half wave dipole antenna
4
Figure‎2.4 Triangular array of dipoles used as a sectoral base-station antenna
5
Figure‎2.5 Two dimensional dipoles
6
Figure‎2.6 Geometry of a two-element array positioned along the z-axis. Two
infinitesimal dipoles (left), Far-field observations (right)
7
Figure‎2.7 Pattern multiplication of element (a), array factor (b) and total
array patterns (c) of a two-element array of infinitesimal horizontal dipoles
with  = 90°, d =  /4.
8
Figure‎2.8 Far field geometry of N element array
8
Figure‎2.9 Geometry of linear array
Figure ‎2.10 Geometry of Planar array
12
Figure‎2.11 Planar array , two dimentional elements
13
Figure‎2.12 Switched-beam system .
16
Figure‎2.13 Switched-beam system in a sectorized cell .
16
Figure‎2.14 Adaptive array system Pattern
17
Figure‎2.15 Functional block diagram of an adaptive array system
17
Figure‎2.16 Comparison between (a) switched-beam , and (b) adaptive array
19
Figure‎2.17 Relative coverage area comparison between sectorized systems,
switched-beam systems, and adaptive array systems in (a) low interference
environment, and (b) high interference environment .
19
Figure‎2.18 SDMA multibeam system. there are multible users and each user
has a separate beam.
20
Figure‎2.19 An incoming signal on a two-element array.
24
Figure‎3.2 Performance of Computer when execusion Code
28
Figure‎3.3 Smart antenna communication system.
29
Figure‎3.4 flow chart of Process steps
32
Figure3.5 DOA function.
33
Figure‎3.6 Beamforming Function Diagram
34
XI
Figure‎3.7 Creating the array factor for a linear/Planar array
35
Figure‎4.1 Generated 10 Bits Signal Message
42
Figure‎4.2 Received No Noisy 10 Bits Signal Message
42
Figure‎4.3 Received 10 Bits Noisy Signal
43
Figure‎4.4 Demodulated 10 Bits Signal
43
Figure‎4.5Radiation Pattern of 10 elements array with 5 bits message
44
Figure‎4.6 two Dimensional Plot Radiation Pattern of 5 element
45
Figure‎4.7 two Dimensional Plot Radiation Pattern of 10 element
45
Figure‎4.8 Array Factor of 10 element linear antenna
46
Figure‎4.9 Array Factor of 5 element linear antenna
47
Figure‎4.10 Array Factor of Single element linear antenna
48
Figure‎4.11 Array Factor of 10x10 Planar antenna
48
Figure‎4.12 Graph represent relation between Number of elements and SNRdB
50
Figure‎4.13 effect of number of elements on number of errors
54
Figure‎4.14 Array Factor of Planar Array Antenna
55
Figure‎4.15 Relationship between BER of linear array with 10 elements and
planar array with 2x5 elements.
57
XII
LIST OF TABLES
Table‎3.1 Outputs of Process Step ............................................................................... 37
Table‎4.1 DOA for Multiple Locations ........................................................................ 49
Table‎4.2 Number of elements versus SNR and SNR - dB.......................................... 50
Table‎4.3 Noise and Number of errors using single element ...................................... 51
Table‎4.4 Noise and Number of errors using 5 elements ............................................. 52
Table‎4.5 Noise and Number of errors using 10 elements ........................................... 53
Table‎4.6 Noise and Number of errors using (2 x 5) elements Planar Array ............... 56
XIII
LIST OF SYMBOLS AND ABBREVIATIONS
AF
Array Factor
AWGN
Additive White Gaussian Noise
BER
Bit Error Rate
dB
Decibel
DOA
Direction Of Arrival
DSP
Digital Signal Processing
XIV
INTRODUCTION
CHAPTER ONE
CHAPTER
ONEINTRODUCTION
The development of a truly personal communications space will rely on the design of
next generation wireless systems based on a whole new concept of fast,
reconfigurable networks, supporting features such as high data rates, user mobility,
adaptability to varying network conditions, and integration of a number of wireless
access technologies, and offering new user-centric flexible service paradigms which
make new challenges to the communication venders.
The field of wireless mobile communications is growing at an explosive rate,
covering many technical areas. Its sphere of influence is beyond imagination. The
worldwide activities in this growth industry are perhaps an indication of its
importance. This encouraged research into design of wireless systems in order to
improve spectrum efficiency and increase link quality. Also the Limitation caused by
the antenna system on the cost, quality and performance of the wireless
communication have left the world to develop antenna system which is much more
prominent and efficient in overall performance. The new challenges require the
consideration of certain enabling technologies, such as smart antennas, under new
performance objectives and design constraints.
1.1 PROBLEM STATEMENT
Existing base station antennas in cellular communication are normally Omni
directional. Omni direction antenna radiates its energy in all directions, will results
waste of frequency band because majority of transmitted signal power radiates in
other directions instead of desired user [1]. Signal power radiated throughout the cell
area, that will increase interference and reduce SNR due to undesired users. Although
sector antenna will increase capacity of system by dividing entire cell into sector but
have the same problem of interface.
A Challenge was to provide a new technology in order to provide the expected
beneficial impact on efficient use of the spectrum, minimization of the cost of
1|Page
INTRODUCTION
CHAPTER ONE
establishing new wireless networks, enhancement of the quality of service, and
realization of reconfigurable, robust, and transparent operation under limited
bandwidth provided for Telecom Companies.
1.2 BACKGROUND AND MOTIVATION
It has been shown by many studies that when an array is appropriately used in a
mobile communications system, it helps in improving the system performance by
increasing channel capacity and spectrum efficiency, extending range coverage,
tailoring beam shape, steering multiple beams to track many mobiles, and
compensating aperture distortion electronically. It also reduces multipath fading,
cochannel interferences, system complexity and cost, BER, and outage probability. It
has been argued that adaptive antennas and the algorithms to control them are vital to
a high-capacity communications system development [2][3]
The antenna array may be used together with other methods such as channel
coding,adaptive equalization, and interference cancelling to enhance the system
performance.A particular and important attraction of the use of antenna arrays is in
high data ratewireless communication, such as transmission of high quality video
information. A primary to this high data rate requirement may be the increase in
bandwidth (BW) or the transmit power. However, these solutions are neither cost
efficient nor satisfactory in practice .
A promising approach to achieve these goals is the use of smart antennas at the base
station and the mobile station. In order to take full advantage of these systems,
advanced space-time signal processing techniques need to be developed [3]. A key
aspect is the DOA estimation for the incoming signals. The development of these
techniques is used to enhance the channel's performance. In fact, the system drives the
beam of emission strictly to the receiver, and rejects the interference signals.
1.3 OBJECTIVES

Understanding the concepts of Smart Antenna antennas

Design and simulate these System on MATLAB and Obtain Results.

Design Algorithm That Calculate related user/target position (DOA) .

Design Algorithm that create target directed radiation patterns (beam forming)

Simulate a Communication system Module include message
generation,modulation,Beam Former (Array),Transmitter, Receiver,
demodulation and sampler. It transmit and create pattern in the direction of
2|Page
INTRODUCTION
CHAPTER ONE
DOA and receive message signal as user/target and measure received signal
quality and BER .

Comparing between the performance of Smart antenna system and the
conventional antennas.
1.4 METHODOLOGIES AND TOOLS
The main software used in this project is the MATLAB all results and measured in
MATLAB environment. Starting from developing Functions and algorithms to
simulate the system based on theoretical equations – will be reviewed in chapter 2 ,
then the features extracting also in MATLAB as matrix , 2D and 3D Drawing and
Plotting features . some tests had been simulated under different conditions and
different parameters which analysis was based on .
1.5 REPORT LAYOUT
Hereweintroducetothecontentsandthemaintopicsinthefollowing chaptersinthis thesis.
Chapter 2 (Literature review)
Literaturereviewcontainsabriefdescriptionoftheliteraturerelatedto the
area of
the
work in the
System . it reviews the Definitions , theoretical equations and
components upon which the system based on . review of antennas , arrays and smart
antennas .
Chapter 3 (Methodology and Tools)
inthischapterhowcreatingthealgorithmsisintroduced,howthedatawasprepared
inordertoberecognized,the general structure and operations of the system, including
all assumptions and considerations for the system‗s operation and steps of work and
Simulation.
Chapter 4 (Results and Discussion)
This chapter describes Simulation Results of the system module described in chapter
3, and discusses the results that were obtained performing smart antenna system
parameters as wellasthemechanismbywhichthesystemwastested .
Chapter 5 (Conclusions and recommendations)
This chapter contains conclusions of system performance, meaning of results, Project
Review, Discussions and indicate improvements or further developments that could
be made asFuture Work.
3|Page
INTRODUCTION
Appendix Agives the M-FILE of MATLAB
CHAPTER ONE
contain the Programs used in
simulation.
4|Page
LITERATURE REVIEW
CHAPTER TWO
2 CHAPTERTWO
LITERATURE
REVIEW
2.1 ANTENNA FUNDMENTALS
An antenna (or aerial) , Generally
Represent a transducer of electrical and
electromagnetic energy which converts electric power into radio waves. The IEEE
Standard Definitions of Terms for Antennas (IEEE Std 145–1993) Defines Antenna as
― That part of a transmitting or receiving system that is designed to radiate or to
receive electromagnetic waves‖ .In other words the antenna is the transitional
structure between free-space and a guiding device [4].
2.1.1 Introduction
To get into antenna and its performance , characteristics .some parameters needs to
be difined.they are interrelated and not all of them need be specified for Complete
description of the antenna performance. Parameter definitions will be givenmost of
them based on Internationally well known Standards like
the IEEE Standard
Definitions of Terms for Antennas (IEEE Std 145-1993) , Attached in Appendix
B.∗and the IEEE Std 145-1983.
2.1.2 Radiation pattern:
There are various parameters used to describe the antennas one of them is the
radiation pattern which is definedas The spatial distribution of a quantity that
characterizes the electromagnetic field generated by an antenna. It represents ―a
mathematical function or a graphical representation of the radiation properties of the
antenna as a function of space coordinates[4].
In most cases, the radiation pattern is determined in the far- field region and is
represented as a function of the directional coordinates. Radiation properties include
1|Page
LITERATURE REVIEW
CHAPTER TWO
power flux density, radiation intensity, field strength, directivity, phase or
polarization.‖ The most common property is the spatial distribution of radiated energy
as a function of the observer‘s position along a path or surface of constant radius. So
it is like we take probe and circle the antenna at a specific radius.When the amplitude
or relative amplitude of a specified component of the electric field vector is plotted
graphically, it is called an amplitude pattern, field pattern, or voltage pattern. When
the square of the amplitude or relative amplitudes plotted, it is called a power
pattern.[5]
2.1.3 Beamwidth
half-power beam width. cut in a radiation pattern containing the direction of the
maximum of a lobe,the angle between the two directions in which the radiation
intensity is one-half the maximum value.[4]
2.1.4 Radiation Intensity
In a given direction, the power radiated from an antenna per unit solid angle .[4]
2.1.5 Directivity
―the ratio of the radiation intensity in a given direction from the antenna to the
radiation intensity averaged over all directions[4]. The average radiation intensity is
equal to the total power radiated by the antenna divided by 4π. If the direction is not
specified, the direction of maximum radiation intensity is implied.‖
2.1.6 Lobe
Various parts of a radiation pattern are referred to as lobes, which may be sub
classifiedintomajor or main, minor, side, andback lobes as shown in Figure
2.1demonstrates a symmetrical three dimensionalpolar pattern with a number of
radiation lobes.A radiation lobe is a ―portion of the radiation pattern bounded by
regions ofrelatively weak radiation intensity.‖ [4] .
2|Page
LITERATURE REVIEW
Figure
2.1Radiation
CHAPTER TWO
Lobs
and
Beamwidth
of
an
antenna
pattern
2.1.7 beam (of an antenna)
The major lobe of the radiation pattern of an antenna. Indicated in good forum in
Figure 2.2
Figure 2.2Linear plot of power pattern and its associated lobes and beamwidth
2.1.8 Gain
is The ratio of the radiation intensity, in a given direction, to the radiation intensity
thatwould be obtained if the power accepted by the antenna were radiated
isotropically. i.e absolute gain (of an antenna).
- The radiation intensity corresponding to the isotropically radiated power is equal to
the power accepted by theantenna divided by 4  .If an antenna is without dissipative
loss, then in any given direction, its gain is equal to its directivity.[4]
2.2 HALF WAVE DIPOLE ANTENNA
A half wavelength antenna,center fed so as to have equal current distribution in both
halves. Mounted vertically, it has a doughnut shapedpattern, circular in the horizontal
plane. It is an antennathat can be constructed. It has some inherent losses.When used
3|Page
LITERATURE REVIEW
CHAPTER TWO
as a gain reference, the half-wave dipole hasa power gain of about 1.7 dBi. A wire
antenna consisting of two straight collinear conductors of equal length, separatedby a
small feeding gap, with each conductor approximately a quarter-wavelength long.
This antenna gets its name from the fact that its overall length is approximately a halfwavelength.Figure 2.3 represent a half wave dipole antenna . In practice,the length is
usually slightly smaller than a half-wavelength—enough to cause the input impedance
to be pure real (jX =0)
Due to its Radiation Resistance (73 ohms) which very near to the 50-ohm or 75ohmcharacteristic impedances of some transmission lines,the half-wavelength (l =
λ/2) dipole antenna considered One of the most commonly used antennas. which its
matching to the line is simplified especially at resonance.[5].
Figure 2.3 Three dimensional pattern of half wave dipole antenna
2.3 ARRAYS ANTENNA
2.3.1 Introduction
Usually the radiation pattern of a single element is relativelywide, and each element
provides low values of directivity (gain). In many applicationsit is necessary to design
antennas with very directive characteristics (very high gains)to meet the demands of
long distance communication.A modified method that we could use to Increase the
antenna radiating and directivity characteristics are by making assembling more than
one radiating antenna elements together in such electrical and geometrical
configuration way . with out increasing size of the individual antenna , which lead to
more directive radiating.this new multi-element antenna known as array antenna
(often called a 'phased array')which define by by IEEE Standards as antenna
comprised of a number of identical radiating elements in a regular arrangementand
excited to obtain a prescribed radiation pattern .[4][5]
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Figure 2.4 indicates an array that is widely used as a base-stationantenna for mobile
communication. It is a triangular array consisting of twelve dipoles,with four dipoles
oneach side of the triangle.
Figure 2.4 Triangular array of dipoles used as a sectoral base-station antenna
for mobile communication.
2.3.2 Arrays Performance
The signals from the antennas are combined or processed in order to achieve
improved performance over that of a single antenna. To provide very directive
patterns, it is necessary that the fields from the elements of the array interfere
constructively in the desired directions and interfere destructively (cancel each other)
in the remaining space. The antenna array can be used to determine the direction of
arrival of the incoming signals and to maximize the Signal to Interference Plus Noise
Ratio (SINR)
2.3.3 Array element
In an array antenna, a single radiating element or a convenient grouping of
radiatingelements that have fixed relative excitations, this is single Radiating antenna
.
2.3.4 Two Element Array
By taking two element array , which means the array consisting of 2 identical
infinitesimalhorizontal dipoles antennas with equal distance between them positioned
along the z-axis . Figure 2.5 shows The totalfield radiated by the two elements,
assuming no coupling between the elements, isequal to the sum of the two and in the
y-z plane it is given by
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LITERATURE REVIEW
Et  E1  E2  a j
CHAPTER TWO
 j  kr   /2 
 j  kr   /2 
kI 0l  e  1   cos 1 e  2   cos  2 



4 
r1
r2

(2.1)
1   2  
for phase variations
(2.2)
d

cos  

2

d
r2  r  cos  

2
r1  r 
Figure 2.5Two dimensional dipolesGeometry of a two-element array positioned
along the z-axis
kI 0l e  jkr1  cos 1  j kd cos    /2  j kd cos    /2
e
e
4
r
kI 0l e  jkr1  cos 1 
1

Et  a j
2 cos   kd cos        
4
r
2


Et  a j


(2.3)
It is clear from (2.3) that the total field of the array is equal to the product of the field
of a single element positioned at the origin and a factor which is known as the array
factor. This property is referred to as pattern multiplication for arrays of identical
elements, although it has been illustrated only for an array of two elements, each of
identical magnitude, it is also valid for arrays with any number of identical elements
which do not necessarily have identical magnitudes, phases, and/or spacing between
them .
the arrayfactor is givenby(2.4) :
1

AF  2 cos   kd cos       
2

(2.4)
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2.3.5 Array Factor
The array factor is a function of the geometry of the array and the excitation phase.
By varying the separation d and/or the phase  between the elements, the
characteristics of the array factor and of the total field of the array can be controlled.
Figure 2.6Geometry of a two-element array positioned along the z-axis. Two
infinitesimal dipoles (left), Far-field observations (right).
Each array has its own array factor. The array factor, in general, is a function of the
number of elements, their geometrical arrangement, their relative magnitudes, their
relative phases, and their spacing. The array factor will be of simpler form if the
elements have identical amplitudes, phases, and spacing. Sincethe array factor does
not depend on the directional characteristics of the radiating elements themselves,
itcan be formulated by replacing the actual elements with isotropic (point) sources.
Once the array factorhas been derived using the point-source array, the total field of
the actual array is obtained by the use of(2.5) .
E (total )  [E(single element at reference point)] x [array factor]
(2.5)
Each point-source is assumed to have the amplitude, phase, and location of the
corresponding
element it is replacing.In order to synthesize the total pattern of an array, the designer
is not only required to select the properradiating elements but the geometry
(positioning) and excitation of the individual elements. To illustratethe principles, in
an example of pattern multiplication is showed [6].
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CHAPTER TWO
Figure 2.7 Pattern multiplication of element (a), array factor (b) and total array
patterns (c) of a two-element array of infinitesimal horizontal dipoles with  =
90°, d =  /4.
2.3.6 N-ELEMENT LINEAR ARRAY: UNIFORM AMPLITUDE
AND SPACING
2.3.6.1 Introduction
Now that the arraying of elements has been introduced and it was illustrated by
thetwo-element array, let us generalize the method to include N elements. Referring to
thegeometry of Figure 2.8 , let us assume that all the elements have identical
amplitudesbut each succeeding element has a β progressive phase lead current
excitation relativeto the preceding one (β represents the phase by which the current in
each element leadsthe current of the preceding element). An array of identical
elements all of identicalmagnitude and each with a progressive phase is referred to as
a uniform array.
Figure 2.8 Far field geometry of N element arraywhen isotropic source
positioned along z axis
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CHAPTER TWO
2.3.6.2 Array Factor for Linear Array
Thearray factor can be obtained by considering the elements to be point sources. If
theactual elements are not isotropic sources, the total field can be formed by
multiplyingthe array factor of the isotropic sources by the field of a single element.
This is thepattern multiplication rule of (6-5), and it applies only for arrays of
identical elements.The array factor is given by :
AF  1  e j ( kd cos   )  e2 j ( kd cos   )  ...  e j ( N 1)( kd cos   )
N
AF   e j ( n 1)( kd cos   )
(2.6)
n 1
Which can be written as :
N
AF   e j ( n 1)
n 1
(2.7)
where,  kd cos   
It is apparent from the phasor diagram that the amplitude and phase of the AF can be
controlled in uniform arrays by properly selectingthe relative phase  between the
elements; in nonuniform arrays, the amplitude aswell as the phase can be used to
control the formation and distribution of the totalarray factor.
Since the total array factor for the uniform array is a summation of exponentials,it
canbe represented by the vector sum of N phasors each of unit amplitude
andprogressive phase ψ relative to the previous one.. the amplitudeand phase of the
AF can be controlled in uniform arrays by properly selectingthe relative phase ψ
between the elements; however in nonuniform arrays, the amplitude asThe array
factor of (2.7)canalso be expressed in an alternate, compact and closedform whose
functions and their distributions are more recognizable. This is accomplishedas
follows.
Multiplying both sides of (2.7) .by e j , it canbe written as
( AF )e j  e j  e j 2  e j 3  ...  e j ( N 1)  e jN
(2.8)
Subtracting(2.7) from(2.8) reduces to
AF (e j  1)  (1  e jN )
(2.9)
which can also be written as
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j ( N /2)
 e jN  1 
 e  j ( N /2) 
j  ( N 1)/2  e
AF   j

e

 e j (1/2)  e j (1/2) 
 e 1 


N 

sin(  ) 

j ( N 1)/2
2
e 


1
 sin(  ) 

2

(2.10)
If the reference point is the physical center of the array, the array factor of(2.10)
reduces to
 AF n
N 

 sin( 2  ) 

1 
 sin(  ) 

2 
(2.11)
For small values of  , the expression can be approximated by
 AF n
N 

 sin( 2  ) 






2

(2.12)
To find the nulls of the array, (2.11) or (2.12) is set equal to zero. That is,
N
N
sin(  )  0 
2
2
 0
  
2n  
  n   n  cos 1 
    
N 
 2 d 
(2.13)
n  1, 2,3,...
n  N , 2 N ,3N ,...
For n = N, 2N, 3N, . . ., (2.11)attains its maximum values because it reduces to
asin(0)/0 form. The values of n determine the order of the nulls (first, second, etc.).
Fora zero to exist, the argument of the arccosine cannot exceed unity. Thus the
numberof nulls that can exist will be a function of the element separation d and the
phaseexcitation difference β. The maximum values of (2.11)occur when

2

1
(kd cos    )
2
 0
 

  m  cos 1 
(   2m ) 
 2 d

(2.14)
m  0,1, 2,...
The array factor of (2.15)has only one maximum and occurs when m = 0 in (2.14)
That is,
  

 2 d 
 m  cos 1 
(2.15)
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which is the observation angle that makes  = 0.
2.3.6.3 Phased (Scanning) Array
As we could control and direct the major radiation from an array by changing and
controlling the phase excitation between the elements . It is then logical to assume
that the maximum radiation can be oriented in any direction to form a scanning array.
The angle between the direction of the maximum of the major lobe or a directional
null and a reference directioncalled Scan angleor beam angle.The reference bore sight
is usually chosen as the reference direction . Let us assume that the maximum
radiation of the array is required to be oriented at an angle 𝜃0(0◦≤𝜃0 ≤180◦).To
accomplish this, the phase excitation  between theelements must be adjusted so that
  kd cos  
 0
 kd cos 0    0    kd cos 0 (2.16)
So we could form a scanning array by controlling the phase difference between the
elements which lead to direct the maximum radiation in any desired direction .
this represent the basic principle of the scanning phased array .
2.3.7 PLANAR ARRAY
2.3.7.1 Introduction
Until now we were dealing with one dimensional linear array , which elements placed
along a lineto form a linear array as in, however individual radiators can be
positionedalong a rectangular grid to form a rectangular or planar array as shown
inFigure 2.10
alsoFigure 2.11 indicates a planar array with a vertical and horizontal crossed
antenna element shape with equal spaces between them .IEEE Standard for
definitions Defines Planar array as A two-dimensional array of elements whose
corresponding points lie in a plane.
Planararrays provide additional variables which can be used to control and shape the
pattern ofthe array. Planar arrays are more versatile and can provide more
symmetrical patternswith lower side lobes. Inaddition , they can be used to scan the
main beam of theantenna toward any point in space , it plays main part in Smart
antennastechnology as two dimensional antennas system . Applications include
tracking radar, search radar,remote sensing, communications, and many others.[1][3]
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Figure 2.9 Geometry of linear array
Figure 2.10 Geometry of Planar array
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Figure 2.11 Planar array , two dimentional elements
2.3.7.2 Array Factor
To get the array factor of such two dimentional array ,assume we have a planar array
has M elements are initially placed along the x-axis of Figure 2.10, a distance dx apart
and with a progressive phase βx . along with N arrays placed next to each other in the
y-direction, a distance dy apart and with a progressive phase βy , a rectangular array
will be formed as shown in Figure 2.10The array factor for the entire planar array can
be written as which consist of both M,N Array Factors :
M
 j ( n1)( kd y sin sin    y )
AF   I1n  I m1e j ( m1)( kd x sin cos   x )  e
i 1
 i 1

N
(2.17)
AF  S xm S yn
or
(2.18)
where
M
S xm   I1m e j ( m 1)( kd x sin  cos   x )
m 1
(2.19)
N
S yn   I1n e
j ( n 1)( kd y sin  sin    y )
n 1
(2.20)
Equation(2.18)indicates that the pattern of a rectangular array is the product of
thearray factors of the arrays inthe x- an dy-directions.If the amplitude excitation
coefficients of the elements of the array in the y-directionare proportional to those
along the x, the amplitude of the (m, n)th element can bewrittenas:
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I mn  I m1 I1n (2.21)
When the amplitude of the entire array is uniform ( I 0 ) , the equation could be
expressed as
M
N
m 1
n 1
AF  I 0  e j ( m 1)( kd x sin cos   x )   e
j ( n 1)( kd y sin  sin    y )
(2.22)
Based on previous equations,The normalized form would be :



M
N


sin(

)
sin(

)
 1
x  1
y


2
2
AFn ( ,  )  


 M sin   x    N sin   y  
 

 2   
 2 
where
 x  kd x sin  cos    x
(2.23)
 y  kd y sin  sin    y
The phases βx and βy are independent of each other, and they can be adjusted sothat
the mainbeam of Sxm is not the same as that of Syn. However, inmost
practicalapplications it is required that the conical main beams of Sxm and Syn
intersect and theirmaxima be directed toward the same direction. If it is desired to
have only one mainbeam that is directed along θ = θ0 and φ =  0 , the progressive
phase shift betweenthe elements in the x- andy-directions must be equal to:
 x  kd x sin  0 cos 0
 y  kd y sin  0 sin 0
(2.24)
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2.4 SMART ANTENNA
2.4.1 INTRODUCTUON
Smart antenna systems uses antenna array in conjunction with a digital signal
processor located at the base station responsible for adjusting various system
parameters to filter out any interferers or signals-not-of-interest (SNOI) while
enhancing desired communication or signals-of-interest (SOI). Thus, the system
forms the radiation pattern in an adaptive manner, responding dynamically to the
signal environment and its alterations [7]. Smart-antenna systems are basically an
extension of cell sectoring in which the sector coverage is composed of multiple
beams .
Smart antennas can focus their radiation pattern towards the desired users while
rejecting unwanted interferences, they can provide greatercoverage area for each base
station. Moreover, because smart antennas have a higherrejection interference, and
therefore lower bit error rate (BER), they can provide asubstantial capacity
improvement .There are two major configurations of smart antennas: Switched-Beam
and Adaptive Array systems.
2.4.2 Switched beams systems:
Switched-beam system is a system that has a set of many predefined patterns. First it
detects the signal strength then it chooses one of these predetermined fixed beams, if
the cellular phone moves throughout the sector, the system switches from one beam to
another beam[6] [5] as illustrated in Figure 2.12.
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Figure 2.12Switched-beam system [7]
Switched beam or switched lobe antennas can be directional antennas deployed at the
cells base stations. There only function is to switch between separate directive
antennas or predefined beams of an array. The configuration that gives the best
performance, usually in terms of received power, is chosen [3]. The outputs of the
various elements are sampled periodically to determine which has the best reception
beam.
Switched beam is an extension of the cellular sectorization method in which a cell is
divided to three sectors each has 120-degree macro-sectors. The switched beam
approach further subdivides macro-sectors into several micro-sectors thus improving
range and capacity. Each micro-sector contains a predetermined fixed beam pattern
with the greatest sensitivity located in the center of the beam and less sensitivity
elsewhere as illustrated inFigure 2.13
Figure 2.13 Switched-beam system in a sectorzed cell [5].
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2.4.3 Adaptive array systems
Adaptive array systems customize an appropriate radiation pattern for each individual
user; it consists of a set of antenna elements that can adapt their antenna pattern to
changes in their environment. Each antenna of the array is associated with a weight
that is adaptively updated so that the overall gain in the desired direction is
maximized, while that in a direction corresponding to interfering signals is
minimized. Figure 2.12illustrates the general idea of adaptive antenna system.
Figure 2.14 Adaptive array system Patterndirects the main lobe of the
radiation pattern toward theuser and direct nulls toward co-channel interferers
[7]
Adaptive array systems can locate and track the signals of users (SOI) and interferers
(SNOI) and dynamically adjust the antenna pattern to enhance reception while
minimizing interference using signal-processing algorithms.Illustrates a functional
block of this system , as shown Figure 2.15shows that the system down converts the
received signals to baseband and digitizes them, it then locates the SOI using the
direction-of-arrival (DOA) algorithm, and it continuously tracks the SOI and SNOI
[5].
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Figure 2.15Functional block diagram of an adaptive array system
2.4.4 Switched beams versus adaptive systems
Both types of smart antenna systems provide significant gains over conventional
systems and thus increased signal strength and performance and increased coverage
area.The problem with switched beams systems is they have fixed beams, so the
intended user may not be in the center of any given main beam and in this case he will
get a reduced gain while in adaptive scheme the maximum gain is in the direction of
the
user
as
illustrated
in
Figure
2.16
.
.
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Figure 2.16Comparison between (a) switched-beam scheme, and (b) adaptive
array scheme showing that adaptive scheme can direct the beam at the user and
null the interferers while switched scheme cannot [5].
Adaptive array systems has less interference levels because they can tune down the
interference but switched beams systems cannot and if there is an interferer near the
center of the active beam is switched beam, the system will increase the interfering
signal more than the desired signal [1]
this leads to adaptive array to have larger coverage area as illustrated inFigure 2.17
Figure 2.17 Relative coverage area comparison between sectorized
systems, switched-beam systems, and adaptive array systems in (a)
low interference environment, and (b) high interference environment
[5].
Adaptive arrays require intensive digital-processing and a complete RF portion of the
transceiver behind each antenna element; therefore they are more expensive than
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switched-beam systems plus switched-beam are easier to implement in existing cell
structures.
2.4.5 Spatial Division Multiple Access (SDMA)
SDMA used advanced spatial-processing capability to locate many users and create a
different beam for each user, as shown inFigure 2.18. Thisis the ultimate goal in the
development of cellular radio systems because it means that more than one user can
be allocated to the same frequency in the same cell [5].
Figure 2.18 SDMA multibeam system. there are multible users and
each user has a separate beam[5].
2.4.6 Smart AntennasBenefits
Capacity increase: the main reason for the growing interest in smart antennas. In
densely populated areas the mobile systems are normally interference-limited,
meaning that interference from other users is the main source of noise in the system
(low SIR)
.since Smart antennas can lower the interference level, increase the SIR it will enable
more users to be serviced. Especially, the adaptive array will give a significant
improvement. Experimental results report up to 10 dB increases in average SIR in
urban areas.[5],[8]
Range Increase:smart antennas can focus their energy toward the intended users,
instead of wasting energy in unnecessary directions like conventional omnidirectional
antennas. thus they can reach further distance, This means that base stations can be
placed further apart, leading to less stations and less cost. This is helpful in rural and
sparsely populated areas, where radio coverage range is more important than capacity.
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Security: Smart antennas make it more difficult to tap a connection because the
intruder must be positioned in the same direction as the user from the base station to
receive the signal and tap the connection.
Locating users: the direction of arrival algorithms can be used to locate humans in
emergencies or for any other location-specific service.[5]
2.4.7 Smart AntennasDrawbacks
The main drawback of smart antenna is their highcost because their transceivers are
much more complex than traditional base station transceivers. The antenna needs
separate transceiver chains for each array antenna element and accurate real-time
calibration for each of them .
Moreover, the antenna beam forming and DOA is computationally intensive, which
requires very powerful digital signal processors. This also increases the system costs
in the short term.[5]
2.4.8 Design considerations
Number of elements:Increasing the number of array elements gives a narrower
beamwidth thus the signals-of-interest (SOIs) can be defined more accurately and the
smart-antenna system to reject more signals-not-of-interest (SNOIs). However there
are two disadvantages. One disadvantage is that more antennas increases the cost and
the complexity of the system, and the other is that it increases the convergence time
for the adaptive algorithms, thereby reducing valuable bandwidth.
Array configuration:The planar array configuration is more suited for mobile
communication. The linear array configuration is not as attractive because of its
inability to scan in 3-D space, while planar array can scan the main beam in any
direction of φ (azimuth) and θ (elevation).
Single element type:the type of the single element in an array is very important in
the overall radiation pattern. An array of printed elements can be used as a single
element because they meet the requirements and capabilities of a mobile
communication. There are a number of printed element geometries, patches as they
are usually referred to The two most popular are the rectangular, and the circular,
discussed in . Such an array possesses the attributes to provide the necessary
bandwidth, scanning capabilities, beamwidth, and side lobe level. Furthermore, it is a
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low-cost technology suitable for commercial products, in addition to being
lightweight and conformal to surfaces [5].
2.4.9 DSP
Digital Signal Processing ,It‘s the part of smart antenna system that acctully make the
system behave smart . depending on processor speed of execusiotn , system
paerformance been measured . logically , DSP contains algorithims that been
performed in the system , Like the Beamforming and DOA .
2.4.10 Beamforming
The purpose of a smart antenna is to dynamically direct main beam of the radiation
pattern toward the user of interest, and null it in the direction of interferers. This is
accomplished by adjusting the weights of antennaarray elements.[5]. Therefore there
are two functions of an antenna :
1-
Calculating the direction of arrival of the user signal.
2-
Applying the specific wights to its elements to direct the beam of the antenna
in the desired direction (beamforming).
To achieve these objectives the smart antenna systems make use of antenna arrays.
The basic idea of antenna arrays is using several antennas and adjusting their weights
so that the radiation of these elements interacts constructively in the desired direction
and destructively in the undesired directions.
2.4.11 Adaptive Beamforming
Using the information supplied by the DOA algorithm, the adaptive Beamforming
algorithm computes the appropriate complex weights to direct the maximum radiation
of the antenna pattern toward the SOI and places nulls toward the SNOIs. There are
several general adaptive algorithms used for smart antennas [2] such as DMI
,LMS…etc; and they are typically characterized in terms of their convergence
properties and computational complexity.
2.4.12 Mutual Coupling
When the radiating elements in the array are in the vicinity of each other, the radiation
characteristics, such as the impedance and radiation pattern, of an excited antenna
element is influenced by the presence of the others. This effect is known as mutual
coupling, [1]. Mutual coupling usually causes the maximum and nulls of the radiation
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CHAPTER TWO
pattern to shift; therefore it must be taken into account or the system will be sending
in a wrong direction.
2.4.13 Optimal Beamforming Techniques
The array system is said to be employing an optimal beamforming when the gain and
the phase of the signal induced on each element are adjusted to achieve the maximum
output SNR (sometimes also referred to as signal to interference and noise ratio,
SINR).Optimal beamforming techniques defines a cost function that is related to one
or more performance measures, the techniques chooses the weight vector that
minimizes a cost function; the cost function is usually inversely associated with the
quality of the signal at the array output so when the cost function is minimized, the
quality of the signal is maximized.[5],[8]
2.4.14 DOA
The DOA ―Direction of Arrival ‖algorithm attempts to determine the direction of the
user directions based on the time delays; it is a very crucial part since the accuracy of
the overall system depends on the accuracy of the DOA algorithm.
Consider that we have two antennas in an array separated by a distance d and a user
at a far distance, When the user transmits the signal it will reach the two antennas at
different times because they are at different distances from the user. The time
difference can be used with the aid of simple geometry to determine the direction of
the user.
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CHAPTER TWO
Figure 2.19An incoming signal on a two-element array.
Thetime delay of the signal s (t) at the Second element compared to the first element
is given by:
𝛥𝑡 = 𝑡1 − 𝑡2 =
𝛥𝑑
𝑣𝑜
[2.26]
Where 𝑣𝑜 represent the speed of light in free-space represent and 𝛥𝑑 is the
differential distance between the two elements according to the signal. From Figure
2.19𝛥𝑑 is given by:
𝛥𝑑 = 𝑑 ∗ 𝑐𝑜𝑠𝜃
[2.27]
And the time difference becomes:
𝛥𝑡 =
𝑑 ∗ 𝑐𝑜𝑠𝜃
𝑣𝑜
[2.30]
And the angle of the user can be defined by:
𝑣𝑜
𝑣𝑜
𝛩 = cos−1
∗ 𝛥𝑡 = cos−1
∗ (𝑡1 − 𝑡2)
𝑑
𝑑
[2.31]
Conventional methods of DOA estimation are are based on the concepts of
beamforming and null steering and do not exploit the statistics of the received signal
examples of these conventional methods are the delay-and-sum method (classical
beamformer method or Fourier method) and Capon‘s minimum variance method.[5]
Unlike conventional methods, subspace methods exploit the structure of the received
data, resulting in a dramatic improvement in resolution. Such as the MultipleSignal
Classification (MUSIC) algorithm and the Estimation of Signal Parameters via
Rotational Invariance Technique (ESPRIT) and there are many more DOA algorithms
not exploited. based on fact that by modifying the algorithm – software part – of the
Digital signal Process unit in the smart antenna system we can enhance system
performance , so it would be possible to have different type of algorithms
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CHAPTER THREE
3CHAPTER THREEMETHODOLOGY AND TOOLS
3.1 INTRODUCTION
In this chapter, a methodology of simulating a communication system that uses smart
antenna using MATLAB had been illustrated. To reduce costs and risks, and to
improve the performance of the arrays, we use simulations. These simulations must
meet certain criteria: They have to be fast and determine the parameters of
performance accurately. Because of the need to design antenna arrays and the current
reliance on expensive programs, it was decided to create an own tool to obtain reliable
results and access the program code to modify the design variables and made
optimization.
The system includes Transmitter of Signal Message, Modulator for the Signal, Beam
former, Transmission Channel, Receiver and Demodulator.A simple modulator and
demodulator, transmitter, receiver, channel, DOA algorithms and a beam forming
algorithm were designed.
Different tests of common antenna arrays like linear array antenna and planar array
antenna and comparing between smart antenna performance and single elements
antenna , also overall system performance had been inspected along with changing
some parameters in the system.
The simulation is divided into simple steps to facilitate easy understanding and also
making it flexible as the person can make any changes in any step without having to
change the other steps (eg: if the person performing the simulation wants to work with
other modulation type he must change the modulation part of the code only).
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3.2 PROJECT REQUIREMENTS

The main goal is to provide a step by step simulation process of a
complete communication system that contains a source, Transmitter,
Modulator, Transmission Channel, Demodulator and a Receive.

Track the signal and give a representation of the signal after each step.

create an array factor that maximizes the radiation towards the user.

Showing the improvement of using smart antennas over conventional
antennas (single element) by comparing the performance of both.

Inspecting the effect of changing the number of elements in the
antenna array.

the system must be capable of measuring the users location (DOA).

Comparing the received message with the transmitted message and
calculating the BER.

The
measurements were derived for different number of array
elements and configurations to facilitate easy comparison between
them.
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CHAPTER THREE
3.3 PROJECT STRATEGY
BEGIN

The Characteristics and Fundamentals
of Antenna

Arrays Antenna.

Similar Researches.

Smart Antennas in Industry.

Theory

DOA

Beamforming

Scannar Arrays

Planar Arrays
Test Simulation and


.. etc
Number of Elements
Parameters

Number of Bits

Noise Power

DOA Angle

SNR

BER
Study and
Research
Analyze The Results
Figure 3.1Flow Diagram of Project Strategy
3.4 MATLAB TOOLS:
3.4.1 Introduction
MATLAB is a programming environment for algorithm development, data analysis,
visualization, and numerical computation. Using MATLAB, technical computing
problems could be solved faster than traditional programming languages, such as C,
C++, and Fortran.
MATLAB can be used in a wide range of applications, including signal and image
processing, communications, control design, test and measurement, financial
modelling and analysis, and computational biology. For a million engineers and
scientists in industry and academia, MATLAB is the language of technical
computing.
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The MATLAB tool for analysis and design of linear and planar antenna arrays is
directed to simulate system to manipulate the input data for proper execution ofthe
larger more comprehensive analysis program. Even though this tool is small in core
requirements ,it is fast in run time, it is capable of analyzing structures to assist the
engineer with design problems.
3.4.2 Key Features
•High-level language for technical computing
•Development environment for managing code, files, and data
•Interactive tools for iterative exploration, design, and problem solving
•Mathematical functions for linear algebra, statistics, Fourier analysis, filtering,
optimization, and numerical integration
•2-D and 3-D graphics functions for visualizing data .
•Tools for building custom graphical user interfaces.
3.4.3 Computer Performance
During execution of project (the Simulation)
the Performance of the code on
Computer as follow
:
Figure 3.2 Performance of Computer when execusion Code
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
CHAPTER THREE
Physical Memory (MB) : Total 3873

cached 1140

available 2098

free 1060

CPU Usage : 37%

Processes 91

Physical Memory 45%(1.73) GB
3.5 SYSTEM ARCHITECTURE
For simulation purposes system was divided into the following Structure shown
inFigure 3.3.based on Communication systems. Its Structure contains a Transmitter
of Signal Message, Modulator for the Signal, Beam former, Transmission Channel,
Receiver and Demodulator.
Figure 3.3 Smart antenna communication system.
3.6 SIMULATION STORY:
Taking normal cellular networks, when user first turn on his receiver ―mobile station‖
it start to have a coverage signal from nearby base station. These base stations records
data about the user signal , position and so on . Based on equations mentioned in
chapter two , and using these data , an algorithm had been developed by us for this
smart antenna simulation . it would calculate the Direction of Arrival of the user and
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CHAPTER THREE
using this angle for creating the Directional Pattern used to transmit data to the mobile
station .
When execution the simulation, the user – who perform the simulation, had to input
parameters required by the simulation by its Interface.Thus, depending on which
parameters had been chosen , the simulation environment change and it gives
different results .
At the end of the execution , the simulation give figures and results of the Created
pattern , Array Factor , The Transmitted and Received Message along with the effect
of Noise and compare of quality of the received signal by calculating BER . This
results gives clear analysis of system performance under these chosen parameters.
3.7 INPUT PARAMETERS:
The simulation code asks the user to insert the following parameters:
3.7.1 Carrier Frequency:
―2 GHZ‖ frequency had been used as carrier frequency in this simulated system , as
it‘s closed commonly used frequency in cellular networks (as in 3G Networks) for
data transmission.
3.7.2 The location of the user:
The simulator has the ability to choose the location of the user to be simulated; this
enable the simulator to choose the desired location and compare the results with the
theoretical results.
3.7.3 The number of elements in the array:
The user can choose the desired number of the arrays that is under study.
3.8 SYSTEM PARAMETERS AND ASSUMPTIONS:
-
Array geometry: The geometry of the array is chosen to be linear at the
first two tests and planar at the third test.
-
Type of Transmission: ―antenna half wave‖ dipoles antenna had been used
to transmit the signal.
-
Spacing between array’s element :A one quarter of the Wavelength had
been used in this system as Spacing between array‘s elements
-
Amplifier: Amplification of 10 times had been used, as averaged value.
-
Type of receiver antenna: Half wave dipoles antenna had been used to
receive the signal.
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-
CHAPTER THREE
Noise: the effect of the channel is considered to be an additive white noise
because the band is narrow in a typical cellular communication system (5
MHZ)
-
Modulation type: BPSK: Binary Phase Shift Keying Type of Modulation
had been used to modulate the signal.
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3.9 SIMULATION STEPS:
The simulation code was divided into several steps to help organize as shown in the
Flow Chart Figure 3.3
Begin
ACCEPT INPUTS
SIMULATING A USER
DOA
GENERATING A MESSAGE
MODULATING MESSAGE
SIGNAL
BEAMFORMING
TRANSMISSION
RECEPTION Of MESSAGE
DEMODULATION
SAMPLING
MEASURE THE BER
END
Figure 3.4 flow chart of Process steps
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3.9.1 Code Inputs
Upon stating the simulation code the user interface will ask the user to insert the
following parameters:The frequency of operation , The location of the user ,The
number of elements in the array .
3.9.2 Simulating a user
After initiating system simulation the simulator simulate a user (mobile station
receiver) at the location inserted to it. The program calculates the time the user‘s
signal reaches the first antenna and the time it reaches the second antenna that will be
needed for DOA estimation.
3.9.3 DOA
A function named ‗DOA‘ was programed that simulates the DOA algorithm. The
function receives the reception time of two elements (antennas) and the distance
between them from the main program.
The algorithm used in this simulation based on time delay algorithm mentioned in
section
. Which locate User Position based on the difference in Signal arriving
time between two array elements. The algorithm calculate DOA using equation
and the returns the angle of the user (DOA).the DOA function is illustrated in Figure
3.5
RECEIVE THE
MEASURE THE
RETURN THE
TIMES AND THE
ANGLE OF THE
ANGLE OF THE
SPACING
USER
USER
Figure 3.5 DOA function.
3.9.4 Signal generation
The simulator must generate string of bits that represent the message to be sent to the
user. The length of this string varied during the project.
3.9.5 Modulation
A function named ―modu‖ was programmed to perform the Modulation which
receives the binary signal (message) and the carrier frequency then it uses this binary
message to modulate a carrier (at carrier frequency) and outputs a BPSK modulated
signal. The function also draws the modulated signal versus time.
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3.9.6 Beamforming
Beamforming is the most important part for implementing such a system. A
beamforming algorithm was designed for the code. It checks the angle of the user
(determined by the DOA algorithm), the geometry of the array (linear of planar) and
the spacing between elements.
Next, it defines the phase shift between the elements required to create beam towards
the user, using algorithm based on the equations in chapter 2. Then the Program code
Create the Array Factor for the antenna Array used in the bearmformer as shown in
Figure 3.6.
.
Figure 3.6 Beamforming Function Diagram
If the geometry of the array is linear the beamforming algorithms will shape the array
factor using equation in chapter two .
If the array is planar (N1 x N2) then the beamforming treats it as an array of linear
arrays and multiply the array factor of N1 linear array with N2 linear array.
How code process in creating the array factor shown inFigure 3.7 , The final result of
this step is the array factor with a maximum towards the DOA. Also a 3- dimension
drawing of the array factor is generated.
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BEGIN
RECIEVES THE DOA
EXAMINES THE ARRAY
GEOMETRY
ARRAY
GEOMETRY
CREATE ARRAY OF LINEAR
ARRAYS
CREATE AN ARRAY FACTOR IN
CREAT AN ARRAY FACTOR IN
CREAT AN ARRAY
VAI DIRECTION FOR N2 LINEAR
THETA DIRECTION FOR N1
FACTOR IN THETA
ARRAY
LINEAR ARRAY
DIRECTION
MULTIPLY THE ARRAY FACTOR OF
BOTH TWO LINEAR ARRAYS
DRAW THE ARRAY FACTOR
DRAW THE ARRAY FACTOR
END
Figure 3.7 Creating the array factor for a linear/Planar array
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3.9.7 Transmission:
In this step the modulated signal is transformed into an electric field using a half wave
dipole antenna and transmitted through the channel (wireless Channel).This electric
field is the electric field of a single element it is then multiplied by the array factor
(generated in the beamforming step) to represent the effect of the array.
3.9.8 Reception:
The electric field is transferred into an electric signal at the receiver using a half wave
dipole receiver.
3.9.9 Channel
The effect of the channel is added in terms of noise power. A function named AWGN
is available in MATLAB which adds a white Gaussian noise to the signal.
3.9.10 Demodulation
The Demodulation is achieved through a function named ―dem‖ that accepts the
received signal and demodulate it to get the binary signal.
3.9.11 Sampling
The demodulated signal is continuous so in order to be converted into binary form a
sampler is used. The sampler takes a sample of the demodulated signal at the Centre
of the pulse.
The sampler makes a decision; if the sample is larger than the threshold it is a one and
if it is less then it‘s a zero.
3.9.12 BER
The BER was calculated by comparing the received message with the source message
and calculating the number of errors.
A table called BER that shows the BER versus the noise power is created at the
beginning of the code.this table has the values of noise that the BER is to be
calculated for.As the code proceeds the values of the BER are inserted into the BER
table.
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3.10 MEASUREMENTS AND OUTPUTS:
During execution of the program each step gives an output, table illustrates the
outputs of each step. Table 3.1 gives a summary outputs of the important simulation
steps.
Table 3.1Outputs of Process Step
Step
Output
DOA
The angle of the user
Modulator
Modulated Signal
Beam forming
Array Factor
Channel
Received Signal + added Noise
Receiver
The received signal
Demodulator
Sampler
The demodulated signal
The received message signal in
binary form.
Other measurements on the received signal:
-
The received Signal Power.
-
Bit Error Rate (BER) for Different values of Noise.
-
Bit Error Rate (BET) for Different numbers of Array Elements.
-
DOA of Different Users.
3.11 SIMULATION OUTPUTS
Different algorithm‘s and Function had been performed to the code using MATLAB ,
how to perform these simulations are illustrated in this section . Outputs Results and
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CHAPTER THREE
comparisons between it and the expected theoretical results are discussed on the
results and discussion chapter
3.11.1 Signal Track Line
In this test , the signal had been tracked starts from message generation , through
modulation , transmitter , channeling , reception , demodulation and sampling . which
represent a simple communication system as shown in figure

10 bits Binary Signal Message

Modulated Signal

Received Signal

Demodulated Signal

Sampled Signal
3.11.2 Array Factor
In this section, the effect of changing number of element on the overall Array Factor
had been tested. First three subsections tests the effect of changing number of element
on the linear array antenna for different number of elements. The forth one test the
effect of using two dimensional linear arrays (Planar Array ) on the Array Factor .
Results had been shown and discussednext.

Array Radiation Pattern in 2D Plot

Ten Elements Array Factor

Five Elements Array Factor

Single Element Array Factor

Planar Array Factor
3.11.3 DOA For Multiple User/Target Locations
Based on DOA algorithm attached in MATLAB code , Appendix A . Different angle
of users had been measured and calculated for different user positions .
3.11.4 SIGNAL TO NOISE RATION
In this subsection , calculating to the SNR with related to the resulted number
offerrors .
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3.11.5 BER:
At this subsection, the estimated BIT ERROR RATE had been measured, By sending
and generating message of 100,000 Bit in Random way using MATLAB function and
comparing the received single with the transmitted one . matrix of BER Created to
contains the Total BER of the 100,000 Bits . BER is measured on the Communication
system designed for the Previous test in section 4.3 . with AWGN as source of noise
in the Channel .
To test BER and effect of Changing Number of elements in two types of antennas
array , Linear array and Planar Array along with the effect of increasing Values of
Noise added to the system .
Results are obtained after Perform a MATLAB Program Code– shown in attached
AppendixA . which Had been Designed using MATLAB , for different number of
elements and analyze the effect of changing it on the overall system performance ,
quality of signal and BER .
Results based on assumptions and parameters as indicated in chaper 3 .
3.11.5.1 Linear array- BER
In this subsection, Result of performing test of effect of Number of elements on the
overall system performance for linear array when using code of appendix A – section
1.

Using Single elements in the array

Using 5 elements in the array

Using 10 elements in the array
3.11.5.2 Planar array - BER
In this subsection, Result of performing test of effect of Number of elements on the
overall system performance for planar array by using code in appendix A – Section 2.
the methodology and mechanisms of performing the simulation tests as illustrated in
chapter 3 before .As the Planar array represent 2D linear arrays , in order to get array
of 10 elements , number of element (2 x 5) had been used to design planar array .
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In this section , two tests will be performed .new MATLAB Program Code had been
developed based on the code , in appendix A . to make it suitable for Planar Array
Antenna . New Code as shown in Appendix A Section Two .

Test 1 : create Array Factor using a Planar Array .

Test 2 : Measure BER for 2 x 5 elements Planar Array and compare its results
with the 10 elements linear array antenna .
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4
CHAPTER FOUR
CHAPTER FOURRESULTS AND DISCUSSION
4.1 OVERVIEW
In this chapter, the system simulation results had been obtained and discussed as well
as the mechanism by which the system was tested. Smart antenna system had been
Simulate a simple communication system and estimate bit error rate using
mechanisms indicated in chapter 3.
Combining tools from The MathWorks – MATLAB provides a complete solution for
Smart antenna System design , some tests had been simulated .
4.2 SIGNAL TRACK LINE TEST
In this test , the signal had been tracked starts from message generation , through
modulation , transmitter , channeling , reception , demodulation and sampling . which
represent a simple communication system as shown in figure
4.2.1 10 bits Binary Signal Message
In this step , a binary signal the had been generated randomlyis : [1 0 1 0 0 0 1 0 1 0]
4.2.2 Modulated Signal
The demodulated signal was obtained as shown in Figure 4.1.
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CHAPTER FOUR
modulated signal
1
Figure
0.8
4.1
0.6
0.4
Amplitude
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.1
0.2
0.3
0.4
0.5
time
0.6
0.7
0.8
0.9
1
-8
x 10
Generated 10 Bits Signal Message
It is observed that when the message changes there is a 180 degree phase shift
as expected.
4.2.3 Received Signal
The signal had been received, under no noisy conditions it can be noticed that
the amplitude was greatly reduced due to the free space loss as shown in Figure 4.2.
-5
2
Recieved signal
x 10
1.5
1
0.5
Amplitude
0
-0.5
-1
-1.5
-2
0
0.1
0.2
0.3
0.4
0.5
time
0.6
0.7
0.8
0.9
1
-8
x 10
Figure 4.2 Received No Noisy 10 Bits Signal Message
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CHAPTER FOUR
By adding Noisy conditions on the Transmission Channel ― AWGN ― as added noise .
the received message was affected by the noise ― Signal + Noise‖ as shown in Figure
4.3.
Amplitude
.
Figure 4.3 Received 10 Bits Noisy Signal
4.2.4 Demodulated Signal
At this step , the output of the BPSK demodulator gave us signal as follow :
demodulated signal
1.4
1.2
1
0.8
0.6
Amplitude
0.4
0.2
0
-0.2
-0.4
-0.6
0
0.1
0.2
0.3
0.4
0.5
time
0.6
0.7
0.8
0.9
1
-8
x 10
Figure 4.4 Demodulated 10 Bits Signal
It is noticed that it is very similar to the generated message [1 0 1 0 0 0 1 0 1 0].
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4.2.5 Sampled Signal
The sent data: [1 0 1 0 0 0 1 0 1 0]
The received data: [1 0 1 0 0 0 1 0 1 0]
No of errors= 0
The final received message is equal to the sent message which means there is no
errors and the system is valid.
4.3 ARRAY RADIATION PATTERN
Some tests had been performed to test the radiation pattern been created by the
simulation . Radiation Pattern of 10 elements array when sending 5 bits as signal
message given in Figure 4.5 .
10
8
6
Array
4
Factor
2
0
-2
-4
0
0.5
1
1.5
2
2.5
3
3.5
Angle
Figure 4.5 Radiation Pattern of 10 elements array with 5 bits message
Result of a two Dimensional Plot of Radiation Patter with 5 elements array , given as
shown in Figure 4.6 .
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90
5
120
60
4
3
150
30
2
1
Array Factor V.S Angle
180
0
210
330
240
300
270
Figure 4.6 two Dimensional Plot Radiation Pattern of 5 element
Another result obtained when using 10 element , it gives more directive pattern with
less beam width than 5 elements as shown in Figure 4.7 ..
90
10
120
60
8
6
150
30
4
2
Array Factor V.S Angle
180
0
210
330
240
300
270
Figure 4.7two Dimensional Plot Radiation Pattern of 10 element
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CHAPTER FOUR
4.4 ARRAY FACTOR
4.4.1 Ten Elements Array Factor
For a linear array antenna used in beam forming , to transmit the signal . when using
10 element in the linear array , the array factor that would be generated from the beam
former is shown in Figure 4.8
Array factor
8
6
4
2
0
-2
10
5
10
5
0
0
-5
-5
-10
-10
Figure 4.8 Array Factor of 10 element linear antenna
By using 10 elements, the array factor took more directive pattern along with Narrow
beam width. The array factor had a maximum toward the desired signal pi/3 angle
used here as Direction Angle of the User .
So when this array factor multiplied with the single elements the radiation pattern will
take more directive radiation pattern towards the direction of user , which give better
signal quality and reduce the interference compare to other linear antennas with less
number of elements as it will be shown next .
4.4.2 Five Elements Array Factor
the number of elements in the linear array affects the total array factor directivity and
exist of null . the array factor have larger beam width than the 10 elements array
factor . By multiplying this array factor with the 5 element array , the resulted
radiation had maximum towards the user , reduced values in other directions ,
however wih less directivity compare with 10 elements array factor and with greater
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CHAPTER FOUR
noise and interference as it would radiate in different directions around the array
antenna .
Array factor
4
3
2
1
0
-1
2
2
0
-2
0
-2
Figure 4.9 Array Factor of 5 element linear antenna
The 5 elements array factor also had a maximum towards the user (pi/3)
however it gave less directivity and larger beam width compared with the 10 elements
array factor reduced values in other directions.
4.4.3 Single Element Array Factor
For the single antenna elements which represent normal used antennas , since
there is no multiple antennas (array) the array factor was expected to be Unity and so
it was as shown in Figure 4.10 . Therefore when it is multiplied by single element the
radiation pattern is equal to the radiation pattern of a single element.
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Array factor
1
0.5
0
-0.5
0.5
0.5
0
0
-0.5
-0.5
Figure 4.10 Array Factor of Single element linear antenna
4.4.4 Planar Array Factor
80
60
40
20
0
-20
60
40
20
0
-20
-100
-50
0
50
100
Figure 4.11 Array Factor of 10x10 Planar antenna
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Using planar arrays, itgave more directive array factor with maximum pattern
towards the desired direction and the undesired interference had been reduced . Using
10 X 10 elements is sort of large number , however this used to indicate effect of
planar array.
4.5 DOA FOR MULTIPLE USER/TARGET LOCATIONS
The results had been obtained after performing DOA algorithim as shown in Table 4.1
.
Table 4.1 DOA for Multiple Locations
User position
DOA
Expected value
500 500 0
1.5709 90
90
200 0 200
0.7854 45
45
0 700 600
0.8622 49.4
49.4
100 400 250
1.0258 58.77
58.77
250 100 300
0.7315 41.9
41.9
Expected Value =

tan 


1
x
 y2  

2

z

2
(3.1)
The DOA algorithm detected the exact user location because this an almost perfect
environment.
4.6 SIGNAL TO NOISE RATIO
Results outputs of the signal to noise ratio when applying Noise of 1 x 1011 for 10
Bits message signal to study the effect of number of element on SNR values , are
given in table Table 4.2
49 | P a g e
RESULTS AND DISCUSSION
CHAPTER FOUR
Table 4.2 Number of elements versus SNR and SNR - dB
Number of elements
SNR
SNR in dB
Single element
0.1561
-8.0664
4 elements
2.4974
3.9748
5 elements
3.9021
5.913
6 elements
5.6191
7.4967
10 elements
15.6086
11.9336
The graph that represent the relation between SNR and Number of elements indicated
in Figure 4.12 .
SNR v.s Number of Elements
Signal to Noise Ratio in dB
15
10
5
0
0
2
4
6
8
10
12
-5
-10
Number of Elements
Figure 4.12 Graph represent relation between Number of elements and SNR-dB
As from previous graph , Signal to Noise Ration of overall system Increase with the
number of elements used in the array .
4.7 BER
At this section, the estimated BIT ERROR RATE had been measured, By
sending a message of 100,000 Bit in Random way using MATLAB function and
comparing the received single with the transmitted one ..
50 | P a g e
RESULTS AND DISCUSSION
CHAPTER FOUR
BER is measured on the Communication system designed for the Previous test
in chapter 3. with AWGN as source of noise in the Channel and the results are based
on the assumptions and parameters as indicated in chaper 3.
4.7.1 Linear Antenna BER
In this subsection, Result of performing test of effect of Number of elements on the
overall system performance.
4.7.1.1 Using Single elements in the array
Results had been obtained by using single element and are indicated in Table 4.3.
Table 4.3 Noise and Number of errors using single element
Noise
No of Errors
BER
1.00000000000000e-16
0
0
5.00000000000000e-16
0
0
1.00000000000000e-15
0
0
5.00000000000000e-15
0
0
1.00000000000000e-14
0
0
5.00000000000000e-14
0
0
1.00000000000000e-13
13
0.00013
5.00000000000000e-13
5869
0.05869
1.00000000000000e-12
13631
0.13631
3.00000000000000e-12
27056
0.27056
5.00000000000000e-12
32075
0.32075
1.00000000000000e-11
37537
0.37537
2.00000000000000e-11
41001
0.41001
3.00000000000000e-11
42732
0.42732
4.00000000000000e-11
43837
0.43837
5.00000000000000e-11
44381
0.44381
6.00000000000000e-11
45280
0.45280
8.00000000000000e-11
45766
0.45766
1.00000000000000e-10
46241
0.46241
51 | P a g e
RESULTS AND DISCUSSION
1.50000000000000e-10
CHAPTER FOUR
47125
0.47125
From Table 4.3, at lower noise values there is no errors when receiving signal
message. however errors occurs when noise start to reach high levels as in in this case
by reaching 1 x 1013 and start to increase by increasing values of Noise giving much
bigger errors values.
4.7.1.2 Using 5 elements in the array
Results had been obtained by using 5 elements and indicated in Table 4.4.
Errors start to appear when noise reaches high values, i.e when Noise 3 x 1012 one 63
errors occurs. then number of errors start to increase by the increase in Noise values
.however it gives better results than using single element .
This shows that single elements give a lot of errors, BER when receiving signal
messages when noise reach some values .
Table 4.4 Noise and Number of errors using 5 elements
Noise
No of Errors
BER
1.00000000000000e-16
0
0
5.00000000000000e-16
0
0
1.00000000000000e-15
0
0
5.00000000000000e-15
0
0
1.00000000000000e-14
0
0
5.00000000000000e-14
0
0
1.00000000000000e-13
0
0
5.00000000000000e-13
0
0
1.00000000000000e-12
0
0
3.00000000000000e-12
63
0.00063
5.00000000000000e-12
672
0.00672
1.00000000000000e-11
3947
0.03947
2.00000000000000e-11
10965
0.10965
3.00000000000000e-11
15831
0.15831
52 | P a g e
RESULTS AND DISCUSSION
CHAPTER FOUR
4.00000000000000e-11
19614
0.19614
5.00000000000000e-11
22456
0.22456
6.00000000000000e-11
24677
0.24677
8.00000000000000e-11
27790
0.27790
1.00000000000000e-10
29751
0.29751
1.50000000000000e-10
33382
0.33382
4.7.1.3 Using 10 elements in the array
This shows that single elements give a lot of errors, BER when receiving signal
messages when noise reach some values.
when number of elements increased , better results given . in comparison between
using single element , 5 elements and the 10 elements , using 10 elements have the
capapility of sending signals without errors for many values of noise , until reach
very high values of noise compare with the single element .
from the Table 4.5, The errors starts to appear at noise levels of 1 x 1011 . first error
occurred at noise levels of more than 3 times the noise value when first error occur at
the 5 elements array.so , using more element will reduce the probability of error to
occur.
Table 4.5 Noise and Number of errors using 10 elements
Noise
No of Errors
BER
1.00000000000000e-16
0
0
5.00000000000000e-16
0
0
1.00000000000000e-15
0
0
5.00000000000000e-15
0
0
1.00000000000000e-14
0
0
5.00000000000000e-14
0
0
1.00000000000000e-13
0
0
5.00000000000000e-13
0
0
1.00000000000000e-12
0
0
3.00000000000000e-12
0
0
53 | P a g e
RESULTS AND DISCUSSION
CHAPTER FOUR
5.00000000000000e-12
0
0
1.00000000000000e-11
20
0.0002
2.00000000000000e-11
619
0.00619
3.00000000000000e-11
2120
0.0212
4.00000000000000e-11
4052
0.04052
5.00000000000000e-11
5876
0.05876
6.00000000000000e-11
7674
0.07674
8.00000000000000e-11
10923
0.10923
1.00000000000000e-10
13658
0.13658
1.50000000000000e-10
18891
0.18891
In comparison between using single element , 5 elements and the 10 elements , using
50000
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
1.00E-16
5.00E-16
1.00E-15
5.00E-15
1.00E-14
5.00E-14
1.00E-13
5.00E-13
1.00E-12
3.00E-12
5.00E-12
1.00E-11
2.00E-11
3.00E-11
4.00E-11
5.00E-11
6.00E-11
8.00E-11
1.00E-10
1.50E-10
Number of Errors
10 elements is more immune to noise as shown in Figure 4.13
Noise
Single element
5 element
10 elements
Figure 4.13 effect of number of elements on number of errors
From Ошибка! Источник ссылки не найден. the ten elements array
provides the least error rate and the 5 elements array provide less BER than a single
element.
The BER reaches saturation at 0.5; this is expected because the noise has a
normal distribution of probability around the zero so there is a 0.5 chance that the
noise is constructive or destructive.
54 | P a g e
RESULTS AND DISCUSSION
CHAPTER FOUR
Small noise increase in single elements will result in large increase in number
of errors , however by increasing number of elements this effect is decreasing as in 10
elements , the increase in noise values will result in less increase in number of errors
with related to 5 elements and single elements.
4.7.2 Planar Antenna BER
In this subsection, Result of performing test of effect of Number of elements
on the overall system performance. the methodology and mechanisms of performing
the simulation tests as illustrated in chapter 3 before .
As the Planar array represent 2D linear arrays , in order to get array of 10
elements , number of element (2 x 5) had been used to design planar array .
In this section , two tests will be performed .new MATLAB Program Code had been
developed based on the code , in appendix A-Section 1 . to make it suitable for Planar
Array Antenna . New Code as shown in Appendix A-Section 2 .

Test 1 : create Array Factor using a Planar Array .

Test 2 : Measure BER for 2 x 5 elements Planar Array and compare its results
with the 10 elements linear array antenna .
4.7.2.1 Array Factor
10
5
0
10
-5
8
5
6
0
4
2
-5
0
-2
-10
Figure 4.14 Array Factor of Planar Array Antenna
55 | P a g e
RESULTS AND DISCUSSION
CHAPTER FOUR
Results obtained from this test for BER as shown in Table 4.6.
Table 4.6 Noise and Number of errors using (2 x 5) elements Planar Array
Noise
No of Errors
BER
1.00000000000000e-16
0
0
5.00000000000000e-16
0
0
1.00000000000000e-15
0
0
5.00000000000000e-15
0
0
1.00000000000000e-14
0
0
5.00000000000000e-14
0
0
1.00000000000000e-13
0
0
5.00000000000000e-13
0
0
1.00000000000000e-12
0
0
3.00000000000000e-12
0
0
5.00000000000000e-12
0
0
1.00000000000000e-11
18
0.00018
2.00000000000000e-11
647
0.00647
3.00000000000000e-11
2133
0.02133
4.00000000000000e-11
3976
0.03976
5.00000000000000e-11
5835
0.05835
6.00000000000000e-11
7778
0.7778
8.00000000000000e-11
10979
0.10979
1.00000000000000e-10
13637
0.13637
1.50000000000000e-10
18783
0.18783
The planar array is also very resistive to noise and the BER is very close to that of the
linear array with the same number of elements as shown in Figure 4.15.
56 | P a g e
RESULTS AND DISCUSSION
CHAPTER FOUR
20000
18000
16000
14000
12000
10000
8000
Planar arrat
6000
Linear array
4000
2000
1.00E-16
5.00E-16
1.00E-15
5.00E-15
1.00E-14
5.00E-14
1.00E-13
5.00E-13
1.00E-12
3.00E-12
5.00E-12
1.00E-11
2.00E-11
3.00E-11
4.00E-11
5.00E-11
6.00E-11
8.00E-11
1.00E-10
1.50E-10
0
Figure 4.15 Relationship between BERof linear array with 10 elementsand
planar array with 2x5 elements.
57 | P a g e
CONCLUSIONS AND RECOMMENDATIONS
CHAPTER FIVE
CHAPTER FIVE
CONCLUSIONS and RECOMMENDATIONS
5
5.1 PROJECT REVIEW
In conclusion to this study ―Smart Antenna ―technology by creating Simulation
System of antenna arrays (smart antenna)using smart signal processingto identify
algorithms such as direction of arrival(DOA) of the signal, and use it to calculate
beam formingvectors and direct the antenna beam on the user/target in order to
achieve enhancement of channel performance and reduce interference.
Objectives of the project mentioned in chapter 1, had been achieved as shown in the
results. A study of smart antenna system concept along with system simulation using
MATLAB was achieved by providing step by step process of communication system
using an Array Factor pointing towards the desired direction for both Linear and
Planar Arrays .
Based on simulation process and results, its evidence that it is possible to direct the
Radiation‗s Maximum pattern for user position into Desired Direction, also Direct a
Null for undesired Interferences and sources.
Smart antenna system technologies had been studied as concept and its uses in
communication systems. Using MATLAB computer simulation, we have seen that
smart antenna has powerful capabilities to reduce interference and sending data
towards the desired direction only. We summarize the results of simulation in the
following points:
• Smart antenna can provide an average better gain as compared to conventional
single element antenna.
• Most suitable spacing for antenna elements is half the wavelength. However,
element spacing of less than the wavelength increases BER.
• The user data rate does not affect the performance. This means the system can
accommodate any kind of user, voice, or data.
58 | P a g e
CONCLUSIONS AND RECOMMENDATIONS
CHAPTER FIVE
• The number of users could be accommodated is not limited by number of elements
•during the receiving of data if error occurs, instead of spreading out over all users it
affects few number of users.
We also found out from our simulation that if accurate DOA estimation is available,
the BER will be much smaller.
5.2 FUTURE WORKS
Our system examines smart antenna as a basic system, it generates Message signal,
modulates, forms the beam and transmits the signal into the desired director for the
user/target. Also receive in the existence of AWGN. For additional external effects
some conditions could be added to the simulation to create similar environment, for
example additional noise, Interferences, distortion sources and Fading which affect
the transmitted signal.
Higher network capacity and further improvements could be achieved by having
smaller beam width radiation patterns and lower side lopes which achieved by
choosing right number of elements and suitable distance between elements in the
array.
With appropriate adaptive algorithms the beam forming can be obtained. As the
system uses a DSP processor, the signals can be processed digitally and the
performance with a high data rate transmission and good reduction of mutual signal
interference could be obtained.
Analysis of the Effect of specific parameters on the overall system performance and
choosing parameters to meet capacity requirements for a network is possible by
changing these parameters through simulation interface i.e changingthe angle of the
user DOA used to modify simulation system algorithms to get better results.
Current DOA estimation algorithms suffer from accuracy or computational
complexity and existence of noise in the channel, which makes this approach less
attractive. If an accurate, computationally non intensive, adaptive DOA becomes
available, an approach that uses DOA directly will be much more attractive , thus
Adaptive algorithms depend on whether there is better algorithms than the existed
ones or not.
59 | P a g e
APPENDIX A
REFRENCES
[1] Susmita Das, "Smart Antenna Design for Wireless Communication using
Adaptive Beam-Forming Approach," in TENCON, 2009,IEEE.
[2] L.C. Godara, "Aoolications of Antenna Arrays to Mobile Communications,
Part1:Performance Improvement, Feasibility and System Considerations," , vol.
85, 1997, pp. 1031-1060,IEEE.
[3] L.C. Godara, "Applications of Antenna Arrays to Mobile Communications , Part
II : Beam-Forming and Direction-of-Arrival Considerations," , vol. 85,
1997,IEEE.
[4] IEEE Standard Definitions of Terms for Antennas (IEEE Std 145–1993).
[5] C.A.Balanis, Antenna Theory Analysis and Design, 2005th ed.: John Wieldy &
Sons, 1981.
[6] C. A. Balanis, ―Introduction to Smart Antennas‖, (with Panayiotis Ioannides),
Morgan and Claypool, Publishers, 2007.
[7] Ivica Stevanovi´c, Anja Skrivervik and Juan R. Mosig,‖Smart Antenna Systems
for Mobile Communications‖ January,2003
[8] IEEE Std 149-1979 (Reaff 1990), IEEE Standard Test Procedures for Antennas
(ANSI)
60 | P a g e
APPENDIX A
61 | P a g e
APPENDIX A
APPENDIXA : MATLAB CODES
Section One :
Program (1) : Give Simulation Results For Linear Array
%step 1: Accept inputs for the simulation , results differ related to
the values of inputs :
%*******************************************************************
% Interface which ask for Inputs
%*******************************************************************
f=input ('Please input the carrier frequency :'); % The Program Ask
For Frequency Which here we use 2 * 10^9
d=input ('Please input the Separations between array elements :'); %
Separation Between element we used in the program are d=y/4
l=input ('Please input the length of the antenna :'); % length of y/2
had been used
c= 3*10^8 ;
x1=0; y1=500; z1=500; % user location , random position in the three
co-ordinateds had been choosen for simulation
y=(3* 10^8)/f; % the wavelength
d=y/4; % distance between elements is quarter the wavelength
d1=sqrt(x1^2 + y1^2 +z1^2); % distance to the first antenna
d2=sqrt(x1^2 + y1^2 +(z1-d)^2); % distance to the second antenna
t1=d1/c;
t2=d2/c;
Oo = DOA(t1,t2,d)
% DOA- Calculating for Specific User Position
(0,500,500)
BER=[1 0 ;5 0 ;10 0 ;50 0 ;100 0; 500 0;1000 0 ; 5000 0; 10000 0;
30000 0;50000 0; 100000 0;200000 0 ;300000 0; 400000 0;500000 0
;600000 0;800000 0;1000000 0;1500000 0].*10^-16; % Bit Error Rate
taken in some random stages to measure error related to Noise Values
for kkk = 1 : 20
% Constants and Variables
N=10 ;
% number of antenna elements
x=randint(1,100000);
% 100,000 bits message
y=3* 10^8/f ;
K=2*3.14/y ;
A-1 | P a g e
APPENDIX A
B=-K*d* cos (Oo)
z=modu(B,f,1,x);
Resistance=75 ; % resistance of 75 Ohm had been taken .
Amplifier=10 ;
I=Amplifier*(z/Resistance);
Imax= Amplifier/Resistance
% * calculating and drawing the array factor
O= -pi/2:pi/36: pi/2;
% theta for 3d
theta=0:pi/18:2*pi;
[theta,O]=meshgrid(theta,O);
A=K*d* sin (O) + B;
V=A/2;
U=sin (N*V);
AF = U./V;
r= U./V;
[X,Y,Z]=sph2cart(theta,O,r);
%* end of drawing and calulating the array factor
% **AF and other parameters for the receiving antenna at the
specified angle (Oo) and distance (Radius)
Radius=1000
% distance between transmitter and receiver
Ao=K*d* sin (Oo) + B; % Calculating of Maximum of Array Factor
Vo=Ao/2;
Uo=sin (N*Vo);
AFo= Uo/Vo;
Eo=AFo*K*I*l*cos(Oo)/(4*pi*Radius);
Eomax=AFo*K*Imax*cos(Oo)/(4*pi*Radius);
Wo=(Eomax*Eomax)/(120 *pi);
% **
S=Eo * l
; % S is the received signal
F=f/10^9
n=length(x);
t = [0:20*n-1]'/(10*f);
Sp=mean((S.*S))
;
Aeff=0.13* y^2
Pr=Aeff*Wo;
% the signal power
%effective aperture area
% the expected received power Boltzmann’s
const=1.38*10^(-23)
A-2 | P a g e
APPENDIX A
No=BER(kkk,1); %noise power
sn=Sp/No
snr=10*log10(sn) % SNR in ( dB )
Snoise = awgn(S,snr,'measured',10);
R=dem(Snoise,f);
fini=zeros(1,length(x));
a=length(x) -1;
for jj=0:a
q=10+jj*20 ;
fin(jj+1)=R(q)
; % sampling the demodulated signal
if fin(jj+1)>0.5
fini(jj+1)=1
;
;
% approximating the samples to one or zero
else fini(jj+1)=0 ;
end
end
newerrs = biterr(x,fini)
BER(kkk,2)= biterr(x,fini) % final Values of Bit Error Rate
end
 Functions : Modulation Function :function [z] = modu(B,f,i,x)
n=length(x)
x2 = rectpulse(x,20);
t = [0:20*n-1]'/(10*f);
z = pmmod(x2,f,10*f,pi/2);
A-3 | P a g e
APPENDIX A
end
 De-Modulation Function :function [R]= dem(y,f)
R = pmdemod(y,f,10*f,pi/2);
n=length(R);
F=f/10^9
t = [0:n-1]'/(10*f);
end
 Direction of Arrival DOA Function :function [ doa ] = DOA( t1,t2,d)
c= 3 * 10^8
del=t1-t2
doa = acos (c*del/d)
end
Section Two
 The code for two dimensional array(2x5) , Planar array :
 N= 2 and N2=5 , Both of Them Detect Angles of User (Oo & Oo2) Using
Direction of Arrival (DOA) Function .
A-4 | P a g e
APPENDIX A
f=input ('Please input the carrier frequency :'); % use 2*10^9
Frequency
c= 3*10^8;
x1=0 ; % Position of User , Used to Detect DOA angle for Antenna
y1=500 ;
z1=500 ;
y=(3* 10^8)/f ;
K=2*3.14/y ;
d=y/4 ;
l=y/2 ;
d1=sqrt(x1^2 + y1^2 +z1^2) ;
d2=sqrt(x1^2 + y1^2 +(z1-d)^2) ;
d3= sqrt(x1^2 + (y1-d)^2 +z1^2) ;
t1=d1/c ; %time for Signal fromUser to Antenna , Used in Calculations
of DOA
t2=d2/c ;
t3=d3/c ;
Oo = DOA(t1,t2,d) ;
(0,500,500)
Oo2= DOA(t1,t3,d) ;
% DOA Calculating for Specific User Position
BER=[1 0 ;5 0 ;10 0 ;50 0 ;100 0; 500 0;1000 0 ; 5000 0; 10000 0;
30000 0;50000 0; 100000 0;200000 0 ;300000 0; 400000 0;500000 0
;600000 0;800000 0;1000000 0;1500000 0].*10^-16; % Bit Error Rate
Calculations
for kkk = 1 : 20
x=randint(1,100000);
N=2
% number of antenna elements for First Antenna
N2=5; % Number of Antenna Elements for the Second Array
y=3* 10^8/f
K=2*3.14/y
d=y/4
% separation between elements
l=y/2
% the length of the antenna
B=-K*d* cos (Oo)
B2=-K*d* cos (Oo2)
z=modu(B,f,1,x);
Resistance=75
Amplifier=10
I=Amplifier*(z/Resistance);
Imax=Amplifier/Resistance
% * calculating and drawing the array factor
O= -pi/2:pi/36: pi/2
theta=0:pi/18:2*pi;
[theta,O]=meshgrid(theta,O)
A=K*d* sin (O) + B
A2=K*d* sin (theta) + B2
V=A/2
A-5 | P a g e
APPENDIX A
V2=A2/2
U=sin (N*V)
U2=sin (N2*V2)
AF = (U.*U2)./(V.*V2)
r= (U.*U2)./(V.*V2)
[X,Y,Z]=sph2cart(theta,O,r) ; % between Coordinates
surf(X,Y,Z) % Drew of Array Factor
%* end of drawing and calculating the array factor
% **AF and other parameters for the receiving antenna at the
specified angle (Oo) and (Oo2) and distance (Radius)
Radius=1000; % distance between transmitter and receiver
Ao=K*d* sin (Oo) + B;
A2o=K*d* sin (Oo2) + B2;
Vo=Ao/2;
V2o=A2o/2;
Uo=sin (N*Vo);
U2o=sin (N2*V2o);
AFo = (Uo*U2o)/(Vo*V2o) ; % Maximum Value of Array Factor
Eo=AFo*K*I*l*cos(Oo)/(4*pi*Radius);
Eomax=AFo*K*Imax*cos(Oo)/(4*pi*Radius);%maximum Value, Total Antenna
Signal
Wo=(Eomax*Eomax)/(120 *pi);
% **
S=Eo * l ; % S is the received signal
F=f/10^9
n=length(x);
t = [0:20*n-1]'/(10*f);
Sp=mean((S.*S)) ; % the signal power
Aeff=0.13* y^2
%effective aperture area
Pr=Aeff*Wo;
% the expected recieved power Boltzmann’s
const=1.38*10^(-23)
No=BER(kkk,1) %noise power
sn=Sp/No
snr=10 *log10(sn) % SNR in dB
Snoise = awgn(S,snr,'measured',10);
R=dem(Snoise,f);
fini=zeros(1,length(x))
a=length(x) -1
for jj=0:a
q=10+jj*20 ;
fin(jj+1)=R(q) ; % sampling the demodulated signal
if fin(jj+1)>0.5
fini(jj+1)=1 ; ; % approximating the samples to one or zero
else fini(jj+1)=0 ;
end
end
x ;
fini ;
newerrs = biterr(x,fini)
BER(kkk,2)= biterr(x,fini)
end
A-6 | P a g e
APPENDIX A
A-7 | P a g e
APPENDIX B
The Institute of Electrical and Electronics Engineers, Inc.
345 East 47th Street, New York, NY 10017-2394, USA
Copyright © 1993 by the Institute of Electrical and Electronics Engineers, Inc.
All rights reserved. Published 1993. Printed in the United States of America
ISBN 1-55937-317-2
IEEE Std 145-1993
(Revision of IEEE Std 145-1983)
IEEE Standard Definitions of Terms
for Antennas
Sponsor
Antenna Standards Committee
of the
IEEE Antennas and Propagation Society
Approved March 18, 1993
IEEE Standards Board
Abstract: Definitions of terms in the field of antennas are provided.
Keywords: antennas, definitions, propagation, terminology
IEEE Standards documents are developed within the Technical Committees of the
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iii
Introduction
(This introduction is not a part of IEEE Std 145-1993, IEEE Standard Definitions of Terms for Antennas.)
This document is a revision of IEEE Std 145-1983, IEEE Standard Definitions of Terms for Antennas, and
corrects minor errors that appeared in that printing. The original standard was issued in 1969.
The following persons were on the working group that developed this document:
Donald G. Bodnar, Chair
Charles C. Allen Edward Joy Antoine G. Roederer
A. David Bresler Walter K. Kahn Allen C. Schell
Richard H. Bryan Flemming H. Larsen Alan J. Simmons
Robert B. Dybdal Richard B. Mack G. P. Tricoles
William J. English Allen C. Newell Michael T. Tuley
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APPENDIX B
E. S. Gillespie H. George Oltman Edward A. Urbanik
Edward Hart A. David Olver A. T. Villeneuve
Doren Hess Harold R. Raemer Jonathan D. Young
The following persons were on the balloting committee that approved this document for submission to the
IEEE Standards Board:
Charles C. Allen Doren Hess Antoine G. Roederer
Donald G. Bodnar Edward Joy Allen C. Schell
A. David Bresler Walter K. Kahn Alan J. Simmons
Richard H. Bryan Flemming H. Larsen G. P. Tricoles
Robert B. Dybdal Richard B. Mack Michael T. Tuley
William J. English Allen C. Newell Edward A. Urbanik
E. S. Gillespie H. George Oltman A. T. Villeneuve
Edward Hart A. David Olver Jonathan D. Young
Harold R. Raemer
When the IEEE Standards Board approved this standard on March 18, 1993 it had the following
membership:
Wallace S. Read, Chair Donald C. Loughry, Vice Chair
Andrew G. Salem, Secretary
Gilles A. Baril Ben C. Johnson Don T. Michael*
Clyde R. Camp Walter J. Karplus Marco W. Migliaro
Donald C. Fleckenstein Lorraine C. Kevra L. John Rankine
Jay Forster* E. G. ―Al‖ Kiener Arthur K. Reilly
David F. Franklin Ivor N. Knight Ronald H. Reimer
Ramiro Garcia Joseph Koepfinger* Gary S. Robinson
Donald N. Heirman D. N. ―Jim‖ Logothetis Leonard L. Tripp
Jim Isaak Donald W. Zipse
*Member Emeritus
Also included are the following nonvoting IEEE Standards Board liaisons:
Satish K. Aggarwal
James Beall
Richard B. Engelman
David E. Soffrin
Stanley I. Warshaw
Christopher J. Booth
IEEE Standards Project Editor
iv
Contents
CLAUSE PAGE
1. Overview............................................................................................................................................. 1
1.1 Scope........................................................................................................................................... 1
1.2 Background................................................................................................................................. 1
1.3 Reference .................................................................................................................................... 3
1.4 Definition structure ...................................................................................................................... 3
2. Definitions........................................................................................................................................... 3
1
IEEE Standard Definitions of Terms for Antennas
1. Overview
1.1 Scope
It is assumed in this standard that an antenna is a passive linear reciprocal device. Thus, where a definition
implies the use of an antenna in a transmitting situation, its use in a receiving situation is also implicit, unless
specifically stated otherwise.
When an antenna or group of antennas is combined with circuit elements that are active, nonlinear, or nonreciprocal,
the combination is regarded as a system that includes an antenna. Examples of such cases are an
adaptive antenna system and a signal-processing antenna system; the complete conical-scanning,
monopulse, and compound interferometer systems also fall in this category.
For terms that are quantitative, it is understood that frequency must be specified. For those in which phase or
polarization is a significant part of the definition, a coherent source of power is implied. Whenever a term is
commonly used in other fields but has specialized significance in the field of antennas, this is noted in the
title.
When applying terms pertaining to radiation characteristics, such as gain, polarization, beamwidth, etc., to
multiple-beam antennas, each port shall be considered to be that of a separate antenna with a single main
beam. For polarization diversity systems that may include active devices, these terms apply to each polarization
state for which the antenna is adjusted.
Throughout this standard, where phasors are used, or are implied, the time convention shall be taken to be
exp(j

1.2 Background
The definitions of terms contained herein, for the most part, stand alone and are easily understood out of
context. The terms pertaining to gain, directivity and polarization, however, are interrelated and hence
require some elaboration.
The viewpoint taken for polarization is that this term can be used in three related meanings. It can apply
a) To a field vector at some point in space
b) To a plane wave
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APPENDIX B
c) To an antenna
The polarization of a field vector specifies the shape, orientation, and sense of the ellipse that the extremity
of the field vector describes as a function of time. This applies to any field vector: electric field, magnetic
field, velocity field in a plasma, displacement field in a solid, etc. In a single-frequency plane wave, a specified
field vector has the same polarization at every point in space. This is taken as the polarization of the
plane wave. Conventionally, in electromagnetics, the electric field is considered rather than the magnetic
field. However, in a nonisotropic medium, the polarization state of the plane wave requires consideration of
all its vector components. The third application of the term polarization is to antennas. The polarization of
an antenna in a given direction is that of the plane wave it radiates at large distances in that direction. By reciprocity,
a plane wave coming from that direction whose polarization ellipse has the same axial ratio, orientation,
and sense will yield the maximum response for a given power flux density. For best understanding,
the three related definitions of polarization should be read in the above order.
One departure from previous usage should be noted. The definition of the tilt angle of the polarization ellipse
now requires that it be measured according to the right-hand rule with the thumb pointing in a reference
direction. For a plane wave, the reference direction is the direction of propagation. This is advantageous,
since it removes any ambiguity about the specification of the orientation of the polarization ellipse. It should
be noted, however, that the polarization of the antenna is defined as that of the wave it radiates, whether it is
used for transmitting or receiving. This means that for the receive case, the coordinate system used to
describe the polarization of the antenna and the incoming wave are oriented in opposite directions. (See
IEEE Std 149-1979, IEEE Standard Test Procedures for Antennas, clause 11, Polarization.1) There are two
ways to handle this situation. One is to transform the polarization of the wave into the antenna‘s coordinate
system; the second is to define a receiving polarization for the antenna, which is that of the wave to which
the antenna is polarization matched. The latter was chosen both here and in IEEE Std 149-1979. This should
not be taken to mean that one cannot use the antenna‘s coordinate system, but rather that if it is done, it
should be clearly specified as the polarization of the incoming wave referred to the antenna‘s (transmitting)
polarization. The term receiving polarization can also be applied to a nonreciprocal antenna that may receive
only.
The interdependence of gain, polarization, and impedance has led to the inclusion of several terms, including
partial gain, partial directivity, and partial realized gain. The interrelationships of these terms and the basic
terms gain, directivity and realized gain are best visualized by referring to the flow chart shown in figure 1. A
similar flow chart can be constructed for a receiving antenna.
1Information on the reference can be found in 1.3.
PA = power available from the generator
PM = power to matched transmission line
PO = power accepted by the antenna
PR = power radiated by the antenna
I = radiation intensity
In = partial radiation intensity†
M1 = impedance mismatch factor 1
M2 = impedance mismatch factor 2
= radiation efficiency
GR = realized gain
G = gain
D = directivity
gR = partial realized gain
g = partial gain
d = partial directivity
p = polarization efficiency
Figure 1—Gain and directivity flow chart
1.3 Reference
This standard shall be used in conjunction with the following publication:
IEEE Std 149-1979 (Reaff 1990), IEEE Standard Test Procedures for Antennas (ANSI).2
1.4 Definition structure
In these definitions, words or phrases in parentheses that are part of the term can be omitted when the term is
used, provided they are understood from context. Those words or phrases in brackets can replace the words
or phrases that immediately precede them. If bracketed words or phrases appear in several places in the definition,
then all bracketed words or phrases must be used together in the definitions. For those cases where
two or more terms are synonyms, the preferred term will be defined; the other terms will refer to the preferred
term and be listed after the definition. Abbreviations appear after the term and are enclosed in parentheses.
Terms that are no longer recommended for use are indicated as being deprecated. Synonyms for a
term are listed at the end of the definition.
2. Definitions
2.1 absolute gain (of an antenna). See: gain (in a given direction).
2.2 active array antenna system. An array in which all or part of the elements are equipped with their own
transmitter or receiver, or both.
NOTES
1—Ideally, for the transmitting case, amplitudes and phases of the output signals of the various transmitters are controllable
and can be coordinated in order to provide the desired aperture distribution.
2—Often it is only a stage of amplification or frequency conversion that is actually located at the array elements, with
the other stages of the receiver or transmitter remotely located.
2.3 active impedance (of an array element). The ratio of the voltage across the terminals of an array element
to the current flowing at those terminals when all array elements are in place and excited.
2.4 active reflection coefficient (of an array element). The reflection coefficient at the terminals of an array
element when all array elements are in place and excited.
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2.5 adaptive antenna system. An antenna system having circuit elements associated with its radiating elements
such that one or more of the antenna properties are controlled by the received signal.
2.6 Adcock antenna. A pair of vertical antennas separated by a distance of one-half wavelength or less, and
connected in phase opposition to produce a radiation pattern having the shape of the figure eight in all planes
containing the centers of the two antennas.
2.7 aerial. [Deprecated.]
2.8 Alford loop antenna. A multi-element antenna having approximately equal amplitude currents that are
in phase and uniformly distributed along each of its peripheral elements and producing a substantially circular
radiation pattern in its principal E-plane.
2IEEE publications are available from the Institute of Electrical and Electronics Engineers, Service Center, 445 Hoes Lane, P.O.
Box
1331, Piscataway, NJ 08855-1331, USA.
IEEE
Std 145-1993 IEEE STANDARD DEFINITIONS
4
NOTE—This antenna was originally developed as a four-element, horizontally polarized, UHF loop antenna.
2.9 amplitude pattern. See: radiation pattern.
2.10 angle tracking. See: tracking.
2.11 annular slot antenna. A slot antenna with the radiating slot having the shape of an annulus.
2.12 antenna. That part of a transmitting or receiving system that is designed to radiate or to receive electromagnetic
waves.
2.13 antenna array. See: array antenna.
2.14 antenna effect. [Deprecated.]
2.15 antenna efficiency of an aperture-type antenna. For an antenna with a specified planar aperture, the
ratio of the maximum effective area of the antenna to the aperture area.
2.16 antenna [aperture] illumination efficiency. The ratio, usually expressed in percent, of the maximum
directivity of an antenna [aperture] to its standard directivity. Syn: normalized directivity. See: standard
[reference] directivity.
NOTE—For planar apertures, the standard directivity is calculated by using the projected area of the actual antenna in a
plane transverse to the direction of its maximum radiation intensity.
2.17 antenna pattern. See: radiation pattern.
2.18 antenna resistance. The real part of the input impedance of an antenna.
2.19 aperiodic antenna. An antenna that, over an extended frequency range, does not exhibit a cyclic behavior
with frequency of either its input impedance or its pattern.
NOTE—This term is often applied to an electrically small monopole or loop, containing an active element as an integral
component, with impedance and pattern characteristics varying but slowly over the extended frequency range.
2.20 aperture (of an antenna). A surface, near or on an antenna, on which it is convenient to make assumptions
regarding the field values for the purpose of computing fields at external points.
NOTE—The aperture is often taken as that portion of a plane surface near the antenna, perpendicular to the direction of
maximum radiation, through which the major part of the radiation passes.
2.21 aperture blockage. A condition resulting from objects lying in the path of rays arriving at or departing
from the aperture of an antenna.
NOTE—For example, the feed, subreflector, or support structure produce aperture blockage for a symmetric reflector
antenna.
2.22 aperture distribution. The field over the aperture as described by amplitude, phase, and polarization
distributions. Syn: aperture illumination.
2.23 aperture illumination. See: aperture distribution.
2.24 aperture illumination efficiency. See: antenna illumination efficiency.
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OF TERMS FOR ANTENNAS Std 145-1993
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2.25 area. See: effective area (of an antenna); equivalent flat plate area of a scattering object; partial
effective area (of an antenna, for a given polarization and direction).
2.26 areal beamwidth. For pencil-beam antennas the product of the two principal half-power beamwidths.
See: principal half-power beamwidths.
2.27 array antenna. An antenna comprised of a number of identical radiating elements in a regular arrangement
and excited to obtain a prescribed radiation pattern. Syn: antenna array.
NOTES
1—The regular arrangements possible include ones in which the elements can be made congruent by simple translation
or rotation.
2—This term is sometimes applied to cases where the elements are not identical or arranged in a regular fashion. For
those cases qualifiers shall be added to distinguish from the usage implied in this definition. For example, if the elements
are randomly located, one may use the term random array antenna.
2.28 array element. In an array antenna, a single radiating element or a convenient grouping of radiating
elements that have fixed relative excitations.
2.29 array factor. The radiation pattern of an array antenna when each array element is considered to radiate
isotropically.
NOTE—When the radiation patterns of individual array elements are identical, and the array elements are congruent
under translation, then the product of the array factor and the element radiation pattern gives the radiation pattern of the
entire array.
2.30 artificial dielectric. A medium containing a distribution of scatterers, usually metallic, that react as a
dielectric to radio waves.
NOTES
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APPENDIX B
1—The scatterers are usually small compared to a wavelength and embedded in a dielectric material whose effective
permittivity and density are intrinsically low.
2—The scatterers may be in either a regular arrangement or a random distribution.
2.31 axial ratio (of a polarization ellipse). The ratio of the major to minor axes of a polarization ellipse.
NOTE—The axial ratio sometimes carries a sign that is taken as plus if the sense of polarization is right-handed and
minus if it is left-handed. See: sense of polarization.
2.32 axial ratio pattern. A graphical representation of the axial ratio of a wave radiated by an antenna over
a radiation pattern cut.
2.33 backfire antenna. An antenna consisting of a radiating feed, a reflector element, and a reflecting surface
such that the antenna functions as an open resonator, with radiation from the open end of the resonator.
2.34 back lobe. A radiation lobe whose axis makes an angle of approximately 180 degrees with respect to
the beam axis of an antenna.
NOTE—By extension, a radiation lobe in the half-space opposed to the direction of peak directivity.
2.35 back-scattering cross section. See: monostatic cross section.
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Std 145-1993 IEEE STANDARD DEFINITIONS
6
2.36 bandwidth of an antenna. The range of frequencies within which the performance of the antenna, with
respect to some characteristic, conforms to a specified standard.
2.37 Bayliss distribution, circular. A continuous distribution over a circular planar aperture that yields a
difference pattern with a sidelobe structure similar to that of a sum pattern produced by a Taylor circular distribution.
2.38 Bayliss distribution, linear. A continuous distribution of a line source that yields a difference pattern
with a side-lobe structure similar to that of a sum pattern produced by a Taylor linear distribution.
2.39 beam (of an antenna). The major lobe of the radiation pattern of an antenna.
2.40 beam angle. See: scan angle.
2.41 beam axis (of a pencil-beam antenna). The direction, within the major lobe of a pencil-beam antenna,
for which the radiation intensity is a maximum.
2.42 beam coverage solid angle (of an antenna over a specified surface). The solid angle, measured in
steradians, subtended at the antenna by the footprint of the antenna beam on a specified surface. See: footprint
(of an antenna beam on a specified surface). Contrast with: beam solid angle.
2.43 beam solid angle. The solid angle through which all the radiated power would stream if the power per
unit solid angle were constant throughout this solid angle and at the maximum value of the radiation intensity.
2.44 beam steering. Changing the direction of the major lobe of a radiation pattern.
2.45 beamwidth. See: half-power beamwidth.
2.46 Beverage antenna. A directional antenna composed of a system of parallel horizontal conductors from
one-half to several wavelengths long, terminated to ground at the far end in its characteristic impedance.
Syn: wave antenna.
2.47 biconical antenna. An antenna consisting of two conical conductors having a common axis and vertex.
2.48 bistatic cross section. The scattering cross section in any specified direction other than back toward the
source. Contrast with: monostatic cross section.
2.49 blade antenna. A form of monopole antenna that is blade-shaped for strength and low aerodynamic
drag.
2.50 boresight. See: electrical boresight; reference boresight.
2.51 boresight error. The angular deviation of the electrical boresight of an antenna from its reference boresight.
2.52 broadside array antenna. A linear or planar array antenna whose direction of maximum radiation is
perpendicular to the line or plane, respectively, of the array.
2.53 cage antenna. A multi-wire element whose wires are so disposed as to resemble a cylinder, in general
of circular cross section; for example, an elongated cage.
2.54 cardinal plane. For an infinite planar array whose elements are arranged in a regular lattice, any plane
of symmetry normal to the planar array and parallel to an edge of a lattice cell.
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NOTES
1—This term can be applied to a finite array, usually one containing a large number of elements, by the assumption that
it is a subset of an infinite array with the same lattice arrangement.
2—This term is used to relate the regular geometrical arrangement of the array elements to the radiation pattern of the
antenna.
2.55 Cassegrain reflector antenna. A paraboloidal reflector antenna with a convex subreflector, usually
hyperboloidal in shape, located between the vertex and the prime focus of the main reflector.
NOTES
1—To improve the aperture efficiency of the antenna, the shapes of the main reflector and the subreflector are sometimes
modified.
2—There are other alternate forms that are referred to as Cassegrainean. Examples include the following: one in which
the subreflector is surrounded by a reflecting skirt and one that utilizes a concave hyperboloidal reflector. When referring
to these alternate forms the term shall be modified in order to differentiate them from the antenna described in the definition.
2.56 cheese antenna. A reflector antenna having a cylindrical reflector enclosed by two parallel conducting
plates perpendicular to the cylinder, spaced more than one wavelength apart. Contrast with: pillbox
antenna.
2.57 circular array. An array of elements whose corresponding points lie on a circle. Syn: ring array.
NOTE—Practical circular arrays may include arrangements of elements that are congruent under translation or rotation.
2.58 circular Bayliss distribution. See: Bayliss distribution, circular.
2.59 circular grid array. An array of elements whose corresponding points lie on coplanar concentric circles.
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APPENDIX B
2.60 circularly polarized field vector. At a point in space, a field vector whose extremity describes a circle
as a function of time.
NOTE—Circular polarization may be viewed as a special case of elliptical polarization where the axial ratio has become
equal to one.
2.61 circularly polarized plane wave. A plane wave whose electric field vector is circularly polarized.
2.62 circular scanning. Scanning where the beam axis of the antenna generates a conical surface.
NOTE—This can include the special case where the cone degenerates to a plane.
2.63 circular Taylor distribution. See: Taylor distribution, circular.
2.64 coaxial antenna. An antenna comprised of an extension to the inner conductor of a coaxial line and a
radiating sleeve that in effect is formed by folding back the outer conductor of the coaxial line. Contrast
with: sleeve-dipole antenna.
2.65 collinear array antenna. A linear array of radiating elements, usually dipoles, with their axes lying in
a straight line.
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Std 145-1993 IEEE STANDARD DEFINITIONS
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2.66 complex conductivity. For isotropic media, at a particular point, and for a particular frequency, the
ratio of the complex amplitude of the total electric current density to the complex amplitude of the electric
field strength.
NOTE—The electric field strength and total current density are both expressed as phasors, with the latter composed of
the conduction current density plus the displacement current density.
2.67 complex dielectric constant. The complex permittivity of a physical medium in ratio to the permittivity
of free space.
2.68 complex permittivity. For isotropic media, the ratio of the complex amplitude of the electric displacement
density to the complex amplitude of the electric field strength.
2.69 complex polarization ratio. For a given field vector at a point in space, the ratio of the complex amplitudes
of two specified orthogonally polarized field vectors into which the given field vector has been
resolved. See: plane wave, NOTE 2.
NOTE—For these amplitudes to define definite phase angles, particular unitary vectors (basis vectors) must be chosen
for each of the orthogonal polarizations. See: polarization vector, especially NOTE 1.
2.70 compound circular horn antenna. A horn antenna of circular cross section with two or more abrupt
changes of flare angle or diameter.
2.71 compound horn antenna. See: compound circular horn antenna; compound rectangular horn
antenna.
2.72 compound interferometer system. An antenna system consisting of two or more interferometer antennas
whose outputs are combined using nonlinear circuit elements such that grating lobe effects are reduced.
2.73 compound rectangular horn antenna. A horn antenna of rectangular cross section in which at least
one pair of opposing sides has two or more abrupt changes of flare angle or spacing.
2.74 conformal antenna [conformal array]. An antenna [an array] that conforms to a surface whose shape
is determined by considerations other than electromagnetic; for example, aerodynamic or hydrodynamic.
2.75 conformal array. See: conformal antenna.
2.76 conical array. A two-dimensional array of elements whose corresponding points lie on a conical surface.
2.77 conical scanning. A form of sequential lobing in which the direction of maximum radiation generates a
cone whose vertex angle is of the order of the antenna half-power beamwidth.
NOTE—Such scanning may be either rotating or nutating according to whether the direction of polarization rotates or
remains unchanged.
2.78 contoured beam antenna. A shaped-beam antenna designed in such a way that when its beam intersects
a given surface, the lines of equal power flux density incident upon the surface form specified contours.
See: footprint (of an antenna beam on a specified surface).
2.79 co-polarization. That polarization that the antenna is intended to radiate [receive]. See: polarization
pattern, NOTES 1 and 2.
2.80 co-polar (radiation) pattern. A radiation pattern corresponding to the co-polarization. See: co-polarization.
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2.81 co-polar side lobe level, relative. The maximum relative partial directivity (corresponding to the copolarization)
of a side lobe with respect to the maximum partial directivity (corresponding to the co-polarization)
of the antenna.
NOTE—Unless otherwise specified the co-polar side lobe level shall be taken to be that of the highest side lobe of the
co-polar radiation pattern.
2.82 corner reflector. A reflecting object consisting of two or three mutually intersecting conducting flat
surfaces.
NOTE—Dihedral forms of corner reflectors are frequently used in antennas; trihedral forms with mutually perpendicular
surfaces are more often used as radar targets.
2.83 corner reflector antenna. An antenna consisting of a feed and a corner reflector.
2.84 corrugated horn (antenna). A hybrid-mode horn antenna produced by cutting narrow transverse
grooves of specified depth in the interior walls of the horn. See: hybrid-mode horn.
2.85 cosecant-squared beam antenna. A shaped-beam antenna whose pattern in one principal plane consists
of a main beam with well-defined side lobes on one side, but with the absence of nulls over an extended
angular region adjacent to the peak of the main beam on the other side, with the radiation intensity in this
region designed to vary as the cosecant-squared of the angle variable.
NOTE—The most common applications of this antenna are for use in ground-mapping radars and target acquisition
radars, since the cosecant-squared coverage provides constant signal return for targets with the same radar cross section
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APPENDIX B
at different ranges but a common height.
2.86 counterpoise. A system of conductors, elevated above and insulated from the ground, forming a lower
system of conductors of an antenna.
NOTE—The purpose of a counterpoise is to provide a relatively high capacitance and thus a relatively low impedance
path to earth. The counterpoise is sometimes used in medium- and low-frequency applications where it would be more
difficult to provide an effective ground connection.
2.87 cross polarization. In a specified plane containing the reference polarization ellipse, the polarization
orthogonal to a specified reference polarization.
NOTE—The reference polarization is usually the copolarization.
2.88 cross-polar (radiation) pattern. A radiation pattern corresponding to the polarization orthogonal to
the co-polarization. See: co-polarization.
2.89 cross-polar side lobe level, relative. The maximum relative partial directivity (corresponding to the
cross polarization) of a side lobe with respect to the maximum partial directivity (corresponding to the copolarization)
of the antenna.
NOTE—Unless otherwise specified, the cross-polar side lobe level shall be taken to be that of the highest side lobe of the
cross-polar radiation pattern.
2.90 cross section. See: bistatic cross section; monostatic cross section; radar cross section; scattering
cross section.
2.91 cylindrical antenna. [Deprecated.] See: cylindrical array; cylindrical dipole.
2.92 cylindrical array. A two-dimensional array of elements whose corresponding points lie on a cylindrical
surface.
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Std 145-1993 IEEE STANDARD DEFINITIONS
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2.93 cylindrical dipole (antenna). A dipole, all of whose transverse cross sections are the same, the shape
of a cross section of a cylinder being circular.
2.94 cylindrical reflector. A reflector that is a portion of a cylindrical surface.
NOTE—The cylindrical surface is usually parabolic, although other shapes may be employed.
2.95 density-tapered array antenna. See: space-tapered array antenna.
2.96 depolarization. The conversion of power from a reference polarization into the cross polarization.
2.97 despun antenna. On a rotating vehicle, an antenna whose beam is scanned such that, with respect to
fixed reference axes, the beam is stationary.
2.98 dielectric constant. The real part of the complex dielectric constant.
2.99 dielectric rod antenna. An antenna that employs a shaped dielectric rod as the electrically significant
part of a radiating element.
NOTE—The polyrod rod antenna is a notable example of the dielectric rod antenna when constructed of polystyrene.
2.100 difference pattern. A radiation pattern characterized by a pair of main lobes of opposite phase, separated
by a single null, plus a family of side lobes, the latter usually desired to be at a low level. Contrast
with: sum pattern.
NOTE—Antennas used in many radar applications are capable of producing a sum pattern and two orthogonal difference
patterns. The difference patterns can be employed to determine the position of a target in a right/left and up/down
sense by antenna pattern pointing, which places the target in the null between the twin lobes of each difference pattern.
2.101 dipole. See: dipole antenna; electrically short dipole; folded dipole (antenna); half-wave dipole;
Hertzian electric dipole; Hertzian magnetic dipole; microstrip dipole; sleeve dipole antenna.
2.102 dipole antenna. Any one of a class of antennas producing a radiation pattern approximating that of an
elementary electric dipole. Syn: doublet antenna.
NOTE—Common usage considers the dipole antenna to be a metal radiating structure that supports a line current distribution
similar to that of a thin straight wire so energized that the current has a node only at each end.
2.103 directional antenna. An antenna having the property of radiating or receiving electromagnetic waves
more effectively in some directions than others.
NOTE—This term is usually applied to an antenna whose maximum directivity is significantly greater than that of a
half-wave dipole.
2.104 directional-null. A sharp minimum in a radiation pattern that has been produced for the purpose of
direction-finding or the suppression of unwanted radiation in a specified direction.
2.105 directional-null antenna. An antenna whose radiation pattern contains one or more directional nulls.
See: null-steering antenna system.
2.106 directive gain. [Deprecated.] See: directivity.
2.107 directivity (of an antenna) (in a given direction). The ratio of the radiation intensity in a given direction
from the antenna to the radiation intensity averaged over all directions.
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NOTES
1—The average radiation intensity is equal to the total power radiated by the antenna divided by 4.
2—If the direction is not specified, the direction of maximum radiation intensity is implied.
2.108 directivity, partial (of an antenna for a given polarization). In a given direction, that part of the
radiation intensity corresponding to a given polarization divided by the total radiation intensity averaged
over all directions.
NOTE—The (total) directivity of an antenna, in a specified direction, is the sum of the partial directivities for any two
orthogonal polarizations.
2.109 director element. A parasitic element located forward of the driven element of an antenna, intended
to increase the directivity of the antenna in the forward direction.
2.110 discone antenna. A biconical antenna with one cone having a vertex angle of 180°. See: biconical
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antenna.
2.111 Dolph-Chebyshev array antenna. [Deprecated.] See: Dolph-Chebyshev distribution.
2.112 Dolph-Chebyshev distribution. A set of excitation coefficients for an equispaced linear array antenna
such that the array factor can be expressed as a Chebyshev polynomial.
2.113 doublet antenna. See: dipole antenna.
2.114 driven element. A radiating element coupled directly to the feed line of an antenna.
2.115 effective area (of an antenna) (in a given direction). In a given direction, the ratio of the available
power at the terminals of a receiving antenna to the power flux density of a plane wave incident on the
antenna from that direction, the wave being polarization matched to the antenna. See: polarization match.
NOTES
1—If the direction is not specified, the direction of maximum radiation intensity is implied.
2—The effective area of an antenna in a given direction is equal to the square of the operating wavelength times its gain
in that direction divided by 4.
2.116 effective area, partial (of an antenna for a given polarization and direction). In a given direction,
the ratio of the available power at the terminals of a receiving antenna to the power flux density of a plane
wave incident on the antenna from that direction and with a specified polarization differing from the receiving
polarization of the antenna.
2.117 effective height of an antenna (high-frequency usage). The height of the antenna center of radiation
above the ground level.
NOTE—For an antenna with a symmetrical current distribution, the center of radiation is the center of distribution. For
an antenna with asymmetrical current distribution, the center of radiation is the center of current moments when viewed
from directions near the direction of maximum radiation.
2.118 effective isotropically radiated power. See: equivalent isotropically radiated power.
2.119 effective length of a linearly polarized antenna. For a linearly polarized antenna receiving a plane
wave from a given direction, the ratio of the magnitude of the open circuit voltage developed at the terminals
of the antenna to the magnitude of the electric field strength in the direction of the antenna polarization.
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NOTES
1—Alternatively, the effective length is the length of a thin straight conductor oriented perpendicularly to the given
direction and parallel to the antenna polarization, having a uniform current equal to that at the antenna terminals and producing
the same far-field strength as the antenna in that direction.
2—In low-frequency usage, the effective length of a vertically polarized ground-based antenna is frequently referred to
as effective height. Such usage should not be confused with effective height of an antenna (high-frequency usage).
2.120 effective radiated power (ERP). In a given direction, the relative gain of a transmitting antenna with
respect to the maximum directivity of a half-wave dipole multiplied by the net power accepted by the
antenna from the connected transmitter. Contrast with: equivalent isotropically radiated power. Syn:
equivalent radiated power.
2.121 electrical boresight. The tracking axis as determined by an electrical indication, such as the null
direction of a conical-scanning or monopulse antenna system, or the beam-maximum direction of a highly
directive antenna.
2.122 electrically short dipole. A dipole whose total length is small compared to the wavelength.
NOTE—For the common case that the two arms are collinear, the radiation pattern approximates that of a Hertzian
dipole.
2.123 electrically small antenna. An antenna whose dimensions are such that it can be contained within a
sphere whose diameter is small compared to a wavelength at the frequency of operation.
2.124 electric dipole. See: Hertzian electric dipole.
2.125 electromagnetic lens. See: lens, electromagnetic.
2.126 electromagnetic radiation. See: radiation, electromagnetic.
2.127 electronic scanning. Scanning an antenna beam by electronic or electric means without moving parts.
Syn: inertialess scanning.
2.128 element. See: array element; director element; driven element; linear electric current element;
linear magnetic current element; multi-wire element; parasitic element; radiating element; reflector
element.
2.129 element cell (of an array antenna). In an array having a regular arrangement of elements that can be
made congruent by translation, an element and a region surrounding it that, when repeated by translation,
covers the entire array without gaps or overlay between cells.
NOTE—There are many possible choices for such a cell. Some may be more convenient than others for analytic purposes.
2.130 elliptically polarized field vector. At a point in space, a field vector whose extremity describes an
ellipse as a function of time.
NOTE—Any single-frequency field vector is elliptically polarized if ―elliptical‖ is understood in the wide sense as
including circular and linear. Often, however, the expression is used in the strict sense meaning noncircular and nonlinear.
2.131 elliptically polarized plane wave. A plane wave whose electric field vector is elliptically polarized.
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2.132 end capacitor. A conducting element or group of conducting elements, connected at the end of a radiating
element of an antenna, to modify the current distribution on the antenna, thus changing its input impedance.
2.133 end-fire array antenna. A linear array antenna whose direction of maximum radiation lies along the
line of the array.
2.134 E-plane, principal. For a linearly polarized antenna, the plane containing the electric field vector and
the direction of maximum radiation.
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2.135 equivalent flat plate area of a scattering object. For a given scattering object, an area equal to the
wavelength times the square root of the ratio of the monostatic cross section to 4.
NOTE—A perfectly reflecting plate parallel to the incident wavefront and having this area, if it is large compared to the
wavelength, will have approximately the same monostatic cross section as the object.
2.136 equivalent isotropically radiated power (EIRP). In a given direction, the gain of a transmitting
antenna multiplied by the net power accepted by the antenna from the connected transmitter. Syn: effective
isotropically radiated power.
2.137 equivalent radiated power. See: effective radiated power.
2.138 equivalent sources. See: Huygens’ sources.
2.139 excitation (of an array antenna). For an array of radiating elements, the specification, in amplitude
and phase, of either the voltage applied to each element or the input current to each element.
2.140 excitation coefficients. The relative values, in amplitude and phase, of the excitation currents or voltages
of the radiating elements of an array antenna. Syn: feeding coefficients.
2.141 fan-beam antenna. An antenna producing a major lobe whose transverse cross section has a large
ratio of major to minor dimensions.
2.142 far-field (radiation) pattern. Any radiation pattern obtained in the far-field of an antenna.
NOTE—Far-field patterns are usually taken over paths on a spherical surface. See: radiation pattern cut; radiation
sphere.
2.143 far-field region. That region of the field of an antenna where the angular field distribution is essentially
independent of the distance from a specified point in the antenna region.
NOTES
1—In free space, if the antenna has a maximum overall dimension, D, that is large compared to the wavelength, the farfield
region is commonly taken to exist at distances greater than 2D2/from the antenna, being the wavelength. The
far-field patterns of certain antennas, such as multi-beam reflector antennas, are sensitive to variations in phase over their
apertures. For these antennas, 2D2/may be inadequate.
2—In physical media, if the antenna has a maximum overall dimension, D, that is large compared to /, the far-field
region can be taken to begin approximately at a distance equal to D2/from the antenna, being the propagation
constant in the medium.
2.144 far-field region in physical media. See: far-field region, NOTE 2.
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2.145 feed of an antenna. (A) For continuous aperture antennas, the feed is the primary radiator; for example,
a horn feeding a reflector. (B) For array antennas, that portion of the antenna system which functions to
produce the excitation coefficients.
2.146 feeding coefficients. See: excitation coefficients.
2.147 feed line. A transmission line interconnecting an antenna and a transmitter or receiver or both.
2.148 field pattern. See: radiation pattern.
2.149 figure of merit (of an antenna) (G/T). The ratio of the gain to the noise temperature of an antenna.
NOTES
1—Usually the antenna-receiver system figure of merit is specified. For this case, the figure of merit is the gain of the
antenna divided by the system noise temperature referred to the antenna terminals.
2—The system figure of merit at any reference plane in the RF system is the same as that taken at the antenna terminals
since both the gain and system noise temperature are referred to the same reference plane.
2.150 fishbone antenna. An end-fire, traveling wave antenna consisting of a balanced transmission line to
which is coupled, usually through lumped circuit elements, an array of closely spaced, coplanar dipoles.
2.151 flat-top antenna. A short vertical monopole antenna with an end capacitor whose elements are all in
the same horizontal plane. See: end capacitor; top-loaded vertical antenna.
2.152 flush-mounted antenna. An antenna constructed into the surface of a mechanism, or of a vehicle,
without affecting the shape of that surface. Contrast with: conformal antenna.
2.153 folded dipole (antenna). An antenna composed of two or more parallel, closely-spaced dipole antennas
connected together at their ends with one of the dipole antennas fed at its center and the others short-circuited
at their centers.
2.154 folded monopole (antenna). A monopole antenna formed from half of a folded dipole with the unfed
element(s) directly connected to the imaging plane.
2.155 footprint (of an antenna beam on a specified surface). An area bounded by a contour on a specified
surface formed by the intersection of the surface and that portion of the beam of an antenna above a specified
minimum gain level, the orientation of the beam with respect to the surface being specified.
2.156 Fraunhofer pattern. A radiation pattern obtained in the Fraunhofer region of an antenna.
NOTE—For an antenna focused at infinity, a Fraunhofer pattern is a far-field pattern.
Fraunhofer region. The region in which the field of an antenna is focused.
NOTES
1—In the Fraunhofer region of an antenna focused at infinity, the values of the fields, when calculated from knowledge
of the source distribution of an antenna, are sufficiently accurate when the quadratic phase terms (and higher order
terms) are neglected.
2—See: NOTE 2 of far-field region for a more restricted usage.
2.157 free-space loss. The loss between two isotropic radiators in free space, expressed as a power ratio.
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NOTE—The free-space loss is not due to dissipation, but rather due to the fact that the power flux density decreases with
the square of the separation distance. It is usually expressed in decibels and is given by the formula 20log(4R/), where
R is the separation of the two antennas andis the wavelength.
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2.158 Fresnel contour. The locus of points on a surface for which the sum of the distances to a source point
and an observation point is a constant, differing by a multiple of a half-wavelength from the minimum value
of the sum of the distances.
NOTE—This definition applies to media which are isotropic and homogeneous. For the general case, the distances along
optical paths must be employed.
2.159 Fresnel lens antenna. An antenna consisting of a feed and a lens, usually planar, that transmits the
radiated power from the feed through the central zone and alternate Fresnel zones of the illuminating field on
the lens. Syn: zone-plate lens antenna.
2.160 Fresnel pattern. A radiation pattern obtained in the Fresnel region.
2.161 Fresnel region. The region (or regions) adjacent to the region in which the field of an antenna is
focused (that is, just outside the Fraunhofer region).
NOTES
1—In the Fresnel region in space, the values of the fields, when calculated from knowledge of the source distribution of
an antenna, are insufficiently accurate unless the quadratic phase terms are taken into account, but are sufficiently accurate
if the quadratic phase terms are included.
2—See: NOTE 2 of near-field region, radiating for a more restricted usage.
2.162 Fresnel zone. The region on a surface between successive Fresnel contours.
NOTE—Fresnel zones are usually numbered consecutively, with the first zone containing the minimum path length.
2.163 front-to-back ratio. The ratio of the maximum directivity of an antenna to its directivity in a specified
rearward direction.
NOTES
1—This definition is usually applied to beamtype patterns.
2—If the rearward direction is not specified, it shall be taken to be that of the maximum directivity in the rearward hemisphere
relative to the antenna‘s orientation.
2.164 gain. See: gain, partial (of an antenna for a given polarization); realized gain; realized gain, partial
(of an antenna for a given polarization).
2.165 gain (in a given direction). The ratio of the radiation intensity, in a given direction, to the radiation
intensity that would be obtained if the power accepted by the antenna were radiated isotropically. Syn: absolute
gain (of an antenna).
NOTES
1—Gain does not include losses arising from impedance and polarization mismatches.
2—The radiation intensity corresponding to the isotropically radiated power is equal to the power accepted by the
antenna divided by 4.
3—If an antenna is without dissipative loss, then in any given direction, its gain is equal to its directivity.
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4—If the direction is not specified, the direction of maximum radiation intensity is implied.
5—The term absolute gain is used in those instances where added emphasis is required to distinguish gain from relative
gain; for example, absolute gain measurements.
2.166 gain, partial (of an antenna for a given polarization). In a given direction, that part of the radiation
intensity corresponding to a given polarization divided by the radiation intensity that would be obtained if
the power accepted by the antenna were radiated isotropically.
NOTE—The (total) gain of an antenna, in a specified direction, is the sum of the partial gains for any two orthogonal
polarizations.
2.167 geodesic lens antenna. A lens antenna having a two-dimensional lens, with uniform index of refraction,
disposed on a surface such that the rays in the lens follow geodesic (minimal) paths of the surface.
2.168 grating lobe. A lobe, other than the main lobe, produced by an array antenna when the interelement
spacing is sufficiently large to permit the in-phase addition of radiated fields in more than one direction.
2.169 Gregorian reflector antenna. A paraboloidal reflector antenna with a concave subreflector, usually
ellipsoidal in shape, located at a distance from the vertex of the main reflector that is greater than the prime
focal length of the main reflector.
NOTE—To improve the aperture efficiency of the antenna, the shapes of the main reflector and subreflector are sometimes
modified.
2.170 ground plane. A conducting or reflecting plane functioning to image a radiating structure. Syn: imaging
plane.
2.171 ground rod. A conducting rod serving as an electrical connection with the ground.
2.172 ground system. That portion of an antenna consisting of a system of conductors or a conducting surface
in or on the ground.
2.173 half-power beamwidth. In a radiation pattern cut containing the direction of the maximum of a lobe,
the angle between the two directions in which the radiation intensity is one-half the maximum value. See:
principal half-power beamwidths.
2.174 half-wave dipole. A wire antenna consisting of two straight collinear conductors of equal length, separated
by a small feeding gap, with each conductor approximately a quarter-wavelength long.
NOTE—This antenna gets its name from the fact that its overall length is approximately a half-wavelength. In practice,
the length is usually slightly smaller than a half-wavelength—enough to cause the input impedance to be pure real (jX =
0).
2.175 helical antenna. An antenna whose configuration is that of a helix.
NOTE—The diameter, pitch, and number of turns in relation to the wavelength provide control of the polarization state
and directivity of helical antennas.
2.176 Hertzian electric dipole. An elementary source consisting of a time-harmonic electric current element
of specified direction and infinitesimal length. Syn: linear [lineal] electric current element.
NOTES
1—The continuity equation relating current to charge requires that opposite ends of the current element be terminated by
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APPENDIX B
equal and opposite amounts of electric charge, these amounts also varying harmonically with time.
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2—As its length approaches zero, the current must approach infinity in such a manner that the product of current and
length remains finite.
2.177 Hertzian magnetic dipole. A fictitious elementary source consisting of a time-harmonic magnetic
current element of specified direction and infinitesimal length. Syn: linear [lineal] magnetic current element.
NOTES
1—The continuity equation relating current to charge requires that opposite ends of the current element be terminated by
equal and opposite amounts of magnetic charge, these amounts also varying harmonically with time.
2—As its length approaches zero, the current must approach infinity in such a manner that the product of current and
length remains finite.
3—A magnetic dipole has the same radiation pattern as an infinitesimally small electric current loop.
2.178 hoghorn antenna. A reflector antenna consisting of a sectoral horn that physically intersects a reflector
in the form of a parabolic cylinder, a part of one of the nonparallel sides of the horn being removed to
form the antenna aperture.
2.179 horizontally polarized field vector. A linearly polarized field vector whose direction is horizontal.
2.180 horizontally polarized plane wave. A plane wave whose electric field vector is horizontally polarized.
2.181 horn (antenna). An antenna consisting of a waveguide section in which the cross sectional area
increases towards an open end that is the aperture.
2.182 horn reflector antenna. An antenna consisting of a portion of a paraboloidal reflector fed with an offset
horn that physically intersects the reflector, part of the wall of the horn being removed to form the
antenna aperture.
NOTE—The horn is usually either pyramidal or conical, with an axis perpendicular to that of the paraboloid.
2.183 H-plane, principal. For a linearly polarized antenna, the plane containing the magnetic field vector
and the direction of maximum radiation.
2.184 Huygens’ source radiator. An elementary radiator having the radiation properties of an infinitesimal
area of a propagating electromagnetic wavefront.
2.185 Huygens’ sources. Electric and magnetic sources that, if properly distributed on a closed surface S in
substitution for the actual sources inside S, will ensure the result that the electromagnetic field at all points
outside S is unchanged. Syn: equivalent sources.
2.186 hybrid-mode horn (antenna). A horn antenna excited by one or more hybrid waveguide modes in
order to produce a specified aperture illumination.
2.187 imaging plane. See: ground plane.
2.188 impedance. See: active impedance (of an array element); impedance mismatch factor; input
impedance (of an antenna); intrinsic impedance; isolated impedance (of an array element); mutual
coupling effect (on input impedance of an array element); mutual impedance; self-impedance of an
array element.
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2.189 impedance mismatch factor. The ratio of the power accepted by an antenna to the power incident at
the antenna terminals from the transmitter.
NOTE—The impedance mismatch factor is equal to one minus the magnitude squared of the input reflection coefficient
of the antenna.
2.190 inertialess scanning. See: electronic scanning.
2.191 input impedance (of an antenna). The impedance presented by an antenna at its terminals.
2.192 integrated antenna system. A radiator with an active or nonlinear circuit element or network incorporated
physically within the structure of the radiator.
2.193 intercardinal plane. Any plane that contains the intersection of two successive cardinal planes and is
at an intermediate angular position.
NOTE—In practice, the intercardinal planes are located by dividing the angle between successive cardinal planes into
equal parts. Often, it is sufficient to bisect the angle so that there is only one intercardinal plane between successive cardinal
planes.
2.194 interferometer antenna. An array antenna in which the interelement spacings are large compared to
wavelength and element size so as to produce grating lobes.
2.195 intrinsic impedance. [Deprecated in the sense of input impedance of an antenna.]
2.196 invisible range. See: visible range.
2.197 isolated impedance (of an array element). The input impedance of a radiating element of an array
antenna with all other elements of the array absent.
2.198 isolation between antennas. A measure of power transfer from one antenna to another.
NOTE—The isolation between antennas is the ratio of power input to one antenna to the power received by the other,
usually expressed in decibels.
2.199 isotropic radiator. A hypothetical, lossless antenna having equal radiation intensity in all directions.
NOTE—An isotropic radiator represents a convenient reference for expressing the directive properties of actual antennas.
2.200 leaky-wave antenna. An antenna that couples power in small increments per unit length, either continuously
or discretely, from a traveling wave structure to free space.
2.201 left-hand polarization of a field vector. See: sense of polarization.
2.202 left-hand polarization of a plane wave. See: sense of polarization.
2.203 lens antenna. An antenna consisting of an electromagnetic lens and a feed that illuminates it.
2.204 lens, electromagnetic. A three-dimensional structure, through which electromagnetic waves can pass,
possessing an index of refraction that may be a function of position and a shape that is chosen so as to control
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APPENDIX B
the exiting aperture illumination.
2.205 lineal electric current element. See: Hertzian electric dipole.
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2.206 lineal magnetic current element. See: Hertzian magnetic dipole.
2.207 linear antenna. An antenna consisting of one or more segments of straight conducting cylinders.
NOTES
1—This term has restricted usage, and applies to straight cylindrical wire antennas. This term should not be confused
with the conventional usage of ―linear‖ in circuit theory.
2—Contrast with: linear array antenna.
2.208 linear array antenna. A one-dimensional array of elements whose corresponding points lie along a
straight line.
2.209 linear Bayliss distribution. See: Bayliss distribution, linear.
2.210 linear electric current element. See: Hertzian electric dipole.
2.211 linear magnetic current element. See: Hertzian magnetic dipole.
2.212 linear Taylor distribution. See: Taylor distribution, linear.
2.213 linearly polarized field vector. At a point in space, a field vector whose extremity describes a straight
line segment as a function of time.
NOTE—Linear polarization may be viewed as a special case of elliptical polarization where the axial ratio has become
infinite.
2.214 linearly polarized plane wave. A plane wave whose electric field vector is linearly polarized.
2.215 line source. A continuous distribution of sources of electromagnetic radiation, lying along a line segment.
NOTE—Most often in practice the line segment is straight.
2.216 line source corrector. A linear array antenna feed with radiating element locations and excitations
chosen to correct for aberrations present in the focal region fields of a reflector.
2.217 loaded linear antenna. See: sectionalized linear antenna.
2.218 loading. The modification of a basic antenna such as a dipole or monopole caused by the addition of
conductors or circuit elements that change the input impedance or current distribution or both.
2.219 lobe. See: back lobe; beam of an antenna; major lobe; minor lobe; side lobe; shoulder lobe; vestigial
lobe.
2.220 lobe switching. A form of scanning in which the direction of maximum radiation is discretely
changed by switching. See: sequential lobing.
2.221 log periodic antenna. Any one of a class of antennas having a structural geometry such that its
impedance and radiation characteristics repeat periodically as the logarithm of frequency.
2.222 long-wire antenna. A wire antenna that, by virtue of its considerable length in comparison with the
operating wavelength, provides a directional radiation pattern.
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2.223 loop antenna. An antenna whose configuration is that of a loop.
NOTE—If the electric current in the loop, or in multiple parallel turns of the loop, is essentially uniform and the loop
circumference is small compared with the wavelength, the radiated pattern approximates that of a Hertzian magnetic
dipole.
2.224 loop stick antenna. A loop receiving antenna with a ferrite rod core used for increasing its radiation
efficiency.
2.225 Luneburg lens antenna. A lens antenna with a circular cross section having an index of refraction
varying only in the radial direction such that a feed located on or near a surface or edge of the lens produces
a major lobe diametrically opposite the feed.
2.226 magnetic dipole. See: Hertzian magnetic dipole.
2.227 main lobe. See: major lobe.
2.228 main reflector. The largest reflector of a multiple reflector antenna.
2.229 major lobe. The radiation lobe containing the direction of maximum radiation. Syn: main lobe.
NOTE—In certain antennas, such as multilobed or splitbeam antennas, there may exist more than one major lobe.
2.230 maximum relative side lobe level. See: side lobe level, maximum relative.
2.231 mean side lobe level. The average value of the relative power pattern of an antenna taken over a specified
angular region, which excludes the main beam, the power pattern being relative to the peak of the main
beam.
2.232 microstrip antenna. An antenna that consists of a thin metallic conductor bonded to a thin grounded
dielectric substrate.
NOTE—The metallic conductor typically has some regular shape; for example, rectangular, circular, or elliptical. Feeding
is often by means of a coaxial probe or a microstrip transmission line.
2.233 microstrip array. An array of microstrip antennas.
2.234 microstrip dipole. A microstrip antenna of rectangular shape with its width much smaller than its
length.
2.235 Mills cross antenna system. A multiplicative array antenna system consisting of two linear receiving
arrays positioned at right angles to one another and connected together by a phase modulator or switch such
that the effective angular response of the output is related to the product of the radiation patterns of the two
arrays.
2.236 minor lobe. Any radiation lobe except a major lobe. See: back lobe; side lobe.
2.237 monopole. An antenna, constructed above an imaging plane, that produces a radiation pattern approximating
that of an electric dipole in the half-space above the imaging plane.
2.238 monopulse. Simultaneous lobing whereby direction-finding information is obtainable from a single
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APPENDIX B
pulse.
2.239 monostatic cross section. The scattering cross section in the direction toward the source. Contrast
with: bistatic cross section. Syn: back-scattering cross section.
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2.240 multi-beam antenna. An antenna capable of creating a family of major lobes from a single non-moving
aperture, through use of a multiport feed, with one-to-one correspondence between input ports and member
lobes, the latter characterized by having unique main beam pointing directions.
NOTE—Often, the multiple main beam angular positions are arranged to provide complete coverage of a solid angle
region of space.
2.241 multiple-tuned antenna. An antenna designed to operate, without modification, in any of a number of
pre-set frequency bands.
2.242 multiplicative array antenna system. A signal-processing antenna system consisting of two or more
receiving antennas and circuitry in which the effective angular response of the output of the system is related
to the product of the radiation patterns of the separate antennas.
2.243 multi-wire element. A radiating element composed of several wires connected in parallel, the assemblage
being the electrical equivalent of a single conductor larger than any one of the individual wires.
2.244 mutual coupling effect (A) (on the radiation pattern of an array antenna). For array antennas, the
change in antenna pattern from the case when a particular feeding structure is attached to the array and
mutual impedances among elements are ignored in deducing the excitation to the case when the same feeding
structure is attached to the array and mutual impedances among elements are included in deducing the
excitation.
(B) (on input impedance of an array element). For array antennas, the change in input impedance of an
array element from the case when all other elements are present but open-circuited to the case when all other
elements are present and excited.
2.245 mutual impedance. The mutual impedance between any two terminal pairs in a multielement array
antenna is equal to the open-circuit voltage produced at the first terminal pair divided by the current supplied
to the second when all other terminal pairs are open-circuited.
2.246 near-field (radiation) pattern. Any radiation pattern obtained in the near-field of an antenna. See:
Fresnel pattern.
NOTE—Near-field patterns are usually taken over paths on planar, cylindrical, or spherical surfaces. See: radiation pattern
cut.
2.247 near-field region. That part of space between the antenna and far-field region.
NOTE—In lossless media, the near-field may be further subdivided into reactive and radiating near-field regions.
2.248 near-field region in physical media. [Deprecated.]
2.249 near-field region, radiating. That portion of the near-field region of an antenna between the farfield
and the reactive portion of the near-field region, wherein the angular field distribution is dependent upon distance
from the antenna.
NOTES
1—If the antenna has a maximum overall dimension that is not large compared to the wavelength, this field region may
not exist.
2—For an antenna focused at infinity, the radiating near-field region is sometimes referred to as the Fresnel region on the
basis of analogy to optical terminology.
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2.250 near-field region, reactive. That portion of the near-field region immediately surrounding the
antenna, wherein the reactive field predominates.
NOTE—For a very short dipole, or equivalent radiator, the outer boundary is commonly taken to exist at a distance /2
from the antenna surface, whereis the wavelength.
2.251 noise temperature of an antenna. The temperature of a resistor having an available thermal noise
power per unit bandwidth equal to that at the antenna output at a specified frequency.
NOTE—Noise temperature of an antenna depends on its coupling to all noise sources in its environment, as well as noise
generated within the antenna.
2.252 normalized directivity. See: antenna [aperture] illumination efficiency.
2.253 null steering. To control, usually electronically, the direction at which a directional null appears in the
radiation pattern of an operational antenna.
2.254 null-steering antenna system. An antenna having in its radiation pattern one or more directional nulls
that can be steered, usually electronically.
2.255 offset paraboloidal reflector. See: paraboloidal reflector.
2.256 offset paraboloidal reflector antenna. A reflector antenna whose main reflector is a portion of a
paraboloid that is not symmetrical with respect to its focal axis, and does not include the vertex so that aperture
blockage by the feed is reduced or eliminated.
2.257 omnidirectional antenna. An antenna having an essentially non-directional pattern in a given plane
of the antenna and a directional pattern in any orthogonal plane. Contrast with: isotropic antenna.
NOTE—For ground-based antennas, the omnidirectional plane is usually horizontal.
2.258 orthogonal polarization (with respect to a specified polarization). In a common plane of polarization,
the polarization for which the inner product of the corresponding polarization vector and that of the
specified polarization is equal to zero. See: polarization vector, NOTE 2 for a definition of the inner product.
NOTES
1—The two orthogonal polarizations can be represented as two diametrical points on the Poincaré sphere.
2—Two elliptically polarized fields having the same plane of polarization have orthogonal polarizations if their polarization
B-13 | P a g e
APPENDIX B
ellipses have the same axial ratio, major axes at right angles, and opposite senses of polarization.
2.259 parabolic torus reflector. A toroidal reflector formed by rotating a segment of a parabola about a nonintersecting
co-planar line.
2.260 paraboloidal reflector. An axially symmetric reflector that is a portion of a paraboloid.
NOTE—This term may be applied to any reflector that is a portion of a paraboloid, provided the term is appropriately
qualified. For example, if the reflector is a portion of a paraboloid but does not include its vertex, then it may be called an
off-set paraboloidal reflector.
2.261 parallel [perpendicular] polarization. A linear polarization for which the field vector is parallel
[perpendicular] to some reference plane.
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NOTE—These terms are applied mainly to uniform plane waves incident upon a plane of discontinuity (surface of the
earth, surface of a dielectric or a conductor). Then, the convention is to take as reference the plane of incidence; that is,
the plane containing the direction of propagation and the normal to the surface of discontinuity. If these two directions
coincide, the reference plane must be specified by some other convention.
2.262 parasitic element. A radiating element that is not connected to the feed lines of an antenna and that
materially affects the radiation pattern or impedance of an antenna, or both. Contrast with: driven element.
2.263 partial directivity (of an antenna, for a given polarization). See: directivity, partial (of an
antenna, for a given polarization).
2.264 partial effective area (of an antenna, for a given polarization and direction). See: effective area,
partial (of an antenna for a given polarization and direction).
2.265 partial gain (of an antenna for a given polarization). See: gain, partial (of an antenna for a given
polarization).
2.266 partial realized gain (of an antenna for a given polarization. See: realized gain, partial (of an
antenna for a given polarization).
2.267 pencil-beam antenna. An antenna whose radiation pattern consists of a single main lobe with narrow
principal half-power beamwidths and side lobes having relatively low levels.
NOTE—The main lobe usually has approximately elliptical contours of equal radiation intensity in the angular region
around the peak of the main lobe. This type of pattern is diffraction-limited in practice. It is often called a sum pattern in
radar applications.
2.268 periscope antenna. An antenna consisting of a very directive feed located close to ground level and
oriented so that its beam illuminates an elevated reflector that is oriented so as to produce a horizontal beam.
2.269 perpendicular polarization. See: parallel polarization.
2.270 phase center. The location of a point associated with an antenna such that, if it is taken as the center of
a sphere whose radius extends into the far-field, the phase of a given field component over the surface of the
radiation sphere is essentially constant, at least over that portion of the surface where the radiation is significant.
NOTE—Some antennas do not have a unique phase center.
2.271 phase of a circularly polarized field vector. In the plane of polarization, the angle that the field vector
makes, at a time taken as the origin, with a reference direction and with the angle counted as positive if it
is in the same direction as the sense of polarization and negative if it is in the opposite direction to the sense
of polarization.
2.272 phase pattern (of an antenna). The spatial distribution of the relative phase of a field vector excited
by an antenna.
NOTES
1—The phase may be referred to any arbitrary reference.
2—The distribution of phase over any path, surface, or radiation pattern cut is also called a phase pattern.
2.273 phase, relative, of an elliptically polarized field vector. The phase angle of the unitary factor by
which the polarization-phase vector for the given field vector differs from that of a reference field vector
with the same polarization.
IEEE
Std 145-1993 IEEE STANDARD DEFINITIONS
24
NOTES
1—The relative phase of an elliptically polarized field can be defined with respect to that of another field having
the same polarization. In that case, the polarization vectors and have the same direction and, being of unit magnitudes,
they differ only by a unitary factor: The angle is the phase difference between and .
2—The field vectors and describe similar ellipses as t varies. The angle is 2
times the area of the sector shown on the figure divided by the area of the ellipse described by the extremity of
For circular polarization, is the angle between and at any instant of time.
3—The phase of an elliptically polarized field vector can be expressed relative to a spatial direction in its plane of polarization.
For example, the phase angle is given by 2times the area of the sector shown on the figure, which is bounded
by and the reference, divided by the area of the ellipse described by The angle is positive if it is in the same
direction as the sense of polarization and negative if it is in the direction opposite to the sense of polarization.
2.274 pillbox antenna. A reflector antenna having a cylindrical reflector enclosed by two parallel conducting
plates perpendicular to the cylinder, spaced less than one wavelength apart. Contrast with: cheese
antenna.
2.275 planar array. A two-dimensional array of elements whose corresponding points lie in a plane.
2.276 plane of polarization. A plane containing the polarization ellipse.
NOTES
1—When the ellipse degenerates into a line segment, the plane of polarization is not uniquely defined. In general, any
plane containing the segment is acceptable; however, for a plane wave in an isotropic medium, the plane of polarization
is taken to be normal to the direction of propagation.
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APPENDIX B
2—In optics, the expression plane of polarization is associated with a linearly polarized plane wave (sometimes called a
plane polarized wave) and is defined as a plane containing the field vector of interest and the direction of propagation.
This usage would contradict the above one and is deprecated.
2.277 plane polarized wave. See: plane of polarization.
2.278 plane wave. A wave in which the only spatial dependence of the field vectors is through a common
exponential factor whose exponent is a linear function of position.
E1

E0

eˆ1 eˆ0
eˆ1 = e jeˆ0. E1

E0

E(t)

E(0)
REFERENCE

E1tRe

E1e jt =

E0 t = Re 
E0e jt

E0t.
E0

E1

E1 (t )

E (t) 0


E0
Et.
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OF TERMS FOR ANTENNAS Std 145-1993
25
NOTES
1—In a linear, homogeneous, and isotropic space the electric field vector, magnetic field vector and the propagation vector
are mutually perpendicular. The ratio of the magnitude of the electric field vector to the magnitude of the magnetic
field vector is equal to the intrinsic impedance of the medium; for free space the intrinsic impedance is equal to
376.730 or approximately 120.
2—A plane wave can be resolved into two component waves corresponding to two orthogonal polarizations. The total
power flux density of the plane wave at a given point in space is equal to the sum of the power flux densities in the
orthogonal component waves.
2.279 Poincaré sphere. A sphere whose points are associated in a one-to-one fashion with all possible
polarization states of a plane wave [field vector] according to the following rules: The longitude equals twice
the tilt angle and the latitude is twice the angle whose cotangent is the negative of the axial ratio of the polarization
ellipse.
NOTES
1—For this definition, the axial ratio carries a sign. See: axial ratio (of a polarization ellipse), NOTE.
2—The points of the northern hemisphere of the Poincaré sphere represent polarizations with a left-hand sense and those
of the southern hemisphere represent polarization with a right-hand sense. The north pole represents left-hand circular
polarization and the south pole right-hand circular polarization. The points of the equator represent all possible linear
polarizations.
2.280 polarization (of an antenna). In a given direction from the antenna, the polarization of the wave
transmitted by the antenna. See: polarization of a wave radiated by an antenna.
NOTE—When the direction is not stated, the polarization is taken to be the polarization in the direction of maximum
gain.
2.281 polarization [of a wave (radiated by an antenna in a specified direction)]. In a specified direction
from an antenna and at a point in its far field, the polarization of the (locally) plane wave that is used to represent
the radiated wave at that point.
NOTE—At any point in the far field of an antenna, the radiated wave can be represented by a plane wave whose electric
field strength is the same as that of the wave and whose direction of propagation is in the radial direction from the
antenna. As the radial distance approaches infinity, the radius of curvature of the radiated wave‘s phase front also
approaches infinity, and thus, in any specified direction, the wave appears locally as a plane wave.
2.282 polarization efficiency. The ratio of the power received by an antenna from a given plane wave of
arbitrary polarization to the power that would be received by the same antenna from a plane wave of the
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APPENDIX B
same power flux density and direction of propagation, whose state of polarization has been adjusted for a
maximum received power. Syn: polarization mismatch factor.
NOTES
1—The polarization efficiency is equal to the square of the magnitude of the inner product of the polarization vector
describing the receiving polarization of the antenna and the polarization vector of the plane wave incident at the antenna.
See: polarization vector, NOTE 2 for definition of the inner product.
2—If the receiving polarization of an antenna and the polarization of an incident plane wave are properly located as
points on the Poincaré sphere, then the polarization efficiency is given by the square of the cosine of one-half the angular
separation of the two points.
2.283 polarization match. The condition that exists when a plane wave, incident upon an antenna from a
given direction, has a polarization that is the same as the receiving polarization of the antenna in that direction.
See: receiving polarization (of an antenna).
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Std 145-1993 IEEE STANDARD DEFINITIONS
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2.284 polarization mismatch factor. See: polarization efficiency.
2.285 polarization mismatch loss. The magnitude, expressed in decibels, of the polarization efficiency.
2.286 polarization pattern (of an antenna). (A) The spatial distribution of the polarizations of a field vector
excited by an antenna taken over its radiation sphere. (B) The response of a given antenna to a linearly
polarized plane wave incident from a given direction and whose direction of polarization is rotating about an
axis parallel to its propagation vector; the response being plotted as a function of the angle that the direction
of polarization makes with a given reference direction.
NOTES
1—When describing the polarizations over the radiation sphere [definition (A)], or a portion of it, reference lines shall be
specified over the sphere, in order to measure the tilt angles of the polarization ellipses [see: tilt angle (of a polarization
ellipse)] and the direction of polarization for linear polarizations. An obvious choice, though by no means the only one,
is a family of lines tangent at each point on the sphere to either the or coordinate line associated with a spherical
coordinate system of the radiation sphere.
2—At each point on the radiation sphere, the polarization is usually resolved into a pair of orthogonal polarizations, the
co-polarization and the cross polarization (See: co-polarization; cross polarization). To accomplish this, the co-polarization
must be specified at each point on the radiation sphere. For certain linearly polarized antennas, it is common
practice to define the co-polarization in the following manner: First specify the orientation of the co-polar electric field
vector at a pole of the radiation sphere. Then, for all other directions of interest (points on the radiation sphere), require
that the angle that the co-polar electric field vector makes with each great circle line through the pole remain constant
over that circle, the angle being that at the pole. In practice, the axis of the antenna‘s main beam should be directed along
the polar axis of the radiation sphere. The antenna is then appropriately oriented about this axis to align the direction of
its polarization with that of the defined co-polarization at the pole. This manner of defining co-polarization can be
extended to the case of elliptical polarization by defining the constant angles using the major axes of the polarization
ellipses rather than the co-polar electric field vector. The sense of polarization must also be specified.
3—The polarization pattern [definition (B)] generally has the shape of a dumbbell. The polarization ellipse of the
antenna in the given direction is similar to one that can be inscribed in the dumbbell shape with points of tangency at the
maxima and minima points; thus, the axial ratio and tilt angle can be obtained from the polarization pattern.
2.287 polarization-phase vector (for a field vector). The polarization vector, among all of those that define
the same polarization, that carries the phase information of the field vector whose polarization it represents.
See: polarization vector (for a field vector).
NOTE—The polarization-phase vector of the field vector is given by where is magnitude of that is, the
positive square root of
2.288 polarization ratio. The magnitude of a complex polarization ratio.
2.289 polarization, receiving (of an antenna). The polarization of a plane wave, incident from a given
direction and having a given power flux density, that results in maximum available power at the antenna terminals.
NOTES
1—The receiving polarization of an antenna is related to the antenna‘s polarization on transmit (see definition above) in
the following way: In the same plane of polarization, the polarization ellipses have the same axial ratio, the same sense
of polarization, and the same spatial orientation. Since their senses of polarization and spatial orientation are specified by
viewing their polarization ellipses in the respective directions into which they are propagating, one should note that (a)
although their senses of polarization are the same, they would appear to be opposite if both waves were viewed in the
same direction; and (b) their tilt angles are such that they are the negative of one another with respect to a common reference.
2—The receiving polarization may be used to specify the polarization characteristic of a non-reciprocal antenna that
may transmit and receive arbitrarily different polarizations.
E

e

E/E E E


E*E.

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2.290 polarization state (of a plane wave [field vector]). See: state of polarization (of a plane wave
[field vector]).
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APPENDIX B
2.291 polarization vector (for a field vector). A unitary vector that describes the state of polarization of a
field vector at a given point in space.
NOTES
1—Polarization vectors differing only by a unitary factor (ejwhere is real) correspond to the same polarization state.
2—The appropriate inner product, < , >, for two polarization vectors in the same planes of polarization is given by
< , > = , where and represent the polarization vectors corresponding to polarizations 1 and 2.
3—The magnitude of the inner product of polarization vectors representing the same polarization is equal to unity. The
inner product of two polarization vectors representing orthogonal polarization is zero.
4—The inner product of a polarization vector corresponding to a specified polarization, and a complex electric field
vector , at a point in space will yield the component of the electric field vector corresponding to the specified polarization,
; that is,
5—The basis vectors for the components of the polarization vector may correspond to any two orthogonal polarizations,
the most common being two orthogonal linear polarizations or right-hand and left-hand circular polarizations.
6—Contrast with: polarization-phase vector (for a field vector).
2.292 Potter horn. A circular horn with one or more abrupt changes in diameter that excites two or more
waveguide modes in order to produce a specified aperture illumination.
2.293 power gain. [Deprecated.] See: gain, partial (of an antenna).
2.294 power pattern. See: radiation pattern.
2.295 power reflectance of a radome. At a given point on a radome, the ratio of the power flux density that
is internally reflected from the radome to that incident on the radome from an internal radiating source.
2.296 power transmittance of a radome. In a given direction, the ratio of the power flux density emerging
from a radome with an internal source to the power flux density that would be obtained if the radome were
removed.
2.297 primary radiator. The radiating element of a reflector or lens antenna that is coupled to the transmitter
or receiver directly, or through a feed line.
NOTE—For some applications, an array of radiating elements is employed.
2.298 principal E-plane. See: E-plane, principal.
2.299 principal half-power beamwidths. For a pattern whose major lobe has a half-power contour that is
essentially elliptical, the half-power beamwidths in the two pattern cuts that contain the major and minor
axes of the ellipse, respectively.
2.300 principal H-plane. See: H-plane, principal.
2.301 printed circuit antenna. An antenna of some desired shape bonded onto a dielectric substrate.
NOTE—The microstrip antenna is a notable example. See: microstrip antenna.
eˆ1 eˆ2
eˆ1 eˆ2 eˆ1* eˆ2 eˆ1 eˆ2
eˆ1
E

E1

E1 eˆ1*

= E eˆ1.
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Std 145-1993 IEEE STANDARD DEFINITIONS
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2.302 proximity-coupled dipole array antenna. An array antenna consisting of a series of coplanar
dipoles, loosely coupled to the electromagnetic field of a balanced transmission line, the coupling being a
function of the proximity and orientation of the dipole with respect to the transmission line.
2.303 pyramidal horn antenna. A horn antenna, the sides of which form a pyramid.
2.304 Q of a resonant antenna. The ratio of 2times the energy stored in the fields excited by the antenna
to the energy radiated and dissipated per cycle.
NOTE—For an electrically small antenna, it is numerically equal to one-half the magnitude of the ratio of the incremental
change in impedance to the corresponding incremental change in frequency at resonance, divided by the ratio of the
antenna resistance to the resonant frequency.
2.305 radar cross section. For a given scattering object, upon which a plane wave is incident, that portion of
the scattering cross section corresponding to a specified polarization component of the scattered wave. See:
scattering cross section.
2.306 radiating element. A basic subdivision of an antenna that in itself is capable of radiating or receiving
radio waves.
NOTE—Typical examples of a radiating element are a slot, horn, or dipole antenna.
2.307 radiating near-field region. See: near-field region, radiating.
2.308 radiation efficiency. The ratio of the total power radiated by an antenna to the net power accepted by
the antenna from the connected transmitter.
2.309 radiation, electromagnetic. The emission of electromagnetic energy from a finite region in the form
of unguided waves.
2.310 radiation intensity. In a given direction, the power radiated from an antenna per unit solid angle.
2.311 radiation pattern. The spatial distribution of a quantity that characterizes the electromagnetic field
generated by an antenna. Syn: antenna pattern.
NOTES
1—The distribution can be expressed as a mathematical function or as a graphical representation.
2—The quantities that are most often used to characterize the radiation from an antenna are proportional to, or equal to,
power flux density, radiation intensity, directivity, phase, polarization, and field strength.
3—The spatial distribution over any surface or path is also an antenna pattern.
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APPENDIX B
4—When the amplitude or relative amplitude of a specified component of the electric field vector is plotted graphically,
it is called an amplitude pattern, field pattern, or voltage pattern. When the square of the amplitude or relative amplitude
is plotted, it is called a power pattern.
5—When the quantity is not specified, an amplitude or power pattern is implied.
2.312 radiation pattern cut. Any path on a surface over which a radiation pattern is obtained.
NOTE—For far-field patterns, the surface is that of the radiation sphere. For this case, the path formed by the locus of
points for which is a specified constant and is a variable is called a ―conical cut.‖ The path formed by the locus of
points for which is a specified constant and is a variable is called a ―great circle cut.‖ The conical cut with equal to
90° is also a great circle cut. A spiral path that begins at the north pole (= 0°) and ends at the south pole (= 180°) is
called a ―spiral cut.‖
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2.313 radiation resistance. The ratio of the power radiated by an antenna to the square of the RMS antenna
current referred to a specified point.
NOTES
1—The total power radiated is equal to the power accepted by the antenna minus the power dissipated in the antenna.
2—This term is of limited utility for antennas in lossy media.
2.314 radiation sphere (for a given antenna). A large sphere whose center lies within the volume of the
antenna and whose surface lies in the far field of the antenna, over which quantities characterizing the radiation
from the antenna are determined.
NOTES
1—The location of points on the sphere are given in terms of the and coordinates of a standard spherical coordinate
system whose origin coincides with the center of the radiation sphere.
2—If the antenna has a spherical coordinate system associated with it, then it is desirable that its coordinate system coincide
with that of the radiation sphere.
2.315 radiator. Any antenna or radiating element that is a discrete physical and functional entity.
2.316 radome. A cover, usually intended for protecting an antenna from the effects of its physical environment
without degrading its electrical performance.
2.317 random array antenna. See: array antenna.
2.318 reactive field (of an antenna). Electric and magnetic fields surrounding an antenna and resulting in
the storage of electromagnetic energy rather than in the radiation of electromagnetic energy.
2.319 reactive near-field region. See: near-field region, reactive.
2.320 reactive reflector antenna. See: reflective array antenna.
2.321 realized gain. The gain of an antenna reduced by the losses due to the mismatch of the antenna input
impedance to a specified impedance.
NOTE—The realized gain does not include losses due to polarization mismatch between two antennas in a complete
system.
2.322 realized gain, partial (of an antenna for a given polarization). The partial gain of an antenna for a
given polarization reduced by the loss due to the mismatch of the antenna input impedance to a specified
impedance.
2.323 receiving polarization (of an antenna). See: polarization, receiving (of an antenna).
2.324 rectangular array. [Deprecated.] See: rectangular grid array.
2.325 rectangular grid array. A regular arrangement of array elements, in a plane, such that lines connecting
corresponding points of adjacent elements form rectangles.
2.326 reference boresight. A direction established as a reference for the alignment of an antenna. See: electrical
boresight.
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NOTE—The direction can be established by optical, electrical or mechanical means.
2.327 reference directivity. See: standard directivity.
2.328 reflective array antenna. An antenna consisting of a feed and an array of reflecting elements
arranged on a surface and adjusted so that the reflected waves from the individual elements combine to produce
a prescribed secondary pattern. Syn: reactive reflector antenna.
NOTE—The reflecting elements are usually waveguides containing electrical phase shifters and are terminated by short
circuits.
2.329 reflector. See: Cassegrain reflector antenna; corner reflector; cylindrical reflector; Gregorian
reflector antenna; horn reflector antenna; main reflector; offset paraboloidal reflector antenna; parabolic
torus antenna; paraboloidal reflector; reflector antenna; reflector element; spherical reflector;
subreflector; toroidal reflector; umbrella reflector antenna.
2.330 reflector antenna. An antenna consisting of one or more reflecting surfaces and a radiating [receiving]
feed system.
NOTE—Specific reflector antennas often carry the name of the reflector used as part of the term used to specify it; for
example, paraboloidal reflector antenna.
2.331 reflector element. A parasitic element located in a direction other than forward of the driven element
of an antenna intended to increase the directivity of the antenna in the forward direction.
2.332 relative co-polar side lobe level. See: co-polar side lobe, relative.
2.333 relative cross-polar side lobe level. See: cross-polar side lobe level, relative.
2.334 relative gain (of an antenna). The ratio of the gain of an antenna in a given direction to the gain of a
reference antenna.
NOTE—Unless otherwise specified, the maximum gains of the antennas are implied.
2.335 relative partial gain (of an antenna with respect to a reference antenna of a given polarization).
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APPENDIX B
In a given direction, the ratio of the partial gain of an antenna, corresponding to the polarization of the reference
antenna, to the maximum gain of the reference antenna.
2.336 relative phase of an elliptically polarized field vector. See: phase, relative, of an elliptically polarized
field vector.
2.337 relative side lobe level. See: side lobe level, relative.
2.338 resistance. See: antenna resistance; radiation resistance.
2.339 resonant frequency (of an antenna). A frequency at which the input impedance of an antenna is nonreactive.
2.340 retrodirective antenna. An antenna whose monostatic cross section is comparable to the product of
its maximum directivity and its area projected in the direction toward the source, and is relatively independent
of the source direction.
NOTE—Active devices can be added to enhance the return signal. For this case, the term shall be qualified by the word
active; that is, active retrodirective antenna system.
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2.341 rhombic antenna. An antenna composed of long wire radiators arranged in such a manner that they
form the sides of a rhombus.
NOTE—The antenna usually is terminated in a resistance. The length of the sides of the rhombus, the angle between the
sides, the elevation above ground, and the value of the termination resistance are proportioned to give the desired radiation
properties.
2.342 ridged horn (antenna). A horn antenna in which the waveguide section is ridged.
2.343 right-hand polarization of a field vector. See: sense of polarization.
2.344 right-hand polarization of a plane wave. See: sense of polarization.
2.345 ring array. See: circular array.
2.346 scan angle. The angle between the direction of the maximum of the major lobe or a directional null
and a reference direction. Syn: beam angle.
NOTES
1—The term beam angle applies to the case of a pencil beam antenna.
2—The reference boresight is usually chosen as the reference direction.
2.347 scanning (of an antenna beam). A repetitive motion given to the major lobe of an antenna.
2.348 scan sector. The angular interval over which the major lobe of an antenna is scanned.
2.349 scattering cross section. For a scattering object and an incident plane wave of a given frequency,
polarization, and direction, an area that, when multiplied by the power flux density of the incident wave,
would yield sufficient power that could produce, by isotropic radiation, the same radiation intensity as that in
a given direction from the scattering object. See: bistatic cross section; monostatic cross section; radar
cross section.
NOTE—The scattering cross section is equal to 4times the ratio of the radiation intensity of the scattered wave in a
specified direction to the power flux density of the incident plane wave.
2.350 secondary radiator. That portion of an antenna having the largest radiating aperture, consisting of a
reflecting surface or a lens, as distinguished from its feed.
2.351 sectionalized [loaded] linear antenna. A linear antenna in which reactances are inserted at one or
more points along the length of the antenna.
2.352 sector scanning. A modification of circular scanning in which the direction of the antenna beam generates
a portion of a cone or a plane.
2.353 self-impedance (of an array element). The input impedance of a radiating element of an array
antenna with all other elements in the array open-circuited.
2.354 self-phasing array antenna system. A receiving antenna system that introduces a phase distribution
among the array elements so as to maximize the received signal, regardless of the direction of incidence.
Contrast with: retrodirective antenna.
2.355 sense of polarization. For an elliptical or circularly polarized field vector, the sense of rotation of the
extremity of the field vector when its origin is fixed.
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NOTE—When the plane of polarization is viewed from a specified side, if the extremity of the field vector rotates clockwise
[counterclockwise] the sense is right-handed [left-handed]. For a plane wave, the plane of polarization shall be
viewed looking in the direction of propagation.
2.356 sequential lobing. A direction-determining technique utilizing the signals of partially overlapping
lobes occurring in sequence.
2.357 series-fed vertical antenna. A vertical antenna that is insulated from ground and whose feed line connects
between ground and the lower end of the antenna.
2.358 shaped-beam antenna. An antenna that is designed to have a prescribed pattern shape differing significantly
from that obtained from a uniform-phase aperture of the same size.
2.359 shielded-loop antenna [probe]. An electrically small antenna consisting of a tubular electrostatic
shield formed into a loop with a small gap, and containing one or more wire turns for external coupling.
2.360 shielded-loop probe. See: shielded-loop antenna.
2.361 shoulder lobe. A radiation lobe that has merged with the major lobe, thus causing the major lobe to
have a distortion that is shoulder-like in appearance when displayed graphically. Syn: vestigial lobe.
2.362 shunt-fed vertical antenna. A vertical antenna that is connected directly to ground at its base and
whose feed line connects to the antenna between ground and a point suitably positioned above the base.
2.363 side lobe. A radiation lobe in any direction other than that of the major lobe. See: back lobe; co-polar
side lobe level, relative; cross-polar side lobe level, relative; mean side lobe level; minor lobe; side lobe
level, maximum relative; side lobe level, relative.
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APPENDIX B
2.364 side lobe level, maximum relative. The maximum relative directivity of the highest side lobe with
respect to the maximum directivity of the antenna.
2.365 side lobe level, relative. The maximum relative directivity of a side lobe with respect to the maximum
directivity of an antenna, usually expressed in decibels.
2.366 side lobe suppression. Any process, action, or adjustment to reduce the level of the side lobes or to
reduce the degradation of the intended antenna system performance resulting from the presence of side
lobes.
2.367 signal processing antenna system. An antenna system having circuit elements associated with its
radiating element(s) that perform functions such as multiplication, storage, correlation, and time modulation
of the input signals.
2.368 simultaneous lobing. A direction-determining technique utilizing the signals of overlapping lobes
existing at the same time.
2.369 sleeve-dipole antenna. A dipole antenna surrounded in its central portion by a coaxial conducting
sleeve.
2.370 sleeve-monopole antenna. An antenna consisting of half of a sleeve-dipole antenna projecting from a
ground plane. Syn: sleeve-stub antenna.
2.371 sleeve-stub antenna. See: sleeve-monopole antenna.
2.372 slot antenna. A radiating element formed by a slot in a conducting surface.
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2.373 solid-beam efficiency. The ratio of the power received over a specified solid angle when an antenna is
illuminated isotropically by uncorrelated and unpolarized waves to the total power received by the antenna.
NOTE—This term is sometimes used to mean the ratio of the power received corresponding to a particular polarization
over the solid angle to the total power received. Equivalently, the term is used to mean the ratio of the power radiated
over a specified solid angle by the antenna corresponding to a particular polarization to the total power radiated.
2.374 space-tapered array antenna. An array antenna whose radiation pattern is shaped by varying the
density of driven radiating elements over the array surface. Syn: density-tapered array antenna.
2.375 spherical array. A two-dimensional array of elements whose corresponding points lie on a spherical
surface.
2.376 spherical reflector. A reflector that is a portion of a spherical surface.
2.377 spillover. In the transmit mode of a reflector antenna, the power from the feed that is not intercepted
by the reflecting elements.
2.378 spiral antenna. An antenna consisting of one or more conducting wires or tapes arranged as a spiral.
NOTE—Spiral antennas are usually classified according to the shape of the surface to which they conform (for example,
conical or planar spirals), and according to the mathematical form (for example, equiangular or archimedean).
2.379 squint. A condition in which a specified axis of an antenna, such as the direction of maximum directivity
or of a directional null, departs slightly from a specified reference axis.
NOTES
1—Squint is often the undesired result of a defect in the antenna; but in certain cases, squint is intentionally designed in
in order to satisfy an operational requirement.
2—The reference axis is often taken to be the mechanically defined axis of the antenna; for example, the axis of a paraboloidal
reflector.
2.380 squint angle. The angle between a specified axis of an antenna, such as the direction of maximum
directivity or a directional null, and the corresponding reference axis.
2.381 standard [reference] directivity. The maximum directivity from a planar aperture of area A, or from
a line source of length L, when excited with a uniform amplitude, equiphase distribution.
NOTES
1—For planar apertures in which A >>2. The value of the standard directivity is 4A/2, withthe wavelength and
with radiation confined to a half space.
2—For line sources with L >>, the value of the standard directivity is 2L/.
2.382 standing-wave antenna. An antenna whose excitation is essentially equiphase, as the result of two
feeding waves that traverse its length from opposite directions, their combined effect being that of a standing
wave.
2.383 state of polarization (of a plane wave [field vector]). At a given point in space, the condition of the
polarization of a plane wave [field vector] as described by the axial ratio, tilt angle, and sense of polarization.
Syn: polarization state (of a plane wave [field vector]).
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2.384 steerable-beam antenna system. An antenna with a non-moving aperture for which the direction of
the major lobe can be changed by electronically altering the aperture excitation or by mechanically moving a
feed of the antenna.
2.385 stepped antenna. See: zoned antenna.
2.386 stub antenna. A short, thick monopole.
2.387 subreflector. A reflector other than the main reflector of a multiple-reflector antenna.
2.388 sum pattern. A radiation pattern characterized by a single main lobe whose cross section is essentially
elliptical, and a family of side lobes, the latter usually at a relatively low level.
NOTE—Antennas that produce sum patterns are often designed to produce a difference pattern and have application in
acquisition and tracking radar systems. Contrast with: difference pattern.
2.389 superdirectivity. The condition that occurs when the antenna illumination efficiency significantly
exceeds 100%.
NOTE—Superdirectivity is only obtained at a cost of a large increase in the ratio of average stored energy to energy radiated
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APPENDIX B
per cycle.
2.390 surface wave antenna. An antenna that radiates power from discontinuities in the structure that interrupt
a bound wave on the antenna surface.
2.391 Taylor distribution, circular. A continuous distribution of a circular planar aperture that is equiphase,
with the amplitude distribution dependent only on distance from the center of the aperture and such as to
produce a pattern with a main beam plus side lobes. The side lobe structure is rotationally symmetric, with a
specified number of inner side lobes at a quasi-uniform height, the remainder of the side lobes decaying in
height with their angular separation from the main beam.
NOTE—Taylor distributions are often sampled to obtain the excitation for a planar array.
2.392 Taylor distribution, linear. A continuous distribution of a line source that is symmetric in amplitude,
has a uniform progressive phase, and yields a pattern with a main beam plus side lobes. The side lobe structure
is symmetrical, with a specified number of inner side lobes at a quasi-uniform height, the remainder of
the side lobes decaying in height with their angular separation from the main beam.
NOTE—Taylor distributions are often sampled to obtain the excitation for a planar array.
2.393 thinned array antenna. An array antenna that contains substantially fewer driven radiating elements
than a conventional uniformly spaced array with the same beamwidth having identical elements. Interelement
spacings in the thinned array are chosen such that no large grating lobes are formed and side lobes are
minimized.
2.394 tilt angle (of a polarization ellipse). When the plane of polarization is viewed from a specified side,
the angle measured clockwise from a reference line to the major axis of the ellipse.
NOTES
1—For a plane wave, the plane of polarization shall be viewed looking in the direction of propagation.
2—The tilt angle is only defined up to a multiple of radians and is usually taken in the range (–/2, +/2) or (0, ).
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2.395 top-loaded vertical antenna. A vertical monopole with an additional metallic structure at the top
intended to increase the effective height of the antenna and to change its input impedance.
2.396 toroidal reflector. A reflector formed by rotating a segment of plane curve about a nonintersecting coplanar
line.
NOTE—The plane curve segment is called the torus cross section and the co-planar line is called the toroidal axis.
2.397 tracking. A motion given to the major lobe of an antenna with the intent that a selected moving target
be contained within the major lobe. Syn: angle tracking.
2.398 traveling-wave antenna. An antenna whose excitation has a quasi-uniform progressive phase, as the
result of a single feeding wave traversing its length in one direction only.
2.399 triangular array. [Deprecated.] See: triangular grid array.
2.400 triangular grid array. A regular arrangement of array elements, in a plane, such that lines connecting
corresponding points of adjacent elements form triangles, usually equilateral.
2.401 turnstile antenna. An antenna composed of two dipole antennas, perpendicular to each other, with
their axes intersecting at their midpoints. Usually, the currents on the two dipole antennas are equal and in
phase quadrature.
2.402 two-dimensional scanning. Scanning the beam of a directive antenna using two degrees of freedom
to provide solid angle coverage.
2.403 umbrella antenna. A type of top-loaded short vertical antenna in which the top-loading structure consists
of elements sloping down toward the ground but not connected to it.
2.404 umbrella reflector antenna. An antenna constructed in a form similar to an umbrella that can be
folded for storage or transport and unfolded to form a large reflector antenna for use.
2.405 uniform linear array. A linear array of identically oriented and equally spaced radiating elements
having equal current amplitudes and equal phase increments between excitation currents.
2.406 V antenna. A V-shaped arrangement of two conductors, balanced-fed at the apex, with included angle,
length, and apex height above the earth chosen so as to give the desired directive properties to the radiation
pattern.
2.407 vertex plate (of a reflector antenna). A small auxiliary reflector placed in front of the main reflector
near its vertex for the purpose of reducing the standing waves in the feed due to reflected waves from the
main reflector.
2.408 vertically polarized field vector. A linearly polarized field vector whose direction is vertical.
2.409 vertically polarized plane wave. A plane wave whose electric field vector is vertically polarized.
2.410 vestigial lobe. See: shoulder lobe.
2.411 visible range. For the case in which the field pattern of a continuous line source, Lwavelengths long,
is expressed as a function of (= Lcos , the angle is measured from an axis coincident with the line
source), that part of the infinite range of that corresponds to a variation in the directional angle from to
0 radians; that is, –L<<L.
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NOTES
1—All values of outside the visible range are said to be in the invisible range.
2—The formulation of the field pattern as a function of is useful because the side lobes in the invisible range are a
measure of the Q of the antenna.
3—This concept of a visible range can be extended to other antenna types.
2.412 voltage pattern. See: radiation pattern.
2.413 wave antenna. See: Beverage antenna.
2.414 whip antenna. A thin, flexible, monopole antenna.
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2.415 wire antenna. An antenna composed of one or more conductors, each of which is long compared to
the transverse dimensions, and with transverse dimensions of each conductor so small compared to a wavelength
that for the purpose of computation the current can be assumed to flow entirely longitudinally and to
have negligible circumferential variation.
2.416 wire-grid lens antenna. A lens antenna constructed of wire grids, in which the effective index of
refraction (and thus the path delay) is locally controlled by the dimensions and the spacings of the wire grid.
Contrast with: geodesic lens antenna; Luneberg lens antenna.
2.417 Wullenweber antenna. An antenna consisting of a circular array of radiating elements, each having
its maximum directivity along the outward radial, and a feed system that provides a steerable beam that is
narrow in the azimuth plane.
2.418 Yagi antenna. [Deprecated.] See: Yagi-Uda antenna.
2.419 Yagi-Uda antenna. A linear end-fire array consisting of a driven element, a reflector element, and one
or more director elements.
2.420 zoned antenna. A lens or reflector antenna having various portions (called zones or steps) that form a
discontinuous surface such that a desired phase distribution of the aperture illumination is achieved. Syn:
stepped antenna.
2.421 zone-plate lens antenna. See: Fresnel lens antenna.
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