Multi-beam Antenna Arrays … · Multi-beam Antenna Arrays Bybi P. Chacko*, Gijo Augustin and Tayeb...

Multi-beam Antenna Arrays

Bybi P. Chacko*, Gijo Augustin and Tayeb A. DenidniCentre for Energy, Materials and Telecommunication, National Institute of Scientific Research (INRS), Montreal, QC, Canada

Abstract

This chapter begins with a brief introduction of basic concepts in antenna arrays which is followed byslightly advanced concepts including smart antennas and related systems. This helps the readers to acquirebasic knowledge necessary to understand the concepts of multi-beam antennas and various beam-formingnetworks outlined in the sessions that follow. The world of engineered materials which become animportant research area is also outlined to broaden the knowledge of the readers. This chapter concludeswith some recent multiple-beam antenna design examples with metamaterial technology.

Keywords

Antenna arrays; Multi-beam antenna arrays; Directive antenna arrays; Cylindrical antennas; Sectoralantennas; Beam scanning; Beam formers; Intelligent antenna system; Nimble radiation pattern;Multifunctional beams

Introduction

In layman’s language, an antenna array is defined as a set of aerials arranged in a specific fashion in spaceso that the resulting radiation characteristics can be modified. As per IEEE standard definition of terms forantennas (IEEE Standard 145–1993), an array antenna can be defined as “an antenna comprised of anumber of identical radiating elements in a regular arrangement that are excited to obtain a prescribedpattern.” As explained by Randy L. Haupt (2010), the antenna array can be visualized as a system tocollect rain. To collect more rain, it is necessary to use a very big bucket or employ large number ofbuckets and combine all of them. In the same way, in order to receive more electromagnetic radiation, itrequires either a large aperture antenna, such as the Arecibo radio telescope in Puerto Rico (305 m wide),or an antenna array with more number of elements such as the square kilometer array as shown in Fig. 1.

The array can be formed by two or more individual elements which may or may not be identical in theirradiation characteristics. However, in most of the simple antenna array designs, each individual element isdesigned to have identical radiation properties. The shape of the radiation pattern in an array with identicalelements is determined by the following parameters (Balanis 2005):

• The shape of physical arrangement of each element in space (linear, rectangular, ring, etc.)• The distance between each element• The amplitude of the excitation signal to individual elements• The phase of the excitation signal to individual elements• The radiation pattern of the individual elements

*Email: [email protected]

Handbook of Antenna TechnologiesDOI 10.1007/978-981-4560-75-7_66-1# Springer Science+Business Media Singapore 2015

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In modern world of wireless communication, this concept of antenna array is of high interest and isemployed in various scenarios outlined above (Table 1).

Before proceeding further in this section, following definitions related to antenna array would behandy:

Radiation pattern: Radiation pattern of an antenna is the plot of radiated power variation around anantenna estimated in a constant distance from it.

Isotropic antenna: An antenna which radiates its energy equally in all directions. In reality, no suchantenna physically exits. An isotropic antenna is used as the reference antenna to compare thecharacteristics of actual antennas.

Omni-directional antenna: Antennas having an isotropic pattern in one plane and directional pattern inan orthogonal plane.

Directional antenna: An antenna which radiates or concentrates its power to a particular direction orangular regions.

Bore sight: It is the direction at which the beam maximum of an antenna is pointed.Beam forming: The process of combining signals from different elements of an antenna array is known as

beam forming. The direction in which the array has maximum gain is said to be the beam-pointingdirection. If the signals from the antenna elements are combined without any change in amplitude orphase, a broadside beam is produced. Beam forming can be generally categorized as analog beamforming and digital beam forming. As the name implies, in analog beam forming, the amplitude andphase of each antenna elements are controlled in the analog part of the system. Phase shifters arecommonly used in the analog beam-forming-phased array configurations to control the phase of eachantenna element and steering the main beam. On the other hand, in digital beam-forming method, theamplitude and phase of a signal are controlled in the digital part of the system.

Table 1 Application of antenna array

Objective Application

Gain enhancement Satellite antennas

Facilitate beam steering Radar systems

Antenna diversity Mobile phones

Improve the S/N ratio Satellite receivers

Find direction of arrival Radar systems

Fig. 1 (a) Arecibo radio telescope in Puerto Rico, (b) square kilometer array


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Beam steering: IEEE standard definition of terms (IEEE Standard 145–1993) defines beam steering as“changing the direction of the main beam of antenna.” By mechanically moving, the main beam fromany given array may be pointing to any direction; this is called mechanical steering. Electronic beamsteering is accomplished by appropriately delaying the signals before combing. That is the beam-pointing direction, or the main beam direction can be controlled by changing the phase differenceamong different antenna elements.

Antenna Array FactorThe concept of an antenna array can be best understood through an example of a simple uniform arrayshown in Fig. 2. It consists of N identical antenna elements arranged in x-axis with an equal distance. Eachantenna element possesses identical radiation characteristics and is fed through separate phase shifters sothat each element is excited with progressive phase shift.

The radiation pattern of the linear array is formed based on the concept of pattern multiplication asexpressed below:

E Total ¼ E Single elementð Þ � Array Factor

where E Total is the total field radiated from the antenna array and E (single element) represents theradiation pattern of the single element (A-1, A-2, etc.).

Array factor: It is a mathematical expression formed by the physical arrangement of an array and alsowith the properties of the excitation signal. The array factor varies from one type of array to another. Thisclearly indicate that the overall radiation pattern of an antenna array can be entirely different than that ofthe antenna element.

Fig. 2 Uniform N elements linear array


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The array factor of the antenna described in Fig. 2 is defined as

AF ¼Sin

N

2j

� �

Sinj2

� � (1)

j ¼ kd cos yþ b (2)

where b is the difference in the phase excitation between the successive elements (progressive phaseshift), d is the distance between the elements, k = 2*pi/ l, and y is the polar angle.

Configuration/Different Types of ArraysThere are various approaches in classifying antenna arrays. On the basis of the arrangement of the antennaelements in three-dimensional surfaces, the arrays are classified as:

1. Linear or one-dimensional array: In this configuration, each antenna element is arranged on astraight line in one dimension. Please note that it is not the shape of the individual antenna elementswhich needs to be in one dimension but the location of the individual elements. The elements can besimple dipoles to 3D conformal structures which are entirely based on the design objective of thecommunication system. Figure 3 illustrates some examples in which the antenna elements aredistributed in a line parallel to x-axis and z-axis. During the design of the linear array, the expectedradiation characteristics need to be taken care of. For example, when designing a linear array orientedalong y-axis with array elements of omnidirectional radiation pattern, the broadside pattern will bedirectional and interferences from the neighboring elements will be minimum. This type of arrays isemployed for application where a directional beam is desired and is useful when broad coverage in oneplane and narrow beam in the orthogonal plane is required.

2. Planar or two-dimensional arrays: The planar array or two-dimensional array is designed withindividual elements in a two dimensional plane as illustrated in Fig. 4. This configuration is widelyemployed for radar applications since it can facilitate highly versatile beam forming.

3. Volumetric or three-dimensional arrays: In this configuration, the array elements are designed toconform inside a three-dimensional space as depicted in Fig. 5. Conformal antenna arrays are alsodefined as a type of volumetric antenna arrays. Compared to the earlier antenna array designs, thevolumetric arrays need relatively complex design strategies.

Fig. 3 Linear array with elements positioned in x-axis and z-axis


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Another classification based on the radiation pattern is:

1. Broadside Array: In broadside arrays (Fig. 6), the direction of the main beam is perpendicular to theaxis in which the array elements are arranged. The IEEE standard definition of terms states broadsideantenna array as “A linear or planar array antenna whose direction of maximum radiation is

Fig. 5 Volumetric array

Fig. 4 Planar array arranged in XZ-plane


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perpendicular to the line or plane, respectively, of the array.” The broadside pattern can be obtained in alinear array with identical elements by exciting them with equal magnitude and phase.

2. End-Fire Array: In these types of antenna array (Fig. 7), the beammaximum is focused along the axisof the array. Most of the planar or linear arrays can be configured to have a beam maximum that ispointing toward the array axis by exciting the individual antenna elements with equal magnitudes andprogressive phase shift.

3. Collinear Array: The term collinear indicates that the individual antenna elements are connected endto end along a single line as shown in Fig. 8. In this configuration, the beammaximum is perpendicularto the axis of the array as in the case of broadside array. However, in this case, the fan beam is focused toevery point perpendicular to the array axis resulting in a “donut”-shaped pattern as illustrated in Fig. 9.In order to get this pattern shape individual array, elements are excited with currents equal in magnitudeand phase.

Fig. 7 End-fire array (a) configuration, (b) radiation pattern

Fig. 6 Broadside array (a) configuration, (b) radiation pattern


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Fig. 9 Collinear array radiation pattern

Fig. 8 Collinear array


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Smart Antenna

In reality, antennas are not smart; an antenna along with its associated systems makes the antenna systemsmart. Basically, a smart antenna is a multielement antenna in which the signals received at each antennaelement are intelligently combined to improve the performance of the wireless system. As illuminated byBalanis and Ioannides (2007), the working of a smart antenna can be better visualized by considering twopersons carrying on a conversion inside an isolated room. Human’s auditory system has the ability todistinguish and concentrate on a particular person’s voice among a group of peoples talking simulta-neously. In the same way, in a smart antenna, any unwanted signal is attenuated. Better range/coverage,increased wireless system capacity, multipath rejection, and reduced expenses are the main advantages ofthe smart antenna system.

The two basic configurations of smart antenna systems are:

Switched – multi-beam antenna: Either a number of fixed beams with one beam turned on toward thedesired signal or a single beam (formed by phase adjustment only) that is steered toward the desiredsignal

Adaptive antenna array: An array of multiple antenna elements where the main beam is put in thedirection of the desired signal, while nulls are in the direction of the interference

Multi-beam Antenna Arrays

In this section, various antenna systems that are employed to generate multiple beams are discussed. In abroad perspective, the multi-beam antennas are defined as antennas that generate either multiple numbersof beams simultaneously or switch between beams in multiple directions. The IEEE standard terms forantennas (IEEE Standard 145–1993) defines multi-beam antenna as “an antenna capable of creating afamily of major lobes from a single non-moving aperture, through use of multiport feed, with one-to-onecorrespondence between input ports and member lobes, the latter characterized by having unique mainbeam pointing directions.”

Some of the earlier designs utilized conventional lenses or modified reflectors to generate multiplenumber of radiating beams. However, the challenges such as shadows created by the cluster feeds led theresearchers to focus on the development of phased array antennas that made the entire antenna systemmore “smart.” The multiple-beam antenna systems facilitate the following advantages compared tosingle-beam antennas:

• Ability to focus the radiation to a desired direction• Increase the capacity of the wireless system• Combat signal fading by suppressing interfering signals• Facilitate tracking of the objects in radar systems

These key benefits are obtained through relatively higher system complexities in contrast with lesscomplex mechanically scanned or switched design concept. In the following section, the classical designsare first discussed that include designs such as a lens fed by various array feed horns, a reflectorilluminated by different feed horns, and phased array concepts. In the later part of the section, relativelynew concepts of using engineered materials for the formation of multi-beam antenna arrays are discussed.


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Historical Review of Multi-beam Antenna Arrays

Early History (1906–1970)Even though the concepts behind the first antenna array design were well established by 1920s (Fleming1919), the natural outgrowth of the array to multiple-beam antennas or beam scanning antennas tookalmost another decade to flourish into the level of successful experiments. In fact, it is reported thatMarconi performed several experiments in the antenna of his wireless communication system to enhancethe performance of his receiver in certain directions as early as 1906 (Marconi 1906). There wereenormous amounts of research interest fuelled by the Second World War to develop an efficientelectromechanically scanned antenna system for radar applications. One classical example is the SCR-270 (Fig. 10) developed during Second World War by the US Army installed in Hawaii that providedJapanese formation during the Pearl Harbor attack. The initial approaches to scan the beam usingelectromechanical systems were successful and widely developed by 1940s. The technological limitationsmade some of the key challenges such as mutual coupling between the array elements a major barrier inthe design optimization in this period (Brown 1937).

In the 1950s, the special situations after Second World War powered considerable funding for thescientific research related to military applications. The invention of ferrite-based phase shifters (Button1984) in between 1954 and 1955 provided the technological seed that led to the development in the fieldof electronically scanning antenna systems (Sarkar et al. 2006). This led to the initial theories andexperimental validation of beam-steering antenna arrays by changing the phase of the signals that excitethe antenna elements (Braun 1925; Friis et al. 1934). These initial discoveries of mechanically scannedarrays led to many advanced design variations including large ground-to-ship radars and complexairborne radar arrays. Due to various system level limitations, most of these initial discoveries werespread across HF band and then later to EHF range. One of the rich resources that outlines the

Fig. 10 SCR 270 antenna array with mechanical rotator


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developments during this postwar period around the globe is entitled “Microwave Scanning Antennas”edited by Hansen (Hansen 1964, 1966). Until 1960s, the system cost was a major factor that preventsfurther developments on radar systems for nonmilitary applications. The evolution of printed circuittechnology by late 1960s played a critical role in reducing the overall system expenses and therebyaccelerating the research and development in broader areas of engineering physics. Even though themicrostrip patch antennas were theoretically visualized by G.A. Deschamps in 1953 (Deschamps 1953), ittook several years until early 1970, when Robert Eugene Munson succeeded in implementing the same ina sprint missile data link (Munson 1972).

Computational Challenges and Early AlgorithmsWhile empathizing the challenges faced by researchers around the globe, it is important to note that by late1950s even if the electromagnetic theory was quite established, the use of computer to solve these theorieswas completely nonexistent. It is quite interesting that, during the 1950s, the JPL in NASA used the word“computer“ to represent an individual than amachine, where a specific group of people were designated toperform mathematical calculations by hand. By 1960s, the invention of mainframe computers made thecomplex electromagnetic calculations based on earlier algorithms (Mei 1965). Many of these initialcomputations were performed using point-matching solutions of Hallen’s integral equation for metallicwires (an earlier version of method of moments) (Harrington and Harrington 1996). Hallen’s equationswere powerful enough to accurately model dipole antenna arrays. The introduction of algorithms based ongeometrical theory of diffraction (GTD) was another breakthrough during the 1960s (Albertsenet al. 1975; Keller 1962). This enabled researchers to utilize well-established theories based on geomet-rical optics to accurately calculate the radiation properties of popular shapes such as edges and corners.Majority of the earlier computational techniques based on Green’s functions were quite general, and mostof them are in frequency domain compared to present-day tools which provide both frequency and time-domain solutions. The contributions from Schelkunoff and Dolph for the analysis of phased arrayantennas were another milestone. These contributions in the late 1940s utilized static weighting schemes(Dolph 1946; Schelkunoff 1943) and accelerated the development of antenna arrays with low side-lobelevel. Another major work during the late 1960 by A.P Applebaum (1966) made key contributions tochange the array weights which become one of the fundamental concepts behind the adaptive andreconfigurable antenna arrays. The concept of a retro-directive array that receives electromagnetic signalsin one direction and retransmits in a mirror-image direction was originated in the late 1950s and creditedwith a US patent to Van Atta (1959).

Advanced era (1970–present): It is logical to classify the advanced era from a period in history whenthere were computational tools available, and many fundamental ideas were matured enough for practicalimplementation. During this period, the application spectrum of multi-beam antennas becomes muchbroader with the technological advancements. The availability of more efficient computational electro-magnetic algorithms along with associate hardware made the research in this field of engineering rich.These scientific advancements enabled the researches to provide contributions with multi-beam antennaarrays with higher number of elements that are operating at the higher end of the spectrum. One of theearlier attempts for the implementation of passive electronically scanned array (PESA) took place by theearly 1970s facilitating more efficient scanning than a mechanically rotating antenna. Another researchfocus during this era was on the development of conformal multi-beam antenna arrays for broadcasting,navigation, and directional finding. A notable development during the Cold War period (1962–1979) wasthe development of experimental Wullenweber arrays that are circular arrays designed for direction-finding applications. One of the prototypes, the 300 m diameter array with 120 radiating elements, wasdeveloped at the University of Illinois (Gething 1966). The initial ideas behind adaptive arrays begin withthe motivation to control the receive pattern so that the interference of signals from unwanted directions


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can be effectively minimized. One of the inventions during the late 1960s by P.W. Howells (1965)triggered the research across the globe leading to various key contributions in this exciting field of beam-scanning antenna arrays. The research during this period also diverted in various related areas includinghuge developments in many classical concepts in the field of multiple-beam antennas. Some of the earlierconcepts to produce multiple beams were the use of digital/analog beam formers. In addition to thesetechniques, the antenna hardware concepts based on Butler matrices also evolved by this time (Butler1961, 1965). The implementation of various lens implementations such as Rotman lens and Gent bootlacelens to produce multiple beams was also introduced in the 1960s (Gent 1957; Rotman and Turner 1963)which facilitated multiple focuses for one scanning plane. A decade later, some of these techniques wereextended for various applications using microstrip technology (Archer 1984). The invention of P-I-Ndiodes and varactor diodes during this period attracted various researchers around the world to focus theirresearch in the development of microwave phase shifters using this technology (White 1968, 1984). Evenafter a decade from the invention of P-I-N diodes and varactor diodes, the technology was not grownenough for high-power applications. At present, there are P-I-N diode-based microwave phase shiftersthat can handle kilowatts of peak power. Another important event in the mid-1970s is the development ofmicrostrip antenna array by Munson. This development along with the cavity-based theory presented byY.T.Lo et al. (1978) accelerated this exciting field of engineering. These developments along with theavailability of low-cost fabrication technologies triggered the research world during the late 1980s withmassive contributions in the development of multi-beam antenna arrays based on printed technology. Themodern world of wireless communication is gifted with plenty of multidisciplinary technologies whichaccelerated this amazing field of engineering. Some of the exciting focus areas of multi-beam antennaresearch in this modern world include reconfigurable reflect arrays (Hum and Perruisseau-Carrier 2014),planar ultra-wideband modular arrays (Logan et al. 2013), and phased arrays with broad scanningcapacity (Kavitha and Jacob 2013).

Types of Multi-beam AntennasIn general, the multi-beam antennas are classified as lens-based designs, reflector antennas, phased arrayantennas, and hybrid designs. These classifications are made based on the key system component thatproduces multi-beam. Each of these designs is detailed in the following sessions.

Lens AntennasThe basic working principle of lens antennas is based on the collimated action of any optical lens whichforms a focused electromagnetic radiation. These antennas can be configured with single-feed or multi-feed elements. One of the generally used configurations of lens-based multi-beam antenna is outlined inFig. 11. In a single-feed configuration, a single source illuminates the aperture and generates a beam basedon the lens characteristics. The multiple-feed configuration or discrete lens array (DLA) excites the lens

Fig. 11 Lens-based multi-beam antenna


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aperture and forms a constituent beam. By simultaneously exciting these beams, multiple beams can beformed based on the principle of superposition. Based on the properties of the lens, either constructive ordestructive interactions can happen at a specific point in space, resulting in the formation of the beampointing to a specific direction.

There are various types of lens antennas based on the principle of operation of the lens system; in abroad perspective, these are classified as:

(i) Fast-wave lenses (refractive index <1)(ii) Slow-wave lenses (refractive index >1)

As the name indicates, these terms are related to the phase velocity of the wave that travels through thelens medium. These structures are illustrated in Fig. 12.

In fast-wave lenses, the electrical path length is decreased by the medium of the lens, and thus the phasevelocity of the wave in the medium will be relatively higher. As shown in Fig. 12a, as the electromagneticwave passes through the lens medium, the electric length is made shorter as the wave progresses. The fastlens antennas are also known as E-plane lens antennas. In contrast, a delay lens antenna is the one in whichthe wavelength in the medium will be increased, and this results in a reduced phase velocity as illustratedin Fig. 12b. The slow lens antennas are also known as dielectric lens antennas or H-plane lens antennasand further classified as:

• Lenses derived from conventional dielectrics such as lucite or polystyrene• Lenses fabricated from artificial dielectric parts, ceramic, or metallic components

There are various lens topologies implemented for various applications including gain enhancementand beam forming. In the following section, various lens topologies that are employed for multi-beamantenna applications are being discussed. A detailed analysis of other lens architectures is detailed inLee (1988).

Fig. 12 (a) Fast-wave lens, (b) slow-wave lens


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The key lens topologies employed in multi-beam antennas are waveguide lens, bootlace lens, Rotmanlens, and Luneburg lens.

Waveguide Lens The basic topology of a waveguide lens is shown in Fig. 13. It is primarily made ofstacking waveguides of different dimensions. The concept is based on the fact that the phase velocity ofelectromagnetic waves exceeds the speed of light inside a waveguide. The shape of the waveguide isdesigned in order to provide corresponding phase velocity. More specifically, the distance travelled by thecenter ray from the source located on one side of the lens to a perpendicular plane on the other side of thelens is made equal to the path travelled by a general ray through other waveguide pieces.

This condition is satisfied from Eq. 3 to Eq. 5:

d ¼ d0 þ z= 1� nð Þ (3)

where d0 is the smallest dimension of the lens.

n ¼ 1� l=lcð Þ2h i1=2

(4)

where n is the refractive index of the lens based on the free space wavelength l and waveguide cutoffwavelength lc.

z ¼ F� F2 � r2� �1=2 ’ r2=2F (5)

where F is the focal length of the lens and r is the distance from the element to the lens axis.One of the classical applications for a waveguide lens antenna is shown in Fig. 14, formed by an array

of waveguides with either circular or spherical cross sections for satellite communication systems. Thelength of the waveguides is made so as to produce corresponding phase delays when electromagneticsignals propagate through them.

One of the design challenges for the waveguide-based antenna array technology is the limitedbandwidth. This is mainly because of the dispersive nature of the waveguide media. That is, the phasevelocity of electromagnetic waves inside the waveguide varies with frequency. One of the classicalsolutions for this challenge is the use of a stepped design as shown in Fig. 15, in which a step is made in thelens. As a general rule, this is done when the lens thickness exceeds [l/(1�m)]. Even though the stepping

Fig. 13 The topology of a waveguide lens


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can be made on either one or both inner sides of the waveguide, it is suggested to avoid the stepping on thefeeding side of the waveguide array to avoid shadow effects.

Bootlace Lens The bootlace lenses are known for its capability to have more than one focal point andthereby provide wide-angle scanning capabilities. It consists of two array geometries that are arrangedback to back to form a combined lens system. The array elements on one side are connected to the otherside through a processing circuitry that consists of amplifiers and transmission lines. The beam charac-teristics of the bootlace lens depend on the length of the transmission lines along with the amplitude andphase between the receiving and transmitting elements. The transmission lines that connect the radiatorson the inner and outer surfaces are connected through transmission lines mostly with coaxial cables. Thisgives an appearance of untightened bootlaces which gives the name bootlace lens. The geometry of abootlace lens is shown below (Fig. 16).

A multi-beam antenna can be formed by employing bootlace lens by placing more than one sourceantennas at various focus points. Even though the initial designs were only capable of providingtwo-dimensional scanning (Kales 1964), later designs provided multifocal three-dimensional scanning

Fig. 15 Stepped waveguide array

Fig. 14 Classical application of waveguide lens array antenna used in DSCS-III satellite


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facility (Rao 1982). One of the general theories developed by Gent in 1957 states that if the lens has aradius of 2R, then its focal points lie on a circle with radius R (Gent 1957).

In general, the bootlace lenses provide the following key features:

• Three-dimensional degrees of freedom for the design.• The embedded microwave components in between the two lens surfaces facilitate illumination control

of the outer surface and thereby provide beam scanning.• The ability to implement stepping without the issues of shadow effect.

Rotman Lens Rotman lens is capable of producing simultaneous multiple beams when implemented onan array configuration. The diagram shown in Fig. 17 represents a Rotman lens which is a modifiedversion of Gent bootlace lens (Gent 1957). Apart from the bootlace lens, the Rotman lens can providemuch wider coverage exceeding scan angles of greater than 50� (Rotman and Turner 1963).

In one of its simplest configurations shown in Fig. 17, the transmitting or receiving antenna elementsare mounted on a curved arc which either radiates or receives from the other curved portion of the lens.The array elements are arranged in a straight line at a geometrical plane perpendicular to the lens axisoutside the lens. This generates multiple beams that are capable of steering toward the preprogrammeddirections without any physical movement of the surface.

In comparison with other lens topologies, Rotman lens is relatively broadband in nature. The feedportion shown in the right-hand side can be implemented either using microstrip or stripline; meanwhile,the bootlace portion represented in the left-hand side can be implemented using coaxial cables. The keydesign parameters are outlined in Fig. 17b. This include:

• Focal angle, a• Focal length, f1• Ratio of beam angle and ray angle, g• Focal ratio, b• Element spacing, d• Peak beam angle, cm

Fig. 16 (a) Diagram of bootlace lens, (b) geometry of one of the earlier versions of multifocal bootlace lens with three-dimensional scanning proposed by Jaganmohan B. L. Rao (1982)


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The design process is a trade-off between mutual coupling reduction and fabrication limits. Based onthe detailed analysis provided in Hansen (2009), the design guidelines are given below:

• The focal ratio b can be calculated from the upper and lower focal length f2 and f1 using

b ¼ f 2f 1

(6)

• The beam angle ratio g is given by

g ¼ Sin cSin a

(7)

where c is the beam angle and a is the focal angle.• Another parameter z relates the distance g3 with f1 and controls a percentage of the phase and amplitude

error the lens possess can be calculated from

Fig. 17 (a) Rotman lens, (b) ray geometry of the Rotman lens


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z ¼ g3gf 1

(8)

• The maximum beam angle, cm, is a critical design parameter that can be derived from

zmax ¼NE� 1ð Þgd

2f 1(9)

where NE represents the number of elements.• The quadratic lens equation is given by

aw

f1

� �2

þ bw

f1þ c ¼ 0 (10)

where the coefficients can be calculated from

a ¼ 1� 1� bð Þ21� bCð Þ2 �

z2

b2(11)

b ¼ �2þ 2z2

b2þ 2 1� bð Þ

1� bC� z2S2 1� bð Þ

1� bCð Þ2 (12)

c ¼ �z2 þ z2S2

1� b C� z4S4 1� bð Þ

4 1� bCð Þ2and C ¼ cos a, S ¼ sin a

(13)

The element spacing is critical since it has high impact on the grating lobes which can be calculated from

d

l¼ 1

1þ sincm(14)

Luneburg Lens In contrast to the earlier lens topologies, Luneburg lens is a spherically symmetricgradient-index lens whose refractive index decreases radially from center to the outer surface (Fig. 18),theoretically proposed by Luneburg (1944). The geometry of this lens includes two spheres in which onehas an infinite radius and the other sphere is the lens surface.

The refractive index, n, of a unit length radius Luneburg lens is defined as

n ¼ 2� r2� �1=2 ¼ ffiffiffiffi

erp

(15)

where r is the radius of the lens.The Luneburg lens produces a plane wave when the feed point is at one of the surface regions of the

sphere. This in turn enables the Luneburg lens to produce multiple beams either by moving the feed pointthrough the sphere surface or by exciting more than one feed locations around the sphere surface.


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Maxwell’s fish-eye lens (Fig. 19) is a classical example of generalized Luneburg lens in which therefractive index varies according to

n ¼ ffiffiffiffier

p ¼ n0

1þ rR

� �2 (16)

Reflector AntennaIn a simple form, a reflector antenna consists of a reflector and an antenna feed. These types of antennasare widely used in long-distance high-gain applications like communication satellites, military satellites,high-resolution radars, etc. In the design, the reflector surface can take any general shape like paraboloid,hyperboloid, spheroid, ellipsoid, cylindrical, etc. The basic working principle of the reflector antenna isthat the reflector converts the spherical wave to a plane wave in transmission mode and vice versa inreception mode. One of the most commonly used focal point-fed parabolic reflector antennas is shown inFig. 20. On receiving mode, as a beam of parallel rays incident up on the parabolic reflector, the reflector

Fig. 19 Cross section of Maxwell’s fish-eye lens, with gray shading representing increasing refractive index

Fig. 18 The cross-sectional view of a Luneburg lens in which the gray shading is proportional to the refractive index, n


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focuses the entire ray to the focal point. Similarly on transmission mode, the beam is produced by theantenna feed, placed at the focal point, and emerges as parallel rays.

By using antenna array as the primary radiator, these antennas can also produce multiple beams. Theperformance of the reflector multi-beam antenna is similar to that of a lens antenna. Some of the mostcommonly used multi-beam antenna configurations based on this concept are shown in Fig. 21.

In a reflector antenna, aperture size of the reflector, type of the reflector, focal length, offset distance,and surface tolerance are the main design parameters to get a desired radiation pattern. The aperture size isa key design parameter that determines the gain and bandwidth of the antenna. In multiple-beam antennaapplications, a large aperture size reflector is quite commonly used.

Aperture blockage by the feed and its support is the main disadvantage of a focal point-fed reflectorantenna. One of the solutions to reduce this blockage which causes side lobes is the offset-fed reflectorantenna. Cassegrain feeding is another solution which helps to overcome both the aperture blockage and

Fig. 21 (a) Parabolic reflector multi-beam antenna, (b) offset-fed parabolic reflector antenna, (c) focal point-fed Cassegrainreflector antenna, (d) offset-fed Cassegrain reflector antenna

Fig. 20 Reflector antenna


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lack of control over the main reflector illumination. As illustrated in Fig. 21b, the reflected wave from asecondary hyperboloidal reflector illuminates the paraboloidal primary reflector. In this design mecha-nism, the reflectors and the feed antenna are positioned in such a way that the focus of the main reflectorand one of the foci of the secondary reflector is coinciding in such a way that the outline of the secondaryreflector controls the illumination of the main reflector. Electrically, such a system is same as that of asingle reflector antenna with a longer focal length. Therefore, it provides better scanning performancethan a single reflector type antenna. The Cassegrain focal point-fed reflector antenna also suffers from theaperture blockage. It can be minimized by choosing the diameter of the secondary reflector same as that ofthe feed. Another solution to minimize the aperture blockage is to employ offset Cassegrain feeding asdepicted in Fig. 21d.

Phased Array AntennaA phased array antenna is a directive antenna composed of an array of equally spaced individual antennasor elements. In such a design, the shape and direction of the radiation pattern is determined by the relativeamplitude and phase of the electromagnetic signal at the individual elements. Similar to reflector or lensantennas, a phased array antenna with a beam-forming network can also be used to produce multiplebeams. This configuration is normally preferred when the number of antenna elements ranges between afew to a few hundred. The beam-forming network in a phased-antenna system mainly combines thesignals from all the elements in an array to form a receiving beam or conversely distributes the transmittedsignal to different elements in an array to form a transmitting beam. Beam forming can be generallycategorized as analog beam forming and digital beam forming. As the name implies, in analog beamforming, the amplitude and phase of each antenna element are controlled by an analog circuitry in thesystem. This includes analog phase shifters that provide smooth beam forming by controlling the phase ofexcitation of each antenna elements. Most of the modern-phased array systems use much advancedtechniques that include digital beam-forming circuits in which the amplitude and phase of excitation ofarray elements can be software controlled with digital hardware.

Butler Matrix Butler matrix is one of the most popular multiple beam-forming networks employed tofeed a uniformly spaced antenna array which was first introduced by Jesse Butler and Ralph Lowe in1961. It is a feed network with N= 2n number of input ports and N= 2n number of output ports, where n isan integer. Thus, a Butler matrix network can provide linear phase distributions when the number ofantenna elements is a power of two. In other words, if a signal is introduced at one input port, the matrixwill produce equal amplitude excitations with constant phase difference at all output ports, resultingradiation in a particular direction in space. A signal introduced at another port will similarly create anotherbeam pointing to different direction. Regarding the structure of the matrix, hybrid couplers and phaseshifters are the basic building blocks of a Butler matrix network. This includes hybrid couplers with 90

�

and 180�designs along with Butler matrices. For example, the design to produce a broadside beam can

employ a 180�hybrid coupler.

A Butler matrix with N = 2n number of input and output ports comprises Nn/2 number of hybridcouplers and (n-1)N/2 phase shifters. The phase difference between radiating elements in this matrix forthe ith beam location is given by (2i�1) 180�/N.

Similarly, the angle of beam title when a signal is introduced at the ith input of the matrix can becalculated by the equation

yi ¼ SinNþ 1� 2i

2N

ld

� �, i ¼ 1, 2, 3 . . . :N (17)


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Figure 22 demonstrates the basic functional block diagram of a 4 � 4 Butler matrix using 90� hybridcouplers. As shown, total of four hybrid couplers are arranged in two columns along with two phaseshifters in the network topology. Table 2 shows the phase distributions produced by the matrix when asignal is introduced at a particular input port. The corresponding main beam directions from the antennaarray are also given.

Another exciting feature of this network is that the antennas can produce multiple beams by simulta-neously exciting two input ports. For example, if port 1 and port 4 are excited at the same time, the phasearray will produce two beams simultaneously with a beam tilt of 48.59� and �48.59�. One of thelimitations of this network is the lack of capability to produce two adjacent beams since there is hightendency to form a merged single beam.

Blass and Nolen Matrix Blass matrix: Another interesting matrix design is depicted in Fig. 23, calledBlass matrix. It is a multi-beam feed network, in which “N” numbers of antenna array element feeders areconnected toM number of beam port lines through directional couplers. In a receiving configuration, eachbeam-port couple signals from each antenna with the help of series feed lines. In this feed network, thecouplers are equally spaced along the transmission line to produce a constant phase shift betweenelements that results in beam steering in a desired angle. In order to prevent reflections, the beam andelement transmission lines are terminated with matched loads. One of the consequences of this

Table 2 Phase distribution and beam direction of a 4 � 4 matrix

Input port I II III IV

Output port I �90� �45� �180� �135�

II �225� �90� �135� 0�

III 0� �135� �90� �225�

IV 135� �180� �45� �90�

Beam direction 48.59� 14.47� �14.47� �48.59�

Fig. 22 (a) 4 � 4 Butler matrix, (b) 90� hybrid coupler


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termination is the reduced efficiency of the entire system. If c m,n is the phase length from the mth port tonth element, then the phase difference of any two adjacent elements is

Dcm ¼ cm, nþ1 �cm, n¼ cm, n �cm, n�1

(18)

The corresponding output beam m is steered to an angle of

us ¼ �Dcm

k d(19)

Nolen matrix: This is a combined design of both Butler matrix and Blass matrix in which the designutilizes a unitary coupling matrix circuit as shown in Fig. 24. As in a Blass matrix, the Nolen matrix alsohas different numbers of antenna elements and beam ports. In the basic configuration, the Mth port iscoupled from the Nth antenna element as demonstrated in Fig. 25. When the number of antenna elementsis a power of two, the Nolen matrix can be reduced to a simple Butler matrix.

Metamaterials and Its Application in Multi-beam Antenna Arrays

For the last two decades, metamaterials have been an interesting research area in the scientific community.The terminology metamaterials originated from the Greek term “meta” meaning “after” or “beyond”which implies metamaterials possess some special characteristics that are beyond the natural materialsexisting in nature. Thus, metamaterials are artificial structures that exhibit electromagnetic properties notusually found. The term metamaterials was first formed by Rodger M. Walser, University of Austin, in1999. It was originally defined as “macroscopic composites having a synthetic, three dimensional,periodic cellular architecture designed to produce an optimized, not available in nature, of two or moreresponses to specific excitations.” Some of the other definitions that have been found in the literatures are“materials whose permeability and permittivity derived from their structure” and “artificial effectivelyhomogeneous electromagnetic structures with unusual properties not readily available in nature” (Calozand Itoh 2006). Based on the way in which these materials treat the incident fields of an electromagneticradiation, they are classified as double-negative materials (DNG), electromagnetic band gap (EBG) or

Fig. 23 Block diagram representation of Blass matrix


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photonic band gap materials (PBG), and frequency-selective surfaces (FSS). In general, they are com-posed of an array of dielectric or metallic elements in one, two, or three dimensions. The electromagneticproperties of these materials are characterized by various design factors including the element shape, arraytexture, electrical parameters of the material, and the distance between elements in the array.

As an electromagnetic wave incident up on a DNG material, it provides negative permittivity andnegative permeability. These types of materials have found applications in beam-steering antennas, lensantennas, and microwave filters. However, metamaterials like PBG or EBG prohibit the propagation ofincident waves across a range of frequency band. As a general rule, the periodicity in these materials is inthe range of half wavelength. These materials also found great applications in antenna engineering toenhance the gain and suppress the surface wave, in microwave filters to create band-stop response, and inelectromagnetic shielding applications. FSS is a kind of planar metamaterials, which is made of an arrayof metallic patches or perforated conductors. As the name implies, these materials are transparent to somefrequency bands while reflective, absorbing, or redirecting to others. These materials found significantapplications in antenna, filters, polarizers, radomes, and electromagnetic shielding. FSS-based EBGsurfaces formed by cascading some FSS layers are also used for antenna applications.

As shown in Fig. 26, in terms of permittivity and permeability, materials are generally classified intofour categories. A material with permittivity and permeability greater than zero is known as double-

Fig. 24 Unitary coupling matrix

Fig. 25 Nolen matrix


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positive metamaterial or right-handedmaterials which support forward propagating wave. Amaterial withpermittivity less than zero and permeability greater than zero will be designated as epsilon-negativemedium. Similarly, a material with permeability less than zero and permittivity positive is known asmu-negative metamaterial. A material with permittivity and permeability less than zero will be designatedas double-negative material or LHM which supports backward propagation of waves.

Applications in Antenna EngineeringShort history: The history of metamaterials started in 1968 when Vaselago (1968) proposed the existenceof a material with simultaneous negative electric permittivity and magnetic permeability. However, due tothe lack of experimental verifications, his invention was ignored for more than three decades. The firstrevolution of metamaterial occurred in the late 1990s (Pendry et al. 1996) when Sir Pendry demonstrated awire medium whose permittivity is negative. Then, in 1999, Sir Pendry discovered the split ringresonators having negative permeability (Pendry et al. 1999). Another important landmark was the firstartificial left-handed material using a combination of wires and SRRs by Dr. Smith in 2001 (Shelbyet al. 2001). The year following this event, LHMwas presented almost simultaneously using transmissionline approach by three research groups (Eleftheriades, Oliner, and Caloz-Ltoh) (Caloz and Itoh 2002; Iyerand Eleftheriades 2002; Oliner 2003). Any one-dimensional RHM can be resented or equivalent to aconventional transmission line composed of series inductance and shunt capacitance, whereas an LHMcan be represented as a transmission line consisting of series capacitance and shunt inductance. In fact, thescenario with a current flow through this structure can be represented as a series capacitance accompaniedby an inductance, and a shunt capacitance is accompanied by a capacitance. Thus, eventually, a compositeright-left-handed transmission line model has been evolved to represent the RHM and LHM (Caloz andItoh 2006).

The second revolution of metamaterial has happened with the concept of electromagnetic wavebending using gradient refractive index medium in 2005 (Smith et al. 2005) and the invisible cloaks in2006 (Leonhardt 2006; Pendry et al. 2006). After these realizations, the interest toward the metamaterialhas been considerably increased, and many scientific papers have been published. Due to the extraordi-nary features, metamaterials have been found and are potential candidates for various engineering

Fig. 26 Material classifications in terms of permittivity and permeability


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applications. Especially in antenna engineering, metamaterials are widely being used to improve itsperformances. Examples include antenna substrates for miniaturization, bandwidth enhancement, gainenhancement, and controlling the direction of radiation. Metamaterials as antenna superstrates can beutilized to improve impedance and directivity bandwidth, change the polarization, increase gain, andbeam tilting. Instead of conventional transmission lines, metamaterial-based transmission lines can beemployed in relatively more efficient feed networks. Compared to conventional design of transmissionline-based feed networks, the metamaterial-based feed networks have the advantage of low profile andbroad bandwidth. In phased array antennas, metamaterials are employed to improve the impedancematching and beam-scanning range. Another area of interest especially in military applications is in thefield of Radom design where the ground plane regions can be realized with metamaterials. In addition, thedesign flexibility of these engineered materials possesses good potential to be embedded in applicationssuch as Luneburg lens antennas and reflector antennas.

Design Examples

This session outlines some of the recent developments in metamaterial-based multi-beam antenna arrays.The objective of this session is to provide an experimental level demonstration of this magnificent field ofengineering.

High-Gain Reconfigurable Sectoral Antenna Using an Active Cylindrical FSS StructureSectoral antennas have been widely reported and are popular in various classical applications such as basestation antennas and point-to-multipoint communications to cover a specific area. It is a type of directionalantenna with a narrow beam width in one plane and a wide beam width in the other plane. A sectoralantenna with radiation pattern reconfigurability provides more design flexibility and in turn enhances theoverall system performance. In addition, since the beam is directed toward the desired user, it providesenergy saving and thereby higher system efficiency.

One of the practical realizations of metamaterial-based beam-scanning antenna is shown in Fig. 27. Itcomposed of active unit cell-based cylindrical FSS structure around an omnidirectional electromagnet-ically coupled coaxial dipole array. An array of discontinuous strips and PIN diodes inserted into theirdiscontinuities forms the active FSS unit cell. They are placed cylindrically with an angular periodicity ofyFSS = 30� and radius of 50 mm on a substrate with permittivity 3, thickness 0.254, and loss tangent0.0013. High-frequency PIN diodes GMP-4201 are used in the prototype. Two narrow DC feeding linesare used at both sides of the strips for supplying diodes. To produce same amount of current in all thediodes, high-value resistors are also used at the top of each line between the strip and DC feeding line. Asshown in Fig. 27b, the ECCD array was also fabricated with a UT-141B semirigid coaxial cable fromMicro-Coax.

In order to produce reconfigurable radiation pattern, the cylindrical FSS structure is divided into twosemicylinder sectors, one with diodes on and the other with diodes off. The semicylinder with the diodeson operates as an array of continuous strips with high reflection, whereas the other semicylinder with thediodes off operates as an FSS with an array of printed dipole below resonance frequency and allows thetransmission of the incident electromagnetic wave. Therefore, the FSS structure converts the omnidirec-tional radiation pattern of the source into directive pattern. By switching the diode states, the direction ofthe high and low reflective sectors changes; therefore, the radiation pattern of the antenna can be swept inthe entire 360� azimuth plane.


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During measurement, five columns of diodes were in the off state and seven columns of diodes in the onstate. A supply voltage of 0 V is given to the diode for off state, whereas 37 V DC is used for the on state.The S11 (Fig. 28) of the reconfigurable antenna indicates ~6 % of 2:1 VSWR bandwidth around the centerfrequency.

Fig. 28 Reflection coefficient of the FSS-based beam-scanning antenna

Fig. 27 Photograph of a metamaterial-based beam scanning antenna prototype, (a) antenna system, (b) source antenna array.(# The Institute of Electrical and Electronics Engineers, Published with permission from (Edalati and Denidni 2011))


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The normalized radiation patterns of the antenna in the E- and H-planes are shown in Fig. 29. Theantenna provides a directional radiation pattern with half power beam width of 20� and 70� in the E- andH-plane respectably with a side-lobe level of �13 dB. The H-plane radiation pattern of the antenna, forswitching the beam toward 0�,�30� with different reconfiguration scenarios, is demonstrated in Fig. 30.The radiation characteristics show a gain of around 13dBi.

Fig. 30 Beam scanning in H-plane with various diode reconfiguration scenarios

Fig. 29 Normalized radiation patterns of the antenna in two principle planes


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Electronically Radiation Pattern Steerable Antennas Using Active Frequency-SelectiveSurfacesCompared to conventional smart antenna systems with phase shifters, the demand for electronicallysteerable antenna solutions is quite demanding in this modern telecommunication era. The advantagesinclude more flexible design and omnidirectional beam formation. One of the interesting design examplescapable of electronic steering of radiation pattern is shown in Fig. 31.

It consists of ten columns of active FSS unit cell-based cylindrical array with a radius of 50 mm. Eachcolumn of cylindrical array has 17 unit cells. Special design schemes are employed for biasing through thebottom of the antenna system. Finally, the pair of bias cables is connected with a programmablemultichannel voltage controller. The structure of the omnidirectional coaxial collinear source antenna atthe center is made of LMR-195 coaxial cable sections.

The antenna operates in three single mode configurations, namely, case-1, case-2, and case-3, asillustrated in Fig. 32. In the case-1 scenario, five columns of the cylindrical FSS are set into reflectivemode, and the other five columns are transparent mode. The reflective FSS arrays block the electromag-netic energy, and the transparent FSS array allows passing the beam. The case-2 also works the same asthat of the case-1 mode with an additional opaque layer resulting steering of the beam. In case-3, onecolumn of the cylindrical FSS is set to partially opaque using appropriately biased varactor diode,resulting a beam in between 0� and 18�. By changing the different sectors, this particular antenna canprovide 360� steerability of the main beam in H-plane. With the same beam control method, multi-beams(two beams) are also generated.

Figure 33 shows the layout of the active FSS unit cell realized on a high-frequency laminate withpermittivity 3.5, loss tangent 0.0007, and thickness 0.8 mm. The top side of the unit cell consists of a pair

Fig. 31 Photograph of an electronically beam reconfigurable antenna (# The Institute of Electrical and Electronics Engineers,Published with permission from (Liang et al. 2013))


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of vertical anchor- shaped metal strips and a varactor mounted in the middle. The unit cells repeat alongvertical direction to form an array. The bottom side comprises the DC biasing network. Vias are used toconnect the front side strip to the biasing network. RF chokes are also applied between two unit cells andnear the vias. BB857 (by Infineon) and 22nH high Q inductor (by Murata) varactor diodes are used. At1.78 GHz, 6 Vand 30 Vare set as the voltage for reflection and transmission mode of the cylindrical FSS,respectively. And the voltage for transparent mode is 12 V.

Figure 34 shows the H-plane radiation pattern of the antenna for various reconfigurations. In case-1, themain beam direction is 178� and 3 dB width is 77�. For case-2 configuration, the main beam direction is196� and 3 dB width is 84�. Meanwhile, with case-3 mode, the main beam direction is 192� and 3 dBwidth is 88�. Moreover, the case-1 also indicates a null point 51.9 dB smaller than the main lobe, which isan interesting characteristic to isolate from noise source, especially in anti-jammer systems. The antenna

Fig. 33 Unit cell layout

Fig. 32 Single-beam configurations


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also exhibits good cross polar level of 20 dB. The gain of the source antenna is 3.6 dBi. The designedAFSS antenna provides a gain of 7dBi for case-1, 6.9 dBi for case-2, and 6.6 dBi for case-3 mode. TheE-plane radiation pattern of the antenna is presented in Fig. 35. The E-plane pattern is mainly decided bythe inner omnidirectional source antenna.

The dual beam configurations are shown in Fig. 36, and the corresponding radiation patterns areillustrated in Fig. 37. The two beams of configuration-C point to 54� and 206�. As expected, they aresupposed to be 54� and 120�. Moreover, there is less lobe pointing at about 120� that is due to the twocolumns that are not wide enough to stop the signal, and signal from the other two lobes also contribute tothis radiation. Both radiation direction and amplitudes can be controlled.

Fig. 35 Radiation pattern in the E-plane for the reconfigurable antenna in various reconfiguration states

Fig. 34 H-plane radiation pattern of the antenna in various pin diode configurations


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Conclusion

In this technological era, wireless communication plays a key role in every phase of life. The modernwireless communication systems and related technologies are synergistic products of interdisciplinaryareas of engineering. The main objective of this chapter was to introduce the concept of classical and mostrecent design concepts of multi-beam antenna arrays. Toward this goal, basics of antenna arrays and smartantenna concepts were first presented. A considerable emphasis was given to classical multiband antennadesigns and their beam-forming circuits. In order to provide the most recent advancements in multi-beamantenna technology, the idea of metamaterial and its applications were then introduced. Finally, somemetamaterial-based multi-beam antenna designs were also provided.

Fig. 37 The gain patterns in the H-plane for various beam-steering configurations

Fig. 36 Dual-beam mode configurations


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Cross-References

▶Antennas in Automobile Radar▶Antennas in Radio Telescope Systems▶Applications of Phased Array Feeders in Reflector Antennas▶Beam-Scanning Leaky Wave Antennas▶Conformal Array Antennas▶ Phased Arrays▶Reconfigurable Antenna Arrays for Wireless Communications▶Reflectarray Antennas

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