Thesis

i

Suan Soo Foo

2/43, Durham Street

St Lucia, QLD 4067

Australia

October 2000

The Dean

School of Engineering

University of Queensland

St Lucia QLD 4072

Dear Sir,

In accordance and partial fulfillment of the requirements for the degree of Bachelor of

Electrical Engineering (Honours) at the University of Queensland, I hereby submit for

your consideration this thesis entitled:

“Smart Antennas for Wireless Applications”

This work was accomplished under the supervision of Associate Professor Marek E.

Bialkowski.

I declared that the work submitted in this thesis is my own, except as acknowledged in

the text, and has not previous been submitted for a degree at the University of

Queensland or any other institution.

Yours faithfully, _____________ Suan Soo Foo

ii

Smart Antennas for

Wireless Applications

Suan Soo Foo

Approved by Assoc. Prof. Bialkowski


School of Computer Science and Electrical Engineering


Queensland 4072

Australia

iii

Acknowledgements

The author would like to express his appreciation to his supervisor, Associate Professor

M.E. Bialkowski, for providing the opportunity to research this interesting topic, for his

valuable advice and the direction he had shown throughout the year.

Many thanks to Danny Kai Pin Tan for giving the opportunity to work with him and the

tolerant he had shown while working together.

Thanks must also go to the laboratory supervisor, Damian Jones for his assistance and

the patient he had given while using the Microwave Laboratory throughout the thesis

project.

Last but no least, the author would like to extend his thanks to his girlfriend, Chai

Weichiun, and his family for their support and encouragement.

iv

ABSTRACT

The smart antenna is set to play a significant role in the development of next-generation

wireless communication system. The purpose of this thesis is to provide the concept on

smart antenna system by studying the performance of antenna array. A brief

introduction will be given before providing the overview of the thesis content.

Antenna theory and the description of different types of antennas will be discussed with

emphasis on array antennas. Two methods of antenna synthesis known as the

Woodward-Lawson and Dolph-Chebyshev will also be introduced before studying the

fundamental parameters of antenna.

With a basic understanding on antenna, this thesis will therefore discuss about the smart

antenna technology. The two types of smart antenna approaches known as the

Switching-Beam Array and Adaptive Array will be addressed after introducing the

benefits of the smart antenna technology. The smart antenna terminology together with

an adaptive algorithm called the Recursive Least Squares Algorithm will also be

presented.

After a brief introduction to the types multiple access schemes, array antennas

simulation and synthesis using the above mentioned methods and algorithm will be

carried out by varying different limiting parameters. Results will be tabulated and

antenna radiation patterns will also be plotted for discussion before wrapping up with a

conclusion and suggestion on future developments.

v

CONTENTS

Page

Chapter 1 Introduction 1

1.1 Introduction 1 1.2 Aim of Thesis 2 1.3 Overview of Content 3

Chapter 2 Antennas 4 2.1 Introduction 4 2.2 Types of Antenna 6 2.2.1 Microstrip Antennas 7 2.2.2 Array Antennas 10 2.3 Linear Array Antenna 11 2.4 Planar Array Antenna 12 2.5 Antenna Synthesis 15 2.5.1 Woodward-Lawson Method 16 2.5.2 Dolph-Chebyshev Method 18

Chapter 3 Parameters of Antenna 21 3.1 Introduction 21 3.2 Radiation Pattern 22 3.2.1 Rectangular/Cartesian Plots 23 3.2.2 Polar Plots 24 3.3 Main Lobe 26 3.3.1 Beamwidth – Half power and 10dB 26 3.3.2 Boresight Directivity/Gain 27 3.4 Sidelobes 28 3.5 Front-to-back Ratio 29 3.6 Aperture Size 29 3.7 Polarization 29

vi

Chapter 4 Smart Antenna System 31 4.1 Introduction 31 4.2 Key Benefits of Smart Antenna Technology 32 4.3 Smart Antenna System 34 4.3.1 Switching-Beam Array (SBA) 35 4.3.2 Adaptive Array 36 4.4 Beam Forming 38 4.4.1 Null Beam Forming 39 4.4.2 Steering Vector 39 4.5 Recursive Least Squares Algorithm 40

Chapter 5 Multiple Access Schemes 43 5.1 Introduction 43 5.2 Frequency Division Multiple Access (FDMA) 44 5.3 Time Division Multiple Access (TDMA) 45 5.4 Code Division Multiple Access (CDMA) 46 5.5 Space Division Multiple Access (SDMA) 47

Chapter 6 Analysis of Array Antennas 49 6.1 Aim and Procedures 49 6.2 Microstrip Patch Antenna Design 49 6.3 Simulation on Linear Array Antenna 54 6.3.1 Effect of Varying Inter-element Spacing, d 54 6.3.2 Effect of Varying Number of Elements, N 56 6.3.3 Effect of Varying Amplitude Distribution 57 6.3.4 Effect of Varying Phase Excitation, β 59 6.4 Simulation on Planar Array Antenna 61 6.4.1 Effect of Varying Inter-element Spacing, d 61 6.4.2 Effect of Varying Number of Elements, N 64 6.4.3 Effect of Varying Amplitude Distribution 68 6.4.4 Effect of Varying Phase Excitation, βx and βy 68 6.5 Discussion 72

Chapter 7 Antenna Synthesis Investigation 74 7.1 Aim and Procedures 74 7.2 Woodward-Lawson Synthesis 75 7.2.1 Effect of Varying Number of Elements, N 75 7.2.2 Effect of Varying Inter-element Spacing, d 77 7.3 Dolph-Chebyshev Synthesis 80 7.3.1 Effect of Varying Number of Elements, N 80 7.3.2 Effect of Varying Sidelobe Level 82

vii

7.3.3 Effect of Varying Inter-element Spacing, d 84 7.4 Discussion 87

Chapter 8 Recursive Least Square Algorithm Analysis 88

8.1 Aim and Procedures 88 8.2 Simulated Results 88 8.3 Discussion 91

Chapter 9 Conclusion and Future Developments 92 9.1 Conclusion 92

9.2 Future Developments 93

References

Appendix A

Appendix B

Appendix C

Appendix D

viii

List of Figures Chapter 2

Figure 2.1a Antenna as a transition device 5

Figure 2.2a Representative shapes of microstrip patch elements 8

Figure 2.2b Typical feed for microstrip antennas 9

Figure 2.3a Linear array of microstrip 11

Figure 2.4a Linear and Planar geometries 13

Chapter 3

Figure 3.2a Rectangular plot of an antenna radiation pattern 24

Figure 3.2b Polar plot of an antenna pattern 25

Figure 3.3a Typical power pattern polar plot 26

Figure 3.4a A radiation pattern showing the sidelobes level and positions 28

Figure 3.7a Variation of the electric field with time at a fixed point in space

for vertical polarization 30

Figure 3.7b Variation of the electric field with time at a fixed point in space

for horizontal polarization 30

Chapter 4

Figure 4.1a Concept of smart antenna system 32

Figure 4.3a Switch-beam array pattern 35

Figure 4.3b Switch-beam network 35

Figure 4.3c Adaptive array pattern 37

Figure 4.3d Network structure of an adaptive array 37

Figure 4.5a Representation of RLS algorithm 41

Chapter 5

Figure 5.2a Spectrum of FDMA systems 44

Figure 5.3a Frame and slot structure with basic TDMA 45

Figure 5.4a Concept of CDMA system 47

ix

Chapter 6

Figure 6.2a VSWR plot for length of 4.75cm 52

Figure 6.2b VSWR plot for length of 4.706cm 53

Figure 6.2c Radiation pattern for single microstrip patch antenna 53

Figure 6.3a Radiation pattern of ¼ λ inter-element spacing 55

Figure 6.3b Radiation pattern of λ inter-element spacing 55

Figure 6.3c Radiation pattern of a 4-elements linear array 56

Figure 6.3d Radiation pattern of a 10-elements linear array 57

Figure 6.3e Radiation pattern of a uniform distribution linear array 58

Figure 6.3f Radiation pattern of a Chebyshev distribution linear array 58

Figure 6.3g Radiation pattern of a Taylor distribution linear array 58

Figure 6.3h Radiation pattern with phase excitation 0° 60

Figure 6.3i Radiation pattern with phase excitation 45° 60

Figure 6.3j Radiation pattern with phase excitation 90° 60

Figure 6.4a Radiation pattern for inter-element spacing of:

½ λ in x-direction & ½ λ in y-direction 63

Figure 6.4b Radiation pattern for inter-element spacing of:

¾ λ in x-direction & ¾ λ in y-direction 63

Figure 6.4c Radiation pattern for inter-element spacing of:

λ in x-direction & λ in y-direction 63

Figure 6.4d Polar plot for a 3x3 planar array 65

Figure 6.4e Polar plot for a 5x5 planar array 65

Figure 6.4f Polar plot for a 8x8 planar array 65

Figure 6.4g Radiation pattern of uniform distribution planar array 67

Figure 6.4h Radiation pattern of Chebyshev distribution planar array 67

Figure 6.4i Radiation pattern of Taylor distribution planar array 67

Figure 6.4j Radiation plots of an planar array in E-plane 70

Figure 6.4k Radiation plots of an planar array in H-plane 71

Chapter 7

Figure 7.2a Radiation pattern for 8 elements linear array 76

Figure 7.2b Radiation pattern for 10 elements uniform linear array of

½ λ wavelength inter-element spacing 76

x

Figure 7.2c Radiation pattern of an 8 elements linear array for an inter-

element spacing of 0.25λ 78

Figure 7.2d Radiation pattern of an 8 elements linear array for an inter-


Figure 7.2e Radiation pattern of a 16 elements linear array for an inter-


Figure 7.2f Radiation pattern of a 16 elements linear array for an inter-


Figure 7.3a Radiation pattern for 10 elements array using MATLAB

and Ensemble 81

Figure 7.3b Radiation pattern for 8 elements array with 25dB sidelobe

level using MATLAB and Ensemble 83

Figure 7.3c Radiation pattern for 8 elements linear array with normalized

inter-element spacing of 0.5using MATLAB and Ensemble 85

Figure 7.3d Radiation pattern for 16 elements linear array with normalized

inter-element spacing of 0.5using MATLAB and Ensemble 86

Chapter 8

Figure 8.2a Radiation pattern for 4 elements linear array at 0° 89

Figure 8.2b Radiation pattern for 4 elements linear array at 45° 90

xi

List of Tables Chapter 6

Table 6.1 Results of varying inter-element spacing in linear array 55

Table 6.2 Results of varying number of element in linear array 56

Table 6.3 Results of varying amplitude distribution in linear array 57

Table 6.4 Results of varying phase excitation in linear array 59

Table 6.5 Results of varying inter-element spacing in planar array 62

Table 6.6 Results of varying number of element in planar array 64

Table 6.7 Results of varying amplitude distribution in planar array 66

Table 6.8 Results of varying phase excitation in planar array 69

Chapter 7

Table 7.1 Results of varying number of elements for Woodward-

Lawson synthesis 76

Table 7.2 Results of varying inter-elements spacing for Woodward-

Lawson synthesis 77

Table 7.3 Results of varying number of elements for Dolph-

Chebyshev synthesis 80

Table 7.4 Results of varying sidelobe level for Dolph-Chebyshev

synthesis 82

Table 7.5 Results of varying inter-element spacing for Dolph-

Chebyshev synthesis 84

Smart Antennas for Wireless Applications Chapter 1: Introduction

1

C hapter 1

Introduction

1.1 Introduction

Since the dawn of civilization, communication has been of foremost importance to

mankind. In the first place, communication was accomplished by sound through voice.

However, as the distance of communication increased, numerous devices were

introduced, such as horns, drums, and so forth. Visual techniques were injected for even

greater distances. Signal flags and smoke signals were used in the daytime while

fireworks in the night. These optical communications utilize the light portion of the

electromagnetic spectrum and it has only been in recent times that the electromagnetic

spectrum, outside the visible region, has been adopted for communication, through the

use of radio.

The radio antenna is a primary component in all radio system. An antenna (also know as

an aerial) is defined as a means for radiating or receiving radio waves [1]. In another

word, radio antennas coupled electromagnetic energy from one medium (space) to

another (e.g., wire, coaxial cable, or waveguide). Therefore, information can be

conveyed between various locations without any intervening structures.

Consequently, the application of wireless communication system has erupted

throughout the world and recent years have witness wireless communications relishing

its fastest growth period in history. Since, fixed antenna systems was first employed in

wireless systems, whereby antenna patterns were cautiously engineered to acquire

desired coverage characteristics, but that could not change to respond dynamically to


2

changing conditions. Besides, the exponential growth and the limiting bandwidth

available for those systems have created problems, which all wireless providers are

working to solve.

One potential solution to the dilemmas is the use of smart antenna systems, a concept

initially developed by the military but now a field that has attracted growing interest for

commercial wireless communication systems [2]. Smart antennas are believed to be the

last major technological innovation that has the capability of leading to massive

increases in wireless communication systems performance.

1.2 Aim of Thesis

The demand for high performance wireless communication systems has led to the

research and studies in this exciting topic. Therefore, it is important to study the basic

concepts of the Smart Antenna System, a system that brings the world of wireless

communication to a new era.

The first move to understanding the smart antenna system leads to the fundamental

studies on antenna theory and their design parameters. Laying a good foundation is

essential, as we will move on to examine the smart antenna system and the algorithm

that earns “smartness” in the antenna system.

The radiation patterns and performance of the antennas will have to be investigated and

thus, further research will be carried out to conceive a better insight by either simulating

or synthesizing different array antennas and different synthesis methods. The area of

study will conclude with analysis on simulations for the smart antenna system

algorithm. Hence, our aim is not only to analysis and study on smart antenna system,

but also how the system can increase capacity in wireless communication system

through Space Division Multiple Access (SDMA).


3

1.3 Overview of Content

The thesis will begin with an introduction on antennas and the types of antennas in

Chapter 2. In addition, the chapter will also provide an in-depth description on

microstrip antenna, array antennas and antenna synthesis techniques before considering

the fundamental parameters of antenna in Chapter 3.

Prior to discussing the multiple access schemes in Chapter 5, we will be analyzing the

smart antenna technology in Chapter 4. All simulations on array antennas were

performed and the results in addition to its discussion will be presented in Chapter 6.

Chapter 7 investigated on two types of antenna synthesis methods (Woodward-Lawson

and Dolph-Chebyshev) before discussing on the results achieved.

Lastly, Chapter 8 analysis and discussion on the Recursive Least Squares algorithm will

see Chapter 9 draws a summary and concludes the thesis with future developments.

Smart Antennas for Wireless Applications Chapter 2: Antennas

4

Chapter 2

Antennas

2.1 Introduction

Communications has become the key to momentous changes in the organization of

businesses and industries worldwide as they themselves adjust to the shift toward an

information economy. Information is indeed the lifeblood of modern economies and

antennas provide mother earth a solution to a wireless communication system.

The antenna is a means of coupling electromagnetic energy from a transmission line

into free space, thus allowing a transmitter to radiate, and a receiver to receive the

incoming electromagnetic power. It is a passive device and therefore, the power radiated

by a transmitting antenna cannot be greater than the power entering to the transmitter.

It can also be seen as a transitional structure between free-space and a guiding device

illustrated in Figure 2.1a. The guiding device or transmission line, which may take the

form of a coaxial line or a hollow pipe (waveguide), is used to transport electromagnetic

energy from the transmitting source to the antenna, or from the antenna to the receiver.

In the former example we have a transmitting antenna and in the latter a receiving

antenna.


5

In addition to transmitting and receiving energy, an antenna in an advance wireless

system is generally required to optimize or accentuate the radiation energy in a

particular direction while suppressing it in others. Physical size may vary greatly and

antennas can be just a lens, an aperture, a patch, an assembly of elements (array), a

reflector, or even a piece of conducting wire.

The antenna is one of the most critical elements for wireless communication systems

and a good design of the antenna can ease system requirements and improve overall

system performance. A typical example is TV for which the overall broadcast reception

can be improved by utilizing a high-performance antenna. The antenna serves to a

communication system the same purpose that eyes and eyeglasses serve to a human [3].

Furthermore, antennas are required in situations whereby it is impossible, impractical,

or uneconomical to provide guiding structures between the transmitter and the receiver.

E-field

Source Transmission line Antenna Radiating free-space wave

Figure 2.1a Antenna as a transition device


6

For example, it is economical to employ antennas in broadcasting where the goal is to

send energy out in literally all direction, since one transmitting terminal can serve

unlimited number of receivers. Antennas are also necessary in non-broadcast radio

applications such as municipal radio (police, fire, and rescue) and in non-

communication applications such as radar. In situation where antennas and guiding

structures are feasible, it is usually the amount of attenuation suffered by the signal that

determines the choice. In general, transmission of high frequency waves over long

distances favours the use of antennas, while small distances and low frequencies favour

the use of transmission lines [1].

In this vigorous and dynamic field, the antenna technology has been an indispensable

partner of the communication revolution over the past years. Many major advances that

took place during this era are now in common use. Despite, numerous challenges and

issues are facing us today, especially since the demands for system performance are

ever greater.

2.2 Types of Antenna

There are various types of antennas and they include wire antennas, aperture antennas,

reflector antennas, lens antennas, microstrip antennas and array antennas. However,

emphasis will be on microstrip antennas and array antennas after giving a brief idea on

wire antennas, aperture antennas, reflector antennas and lens antennas.

Wire antennas are the oldest and still the most prevalent of all antenna configurations

and they are seen virtually everywhere. There are different shapes of wire antennas such

as a straight wire (dipole), loop, and helix.

Aperture antennas are mostly utilized for higher frequencies and antennas of this class

are very useful for aircraft and spacecraft applications, because they can be easily flush-

mounted onto the surface of the aircraft or spacecraft. Furthermore, they can be coated

with a dielectric material to cushion them hazardous conditions of the environment.


7

Reflector antennas are sophisticated forms of antennas used for communication over

great distances (millions of miles). They are large in dimension as to achieve high gain

required to transmit or receive signals after millions of miles of travel.

Lenses are mainly employed to collimate incident divergent energy to prevent it from

spreading in undesired directions. Proper modeling the geometrical configuration and

using the correct material for the lenses can transform various forms of divergent energy

into plane waves and these lens antennas are used in most of the applications at higher

frequencies.

2.2.1 Microstrip Antennas

Microstrip antennas became very popular in the 1970s primarily for spaceborne

applications [3]. They are low-profile antennas that are being used in high-performance

aircraft, spacecraft, satellite and missile applications, where size, weight, cost,

performance, ease of installation, and aerodynamic profile are constraints.

On the other hand, there are also some drawbacks of microstrip antennas. They have a

low efficiency, low power, high Q, poor polarization purity, poor scan performance,

spurious feed radiation and very narrow frequency bandwidth.

Microstrip antennas are classified into three basic types: microstrip patch antennas,

microstrip travelling-wave antenna and microstrip slot antennas. The physical structure

of the microstrip antenna is very simple and they may take the form of any geometrical

shape and sizes. Figure 2.2a shows some of the shapes of microstrip patch elements.


8

However, rectangular and circular patches are most favorable because of the ease

analysis and fabrication, and their attractive radiation characteristics, especially low

cross-polarization radiation. Thus, rectangular microstrip antenna patches are chosen for

our analysis.

Typically, microstrip antenna consists of a conducting patch of any planar geometry on

one side of a dielectric substrate backed by a ground plane on the other side and the

conducting patch is printed on top of a grounded substrate. There are various methods

that can be used to feed microstrip antennas and Figure 2.2b shows the four most widely

adopted techniques: the microstrip line, coaxial probe, aperture coupling and proximity.

(a) Square (b) Rectangular (c) Dipole (d) Circular (e) Elliptical

(f) Triangular (g) Disc sector (h) Circular ring (i) Ring sector

Figure 2.2a Representative shapes of microstrip patch elements


9

Linear and circular polarizations can be achieved with either single elements or array of

microstrip antennas. Arrays of microstrip elements, with single or multiple feeds, may

also be used to introduce scanning capabilities and achieve greater directivity [3].

(i) Microstrip line feed (ii) Probe feed

(iii) Aperture-coupled feed

(iv) Proximity-coupled feed

Figure 2.2b Typical feed for microstrip antennas


10

2.2.2 Array Antennas

A directional radiation pattern can be produced when several antennas are arranged in

spaced or interconnected. Such an arrangement of multiple radiating elements is

referred to as an array antenna, or plainly, an array.

Instead of a single large antenna, many small antennas can be used in an array to

achieve a similar level of performance. The mechanical problems associated with a

single large antenna are traded for the electrical problems of feeding several small

antennas. With the advancements in solid state technology, the feed network required

for array excitation is of improved quality and reduced cost [4].

Arrays offer the unique ability of electronic scanning of the main beam, which can be

achieved by altering the phase of the exciting currents in each element antenna of the

array. Thus, it enables the capability of scanning the radiation pattern through space.

The array is hereby known as a phased array. Arrays can be of any form of geometrical

configurations and antenna arrays include the Linear Array, Planar Array and Circular

Array.

The overall field of the array is determined by the vector addition of the fields radiated

by the individual elements and this assumes that the current in each element is the same

as that of the isolated element. In order to render a very directive pattern, it is essential

that the fields from the elements of the array interfere constructively in the required

directions and interfere destructively in the remaining space.

There are five factors that contribute to the shaping of the overall pattern of antenna

array with identical elements and there are:

• Geometrical configuration of the array (linear, circular, rectangular, etc)

• Displacement between the elements

• Excitation amplitude of individual elements

• Excitation phase of individual elements


11

• Relative pattern of the individual elements

Some of the above mentioned parameters will thus be used for our simulations analysis.

In addition, this thesis will only be covering on linear and planar arrays.

2.3 Linear Array Antenna

A linear array of discrete elements is an antenna consisting of several individuals and

indistinguishable elements whose centers are finitely separated and fall on a straight-

line [5]. One dimension uniform linear array is mere and the most frequently used

geometry with the array elements being spaced equally. Figure 2.3a shows a typical

linear array of microstrip antennas, which is one of the emphases in this report.

The total field of the array is equal to the field of a single element positioned at the

origin multiple by a factor which is widely known as the array factor (AF). The array

factor is a function of geometry of the array and the excitation phase. By varying the

separation d and/or the phase β between the elements, the characteristics of the array

factor and the total field of the array can be controlled [3]. In other words, the far-zone

field of a uniform array with any number of identical elements is:

E(total) = [E(single element at reference point)] X [array factor] (2.1)

Figure 2.3a Linear array of microstrip

Microstrip Patch


12

Every array will have its own array factor and thus, the array factor is generally a

function of the number of elements, geometrical sequence, relative magnitudes, relative

phases and the inter-element spacing. Nevertheless, elements having identical

amplitudes, phases and spacing will result in an array factor of simpler form.

Assuming a N elements array with identical amplitudes but each succeeding element

has a β progressive phase lead current excitation relative to the preceding one (β

represents the phase by which the current in each element leads the current of the

preceding element). The array factor can thus be obtained by considering the elements

to be point sources. However, if the actual elements are not isotropic sources, the total

field can be form by multiplying the array factor of the isotropic sources by the field of

a single element, which is given by:

∑=

Ψ−=N

n

nje1

)1( AF (2.2)

where Ψ = kd cosθ + β

and since the total array factor for the array is a summation of exponentials, it can be

represented by the vector sum of N phasors each of unit amplitude and progressive

phase Ψ relative to the previous one [3].

2.4 Planar Array Antenna

In addition to placing elements along a straight row to form a linear array, individual

elements can be positioned along a rectangular grid to form a rectangular or planar

array, which is capable of providing more variables for controlling and modeling of

beam pattern. Moreover, planar arrays are also more versatile with lower sidelobe levels

and they can be used to scan the main beam of the antenna towards any point in space.

Referring to Figure 2.4a, the array factor can be derived for a planar array.


13

Placing M elements along the x-axis as shown in Figure 2.4a(i) will have an array factor

represented by

)cossin)(1(

11

AFxxkdmjM

mmeI

βφθ +−

=∑= (2.3)

where,

Im1 = Excitation coefficient of individual element

dx = Inter-element spacing along x-axis

βx = Progressive phase shift between elements along x-axis

(i) Linear array

(ii) Planar array

Figure 2.4a Linear and Planar geometries


14

A rectangular array shown in Figure 2.4a(ii) will be formed if N elements array with a

distance dy apart and with a progressive phase βy, is placed in the y-direction. Thus, the

array factor for the entire planar array can be written as

{ } )cossin)(1(N

1n 1

)cossin)(1(

11 AF yyxx kdnj

M

m

kdmj

mneeII βφθβφθ +−

= =

+−∑ ∑= (2.4)

or

AF = SxmSyn (2.5)

where

∑=

+−=M

kdmj

m

xxeI1m

)cossin)(1(

1xm S βφθ

(2.6)

∑=

+−=N

kdnj

n

yyeI1n

)cossin)(1(

1yn S βφθ

(2.7)

From equation (2.5), it can be seen that the pattern of a rectangular array is the product

of the array factors of the arrays in the x- and y-direction.

The amplitude of the (m,n)th element can be written as shown in equation (2.8) if the

amplitude excitation coefficients of the elements of the array in the y-direction are

proportional to those in the x.

Imn = Im1I1n (2.8)

However, if the amplitude excitation of the array is uniform (Imn = Io), then equation

(2.4) can be represented by


15

∑∑=

+−

=

+−=N

n

kdnjM

kdmj yyxx ee1

)cossin)(1(

1m

)cossin)(1(

oI AF βφθβφθ

(2.9)

and the normalized form will be

Ψ

Ψ

Ψ

Ψ

=

2sin

2sin

1

2sin

2sin

1 ),(AF

n

y

y

x

x

N

N

M

Mφθ (2.10)

where

ψx = kdxsinθcosφ + βx (2.11)

ψy = kdysinθsinφ + βy (2.12)

The above derivation assumed that each element is an isotropic source. However, if the

antenna is an array of identical elements, the total field can be obtained by applying the

pattern multiplication rule of (2.1) in a manner similar as for the linear array.

2.5 Antenna Synthesis

Till now, attention has been on antenna analysis and design. The analysis problem is the

solving for the antenna radiation characteristics (pattern, directivity, beamwidth,

impedance, efficiency, polarization and bandwidth) for a given antenna configuration.

Practically, it is often necessary to design an antenna system that will produce desired

radiation characteristics. In general, there are common demands to design antenna

whose far-field pattern posses nulls in certain directions or to yield pattern that exhibit a

desired distribution, narrow beamwidth and low sidelobes, decaying minor lobes, and so

forth.


16

Therefore, there are requirements whereby there is a need to find not only the antenna

configuration but also its geometrical dimensions and excitation coefficient. Hence,

antenna synthesis is an approach that uses a systematic method or combination of

methods to arrive at an antenna configuration which yields a pattern that is either

exactly or approximately the same to the initial specified pattern, while satisfying other

system constrains.

Generally, antenna pattern synthesis can be classified into three categories. The first

group that normally utilizes the Schelkunoff Method requires the antenna patterns to

possess nulls in certain desired direction. The next category, which requires the patterns

to exhibit a desired distribution in the entire visible region, is referred to beam shaping.

It can be achieved by using the Fourier Transform and Woodward-Lawson Methods.

Finally, the Binomial Technique and Dolph-Chebyshev Method are usually used to

produce radiation

patterns with narrow beamwidth and low sidelobes. However, only the Woodward-

Lawson method and the Dolph-Chebyshev method will be discussed.

2.5.1 Woodward-Lawson Method

Woodward and Lawson introduced a very popular antenna pattern synthesis method

used for beam shaping. The synthesis is accomplished by sampling the desire pattern at

various discrete locations. Each pattern sample is associated with a harmonic current of

uniform amplitude distribution and uniform progressive phase, whose corresponding

field is known as a composing function. Each composing function for a linear array is of

an bmsin(Nφm)/Nsin(φm) form.

The excitation coefficient bm of every harmonic current is such that its field strength is

similar to the amplitude of the desired pattern at its corresponding sampled point. The

total excitation of the source is comprised of a finite summation of space harmonic, and

the corresponding synthesized pattern is represented by a finite summation of


17

composing functions with each term representing the field of a current harmonic with

uniform amplitude distribution and uniform progressive phase [3].

The overall pattern produced by this method is as followed. The first composing

function yields a pattern whose main beam position is decided by the value of its

uniform progressive phase with the innermost sidelobes level approximately –13.5dB,

and while the rest of the sidelobes decreases monotonically. Having a similar pattern,

the second composing function will adjust its uniform progressive phase so that its main

lobe corresponds to the innermost nulls of the first composing function. This will

contribute to the filling-in of the innermost null of the first composing function pattern,

in which, the amount of filling-in is restrained by the amplitude excitation of the second

composing function. Thus, this procedure will carry on for the remaining finite number

of composing functions.

When Woodward-Lawson method is implemented to synthesized discrete linear arrays,

the pattern of each sample will be written as

−

−

=)cos(cos

21sin

)cos(cos2

sin )(

m

m

mm

kdN

kdN

bfθθ

θθθ (2.13)

l = Nd assumes the array is equal to the length of the line source. The overall array

factor can be written as a superposition of 2M or 2M+1 terms each of the form of (2.13)

[3]. Therefore,

∑=

−

−

=M

-Mmm

)cos(cos21sin

)cos(cos2

sinb )( AF

m

m

kdN

kdN

θθ

θθθ (2.14)


18

Generally, although Woodward-Lawson synthesis technique reconstructs pattern whose

values at the sampled points are similar to the ones of the desired signal, but it is unable

to control the pattern between the sample point. The quality of fit to the desired pattern

fd(w) by the synthesis pattern f(w) over the main beam is measured by the ripple, R,

which is defined as

dB )()(

maximumlog20 R

=ufuf

d

(2.15)

over the main beam. Also of interest is the region between the main beam and sidelobe

region, referred to as the transition region. It is desirable to have the main beam fall off

shapely into the sidelobe region. Thus, the transition width T is introduced and defined

as

T = |wf=0.9 – wf=0.1| (2.16)

Where wf=0.9 and wf=0.1 are the values of w where the synthesized pattern f equals 90%

and 10% of the local discontinuity in the desired patter [4].

2.5.2 Dolph-Chebyshev Method

Comparing the Uniform, Dolph-Chebyshev and Binomial distribution arrays, the

uniform amplitude arrays will yield the smallest half-power beamwidth while the

binomial arrays usually possess the smallest sidelobes. On the other hand, Dolph-

Chebyshev array is mainly a compromise between uniform and binomial arrays.

Its excitation coefficients are affiliated to the Chebyshev polynomials and a Dolph-

Chebyshev array with zero sidelobes (or sidelobes of -∞ dB) is simply a binomial

design. Thus, the excitation coefficients for this case would be the same if both methods

were used for calculation.


19

The array factor of an array of odd and even number of elements with symmetric

excitation is given by

∑ −==

M

nn

una1

2M])12cos[( (even)(AF) (2.17)

∑ −=+

=+

1

112M

])1(2cos[ (odd)(AF)M

nn

una (2.18)

where M is an integer, an is the excitation coefficients and

θλπ

cos d

u = (2.19)

The array factor is merely a summation of M or M+1 cosine terms. The largest

harmonic of the cosine terms is one less than the total number of elements in the array.

Each cosine term, whose argument is an integer times a frequency, can be rewritten as a

series of cosine functions with the fundamental frequency as the argument [3], which is,

m = 0 cos(mu) = 1

m = 1 cos(mu) = cos u

m = 2 cos(mu) = cos (2u) = 2cos2u -1

m = 3 cos(mu) = cos (3u) = 4cos3u – 3cos u

m = 4 cos(mu) = cos (4u) = 8cos4u – 8cos2u + 1 (2.20)

The above are achieved by using the Euler’s formula

[eju]m = (cos u + jsin u)m = ejmu = cos(mu) + jsin(mu) (2.21)

and the trigonometric identity sin2u = 1 – cos2u.


20

Assuming the elements of the array is placed along the z-axis, and thus, replacing cos u

with z in (2.20), will relate each of the expression to a Chebyshev polynomial Tm(z).

m = 0 cos(mu) = 1 = T0(z)

m = 1 cos(mu) = z = T1(z)

m = 2 cos(mu) = 2z2 –1 = T2(z)

m = 3 cos(mu) = 4z3 – 3z = T3(z)

m = 4 cos(mu) = 8z4 – 8z2 + 1 = T4(z) (2.22)

These relations between the cosine functions and the Chebyshev polynomials are valid

only in the range of –1 ≤ z ≤ +1. Because |cos(mu)| ≤ 1, each Chebyshev polynomial is

|Tm(z)| ≤ 1 for –1 ≤ z ≤ +1. For |z| > 1, the Chebyshev polynomials are related too the

hyperbolic cosine function [3].

The recursive formula can be used to determine the Chebyshev polynomial if the

polynomials of the previous two orders are known. This is given by

Tm(z) = 2zTm-1(z) – Tm-2(z) (2.23)

It can be seen that the array factor of an odd and even number of elements is a

summation of cosine terms whose form is similar with the Chebyshev polynomials.

Therefore, by equating the series representing the cosine terms of the array to the

appropriate Chebyshev polynomial, the unknown coefficients of the array factor can be

determine. Note that the order of the polynomial should be one less than the total

number of elements of the array.

Smart Antennas for Wireless Applications Chapter 3: Parameters of Antenna

21

Chapter 3 Parameters of Antenna

3.1 Introduction

Definitions of various parameters are necessary to describe the performance of an

antenna. Although the parameters may be interrelated, it is however, not a requirement

to specify all of the parameters for complete description of the antenna performance. An

antenna is chosen for operation in a particular application according to its physical and

electrical characteristics. Furthermore, the antenna must perform in a required mode for

the particular measurement system.

An antenna can be characterized by the following elements, not all of which apply to all

antenna types:

1. Radiation resistance;

2. Radiation pattern;

3. Beamwidth and gain of main lobe;

4. Position of magnitude of sidelobes;

5. Magnitude of back lobe;

6. Bandwidth;

7. Aperture;

8. Antenna correction factor;

9. Polarization of the electric field that it transmits or receive;

10. Power that it can handle in the case of a transmitting antenna.


22

Typically, antenna characteristics are measured in two principal planes and they are

known as the azimuth and elevation planes, which can also be considered as the

horizontal and vertical planes respectively, for land-based antennas. Conventionally, the

angle in the azimuth plane is denoted by the Greek letter phi, φ, while the Greek letter

theta, θ, represents the angle in the elevation plane.

Some characteristics such as beamwidth and sidelobes are the same in both planes for

symmetrical antennas such as circular waveguide horns and reflector. Other

characteristics such as the gain on boresight (i.e., where the azimuth and elevation

planes intersect) can only have a single value. In general, for unsymmetrical antennas

the characteristics are different in the two principal planes, with a gradual transition in

the intervening region between these two planes [6].

Not all of the antenna characteristic factors will be discussed here. The following

subsection will touch on some of the elements, which are essential for the understanding

of this thesis.

3.2 Radiation pattern

The antenna, which radiates or receives the electromagnetic energy in the same way, is

a reciprocal device. Radiation pattern is a very important characteristic of an antenna. It

facilitates a stronger understanding of the key features of an antenna that otherwise

cannot be achieved from the textual technical description of an antenna.

The radiation pattern is peculiar to class of antenna and its electrical characteristics as

well as its physical dimensions. It is gauged at a constant distance in the far field of the

antenna and its radiation pattern is usually plotted in terms of relative power. The power

at boresight, that is, at the position of maximum radiated power, is usually plotted at 0

dB; thus, the power at all other position appears as negative value. In other words, the

radiation power is normalized to the power at boresight. If the power were plotted in

linear units, the normalized power would be one at boreight [6].


23

The radiation is usually measured in the azimuth and the elevation planes and the

radiation power is plotted against the angle that is made with boresight direction. If the

antenna were not physically symmetrical about each of its principal planes, then it

would result in an unsymmetrical radiation patter in these planes.

The radiation pattern can be plotted using rectangular/cartesian or polar coordinates.

The rectangular plots can be read more precisely (since the angular scale can be

enlarged), but the polar plots offers a more pictorial representation and are thus easier to

visualize.

3.2.1 Rectangular/Cartesian Plots

Rectangular/Cartesian plots are standard x-y plots where the axes are plotted at right

angle to each other. The y-coordinate, which is called the ordinate, is used for the

dependent variable while the x-coordinate, known as abscissa, is used for the

independent variable.

In a radiation plot, the angle with respect to boresight is varied and the magnitude of the

power radiated is measured; thus, the angle is the independent variable and the power

radiated is the dependent variable. Thus, the magnitudes of the powers are the ordinate

while the angles are the abscissa. A typical rectangular plot of an antenna radiation

pattern is shown in Figure 3.2a.


24

The y-axis can show two sets of scales: one graduated from 0 dB to 4 dB and another

from 0 dB to 8 dB. Scales of 40 dB and 80 dB are calculated by multiplying the scales

by ten. It should be noted that the numbers below should really by negative values of –4

dB and –8 dB because the zero is at the top.

On the hand, the x-axis can show three sets of angular scales of 5°, 30° and 180° on

either side of the zero, representing the angles measured clockwise and anti-clockwise

from the boresight position and in standard mathematical convention denoted by

positive and negative signs disregarded on radiation graph paper.

3.2.2 Polar Plots

In a polar plot the angles are plotted radially from boresight and the power or intensity is plotted along the radius as illustrated in Figure 3.2b.

Figure 3.2a Rectangular plot of an antenna radiation pattern


25

This gives a pictorial representation of the radiation pattern of the antenna and is easier

to visualize than the rectangular/cartesian plots. Although the accuracy cannot be

increased as in the case of rectangular plot because the scale of the angular positions can

only be plotted from 0° to 360°, however, the scale of the intensity or power can be

varied.

Each circle on the polar plot represents a contour plot where the power has the same

magnitude and is shown relative to the power at boresight. These levels will always be

less than the power at boresight and values should be shown as negative because the

power is in generally a maximum value at boresight. However, they are normally

written without a sign and should be assumed to be negative, contrary to standard

arithmetic convention.

Figure 3.2b Polar plot of an antenna pattern


26

3.3 Main Lobe

The main lobe of the antenna is in the direction of maximum radiation. The

characteristics of an antenna such as beamwidth and gain are associated to the main lobe

alone. The peak/tip of the main beam is called the boresight of the antenna and the

radiation pattern is often positioned so that its boresight corresponds with the zero

angular position of the graph, even when the antenna is not physically symmetrical.

Figure 3.3a gives an idea of the main lobe, its maximum direction and beamwidth of a

typical power pattern polar plot.

3.3.1 Beamwidth – Half power and 10 dB

The beamwidth only relates to the main beam of the antenna and not the sidelobes and

in general, it is inversely proportional to its physical size. In other words, the larger the

antenna, the smaller is its beamwidth for the corresponding frequency. The plane

Figure 3.3a Typical power pattern polar plot


27

containing the largest dimension will have the narrowest beamwidth if the antenna does

not have the same dimensions in all planes.

The beam width of an antenna is usually defines in two ways. The most well known

definition is the 3-dB or half-power beamwidth. However, for antennas with very

narrow beams, the 10-dB beamwidth can also be applied. The 3-dB or half-power

beamwidth (HPBW) of an antenna is taken as the width at the points on either side of

the main beam where the radiated power is half the maximum value, and it is measured

in degrees or radians. Figure 3.3a shows the two points, half-power point (left) and half-

power (right), where the 3-dB beamwidth can be obtained.

3.3.2 Boresight Directivity/Gain

Although the terms directivity (or directive gain) and gain are frequently used

synonymously, but in fact they are not the same. The gain allows for efficiency of the

antenna, whereas directivity does not [6]. As a matter of fact, the gain of the antenna is

the product of the directivity and the efficiency. The IEEE definition of gain of an

antenna relates the power radiated by the antenna to that radiated by an isotropic

antenna (that radiates equally in all direction) and is quoted as a linear ratio or in

decibels [3].

The gain G as a linear ratio is defined as

antena isotropican by radiatedPower boresighton radiatedPower =G (3.1)

The gain GdB expressed in decibels is defined as

(G)10log 10=dBG (3.2)

Directivity of an antenna is defined as “the ratio of the radiation intensity in a given

direction from the antenna to the radiation intensity average over all direction. The


28

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” [3].

3.4 Sidelobes

The sidelobes are, strictly speaking, any of the maxima marked, for examples, as A, B,

C, D, E in Figure 3.4a. Nevertheless, in practice only the “near-in” lobes marked A are

referred to as sidelobes. Sometimes, due to the irregularities in the main beam of the

radiation pattern, it may result in small peaks such as those marked F in Figure 3.4a,

which could be mistaken for sidelobes.

Therefore, for this reason, the sidelobes are sometimes defined as the peaks, where the

difference between the peak and an adjacent trough is at least 3-dB. The sidelobes are

characterized by their level below the boresight gain and their angular position relative

to boresight. Although the sidelobe level (SLL) is usually cited as a positive quantity,

but it is a value in negative decibels since the radiation pattern is plotted with the

boresight gain at 0-dB.

Figure 3.4a A radiation pattern showing the sidelobe levels and positions


29

On top of sidelobes and main lobe, there are cases where multiple maxima occur, which

are referred to as grating lobes. Thus, one of the objectives in many designs is to avoid

grating lobes. Often it may be essential to select the largest spacing between elements

but with no grating lobes. However, the largest spacing between elements should be less

than one wavelength in order to avoid any grating lobes.

3.5 Front-to-back Ratio

The measure of the ability of a directional antenna to concentrate the beam in the

required forward direction is known as the front-to-back ratio (F/B). In linear terms, it is

determined as the ratio of the maximum power in the main beam to that in the back lobe

and it is usually expressed in decibels, as the different between the levels on boresight

and at 180° off boresight.

3.6 Aperture Size

The beamwidth is also influenced by the aperture size of an antenna. Generally, the

beamwidth gets narrower and the gain increases with an increasing aperture size at a

given frequency. The aperture size can be defined in two ways: either in terms of

wavelengths, or in terms of the actual physical size, in meters or feet.

3.7 Polarization

The polarization is another importance factor that would affect the radiation pattern.

The polarization of an antenna is defined as the polarization of the wave radiated by the

antenna in a given direction. However, the polarization is considered to be the

polarization in the direction of maximum gain when the direction is not stated.

Polarization may be classified as linear, circular, or elliptical. However, this thesis will

only touch on linear polarization.


30

As shown in Figure 3.7a, the electric field varies sinusoidally in one plane for the case

of linear polarization. In this case of a vertical polarization, it is noted that the extremity

of the electric field vector at any fixed point in space is a straight line with maximum

value, which is equal to twice the amplitude of the sinc curve that depicts the variation

of the electric field with time.

While horizontal polarization is illustrated in Figure 3.7b, it is important to note that the

polarization of a receiving antenna must match that of the incident radiation in order to

detect the maximum field.

Figure 3.7a Variation of the electric field with time at a fixed point in space for vertical polarization

Figure 3.7b Variation of the electric field with time at a fixed point in space for horizontal polarization

Smart Antenna for Wireless Applications Chapter 4: Smart Antenna System

31

Chapter 4

Smart Antenna System

4.1 Introduction

The field of wireless communication is growing at a dynamic rate, covering many

technical areas. Its sphere of influence is beyond imagination. An indication of its

importance is perhaps the immeasurable worldwide activities in this industry.

Since the early days of wireless communications, there have been simple antenna

designs that radiate signals omnidirectionally in a pattern resembling ripples in a pool of

water. Without the knowledge of the users’ locations, this unfocused technique

disseminates signals that reaches the intended user with a small percentage of overall

energy radiated out in the environment. Therefore, these strategies overcome the

problem by boosting the power level of the broadcasting signals. Moreover, there is also

additional problem of interference, which is likewise faced by directional antennas: a

system constructed to have certain fixed preferential transmission and reception

directions.

Therefore, the smart antenna systems, as shown in Figure 4.1a, have been introduced in

recent years to improve systems performance by increasing spectrum efficiency,

extending coverage area, tailoring beam shaping, steering multiple beams. Most

importantly, smart antenna system increases long-term channel capacity through Space

Division Multiple Access scheme (See Chapter 5 on Multiple Access Schemes). In

addition, it also reduces multipath fading, cochannel interferences, initial setup cost and

bit error rate (BER).


32

In this chapter, the key benefits of the smart antenna technology are covered before

looking through the smart antenna systems and the types of approaches. This chapter

will wrap up with descriptions on the Recursive Least Squares Adaptive Algorithms

after introducing to Beam Forming and Steering Vector.

4.2 Key Benefits of Smart Antenna Technology

An understanding of signal propagation environment and channel characteristics is

significant to the efficient use of a transmission medium. In recent years, there have

been signal propagation problems associated with conventional antennas and

interference is the major limiting factor in the performance of wireless communication.

Thus, the introduction of smart antennas is considered to have the potential of leading to

a large increase in wireless communication systems performance.

A smart antenna system in the wireless communication contributes to the following

major benefits:

Figure 4.1a Concept of smart antenna systems: Able to form different beam for each user, extending coverage range, minimizing the impact of noise and interference for each subscriber.


33

• Larger Range Coverage – Smart antennas provide enhanced coverage through range

extension, hole filling, and better building penetration. Given the same transmitter

power output at the base station and subscriber unit, smart antennas can increase

range by increasing the gain of the base station antenna [8].

• Reduced Initial Deployment Cost – Conventional wireless system networks are

initially often designed to satisfy coverage requirements, even though there are few

subscribers in the network. However, when the number of subscribers increases in

the network, system capacity can be increased at the expense of reducing the

coverage area and introducing additional cell sites. Nevertheless, smart antenna can

ease this problem by providing larger early cell sizes and thus, initial deployment

cost for the wireless system can be reduced through range extension.

• Reduced Multipath Fading – Multipath in radio channels can result in fading or time

dispersion. The effects of multipath fading in wireless communications

environments can be significantly reduced through smart antenna systems. This

reduction variation of the signal (i.e., fading) greatly enhances system performance

because the reliability and quality of a wireless communications system can strongly

depend on the depth and rate of fading [9].

• Better Security – The employment of smart antenna systems diminish the risk of

connection tapping. The intruder must be situated in the similar direction as the user

as seen from the transmitter base station.

• Better Services – Usage of the smart antenna system enables the network to have

access to spatial information about the users. This information can be used to assess

the positions of the users much more precisely than in existing network. This can be

applied in services such as emergency calls and location-specific billing.

• Increased Capacity – Smart antennas can also improve system capacity. They can

be used to allow the subscriber and base station to operate at the same range as a

conventional system, but a lower power. This may permit FDMA and TDMA


34

systems, which will be discussed in the later section, to be rechannelized to reuse

frequency channels more frequently than conventional systems using fixed

antennas, since the carrier-to-interference ratio is much greater when smart antennas

are used. In CDMA systems, if smart antennas are used to allow subscribers to

transmit less power for each link, then the Multiple Access Interference is reduced,

which increases the number of simultaneous subscribers that can be supported in

each cell.

Although the smart antenna systems are favorable in many ways, there are also

drawbacks which include a more complex transceiver structure compared to traditional

base station transceiver and a growing need for development of efficient algorithm for

real-time optimizing and signal tracking. Thus, smart antenna base stations will no

doubt be much more expensive than conventional base stations and the advantages

should always be evaluated against the cost.

4.3 Smart Antenna System

A smart antenna system can be define as a system which uses an array of low gain

antenna elements with a signal-processing capability to optimize its radiation and/or

reception pattern automatically in response to the ever changing signal environment.

This can be visualized as the antenna focussing a beam towards the communication user

only.

Truly speaking, antennas are only mechanical construction transforming free

electromagnetic (EM) waves into radio frequency (RF) signals travelling on a shielded

cable or vice-versa. They are not smart but antenna systems are. The whole system

consists of the radiating antennas, a combining/dividing network and a control unit. The

control unit is usually realized using a digital signal processor (DSP), which controls

several input parameters of the antenna to optimize the communication link. This shows

that smart antennas are more than just the “antenna,” but rather a complete transceiver

concept.


35

Smart antenna systems are customarily classified as either Switching- Beam Array

(SBA) or Adaptive Array (also known as Tracking-Beam Array – TBA) systems, and

they are the two different approaches to realizing a smart antenna.

4.3.1 Switching-Beam Array (SBA)

In the smart antenna systems, the SBA approach forms multiple fixed beams with

enhanced sensitivity in specific area. These antenna systems will detect signal strength,

and select one of the best, predetermined, fixed beams for the subscribers as they move

throughout the coverage sector. Instead of modeling the directional antenna pattern with

the metallic properties and physical design of a single element, a SBA system couple

the outputs of multiple antennas in such a manner that it forms a finely sectorized

(directional) beams with spatial selectivity.

Figure 4.3a shows the SBA patterns and Figure 4.3b illustrated the design network of a

typical SBA system. The SBA system network illustrated is relatively simple to

implement, requiring only a beamforming network, a RF switch, and control logic to

select a specific beam.

Figure 4.3b A Switch-Beam network uses a beamforming network to form M beams from M array elements

Figure 4.3a Switch-Beam Systems can select one of the several beams to enhance receive signals. Beam 2 is selected here for the desired signal


36

Switched beam systems offer numerous advantages of more elaborate smart antenna

systems at a fraction of the complexity and expense. Nevertheless, there are some

limitations to switched beam array, which comprise of the inability to provide any

protection from multipath components that arrive with Directions-of-Arrival (DOAs)

near that of the desire components, and also the inability to take advantage of path

diversity by combining coherent multipath components. Lastly, due to scalloping, the

received power from a user may fluctuate when he moves around the base station.

Scalloping is the roll-off of the antenna pattern as a function of angles as the DOA

varies from the boresight of each beam produced by the beamforming network [8].

In spite of the drawbacks, SBA systems are widespread for various reasons. They

provide some range extension benefits and offer reduction in delay spread in certain

propagation environments. In addition, the engineering costs to implement this low

technology approach are lesser than those associated with more complicated systems.

4.3.2 Adaptive Array

It is possible to achieve greater performance improvements than that obtained using the

SBA system. This can be accomplished by increasing the complexity of the array signal

processing to form the Adaptive Antenna Systems, which is considered to be the most

advance smart antenna approach to date.

The adaptive antenna systems approach communication between a user and the base

station in a different way, in effect adding a dimension in space. By adapting to the RF

environment as it changes, adaptive antenna technology can dynamically modify the

signal patterns to near infinity to optimize the performance of the wireless system.

Adaptive arrays continuously differentiate between the desired signals, multipath, and

interfering signals as well as calculate their directions of arrival by utilizing

sophisticated signal-processing algorithms. The technique constantly updates its

transmitting approach based on changes in both the desired and interfering signal

locations. It ensures that signal links are maximized by tracking and providing users


37

with main lobes and interferers with nulls, because there are neither microsectors nor

predefined patterns.

Although both systems seek to increase gain with respect to the location of the users,

however, only the adaptive system is able to contribute optimal gain while

simultaneously identifying, tracking, and minimizing interfering signals. This can be

seen from Figure 4.3c that only the main lobe is directed towards the user while a null

being directed at a cochannel interferer. Illustrated in Figure 4.3d is the network

structure of an adaptive array.

Figure 4.3c An adaptive antenna can adjust its antenna pattern to enhance the desired signal, null or reduce interference, and collect correlated multipath power

Figure 4.3d Network structure of an adaptive array structure


38

4.4 Beam Forming

A single output of the array is formed when signals induced on different elements of the

array are combined. A plot of the array response as a function of angle is usually

specified as the array pattern or beam pattern. It can also be known as power pattern

when the power response is plotted.

This method of combining the signals from several elements is understood as beam

forming. The direction in which the array has maximum response is said to be the beam

pointing direction, and thus this is the bearing where the array has the utmost gain.

Conventional beam pointing or beam forming can be achieved by adjusting only the

phase of the signals from different elements. In other words, pointing a beam in the

desired direction. However, the shape of the antenna pattern in this case is fixed, that is,

the side lobes with respect to the main do not change when the main beam is pointed in

different directions by adjusting various phases. Nevertheless, this can be overcome by

adjusting the gain and phase of each signal to shape the pattern as required and the

degree of change will depend upon the number of elements in the array.

For example, signals can also be coupled together without any gain or phase shift in a

linear array, and it is known as broadside to the array, which is, perpendicular to the row

joining all the elements of the array. The array pattern formed thus falls to a low value

on either side of the beam pointing direction and the region of the low value is known as

a null. In this case, it must be noted that the null is actually a position where the array

response is zero and the term should not be misused to denote the low value of the

pattern.

Lastly, it is very convenient to make use of vector notation while working with array

antennas. Thus the term weight vector (w) is introduced. It is important because the

weight vector will have significant impact on the array output.


39

4.4.1 Null Beam Forming

The flexibility of array weighting to being adjusted to specify the array pattern is an

important property. This may be exploited to cancel directional sources operating at the

same frequency as that of the desired source, provided these are not in the direction of

the desired source [10].

In circumstances where the directions of these interferences are identified, cancellation

is feasible by positioning the nulls in the pattern corresponding to these directions and

concurrently steering the main beam in the direction of the desired signal. This approach

of beam forming by placing nulls in the directions of interferences is commonly referred

to as null beam forming or null steering.

4.4.2 Steering Vector

The steering vector contains the response of all elements of the array to a narrow-band

source of unit power. As the response of the array is different in different directions, a

steering vector is associated with each directional source. The uniqueness of this

association depends upon the array geometry [10].

Every component of this vector has unit magnitude for an array of identical elements.

The phase of its ith component is similar to the phase difference between signals

induced on the ith element and the reference element due to the source associated with

the steering vector.

This vector is also known as the space vector because each component of the vector

represents the phase delay that is resulted from the spatial position of the corresponding

element of the array. In addition, it can also be referred to as the array response vector

for it measures the response of the array due to the source under consideration.


40

4.5 Recursive Least Squares Algorithm

For an adaptive array network as shown in Figure 4.3d, it is essential that the weight

vector to be updated or adapted periodically because the environment (e.g. mobile

environment) is time-variable. Generally, the weight vector computed differs by a small

but significant amount at different cycles.

In addition, because the necessary data to estimate the optimal solution is noisy, it is

beneficial to use an update technique, which uses previous solutions for the weight

vector to smooth the estimate of the optimal response. Thus, an adaptive algorithm is

exploited for updating the weight vector periodically.

There are many types of adaptive algorithms and the majorities are iterative. They

utilized the past information to minimize the computations required at each update

cycle. In iterative algorithms, the current weight vector, w(n), is modified by an

incremental value to form a new weight vector, w(n+1) at each iteration n.

In the later development of adaptive algorithm, the Least Mean Square (LMS) algorithm

and Recursive Least Squares (RLS) algorithm are viewed to be more efficient. However,

in this chapter, we will be only looking at the RLS algorithm as it is regarded to have a

faster convergence speed (the speed for the initial weight vector to reach the optimum

weight vector) compared to LMS. Nevertheless, it is a result of greater computation

complexity. Figure 4.5a illustrated the block diagram representation and signal flow

graph of the RLS algorithm.


41

The RLS algorithm can be summarized as follow [14]:

Initialization

P(0) = δ-1I (4.1)

w(0) = 0 (4.2)

Weight Update

k(n) = λ -1P(n-1)u(n) / 1+λ -1uH(n)P(n-1)u(n) (4.3)

αα (n) = d(n) – wH(n-1)u(n) (4.4)

w(n) = w(n-1) + k(n) α*(n) (4.5)

(i)

(ii)

Figure 4.5a Representation of RLS algorithm: (i) block diagram (ii) signal-flow graph


42

P(n) = λ -1P(n-1) - λ -1k(n)uH(n)P(n-1) (4.6)

Convergence Coefficient

0 < λ <1

where,

δ is a small positive number,

I is the M X M identity matrix,

λ is the forgetting factor

k(n) is the gain vector,

αα (n) is the innovation,

w(n) is the weight vector,

P(n) is the inverse of the correlation matrix ΦΦ (n),

u(n) is the input vector and

d(n) is the desired response.

In the RLS method, the desired signal must be supplied using either a training sequence

or decision direction. For the training sequence approach, a brief data sequence is

transmitted which is known by the receiver. The receiver uses the adaptive algorithm to

approximate the weight vector in the training duration, then retains the weights constant

while information is being transmitted. This technique requires that the environment be

stationary from one training period to the next, and it reduces channel throughput by

requiring the use of channel symbols for training. However, in the decision approach,

the receiver uses recreated modulated symbols based on symbol decisions, which are

used as the desired signal to adapt the weight vector [8].

Smart Antenna for Wireless Applications Chapter 5: Multiple Access Schemes

43

Chapter 5

Multiple Access Schemes

5.1 Introduction

Due to the recent development of wireless communication systems, the range of

frequencies available for wireless communication technologies can be utilized in

various ways/schemes, and this is referred to as multiple access schemes. These

techniques are adopted to allow numerous users to share simultaneously a finite amount

of signal spectrum.

The distribution of spectrum is required to achieve this high system capacity by

simultaneously allocating the available bandwidth (or available amount of channels) to

multiple users. This must be accomplished without severe degradation in the

performance of the system in order to achieve high quality communications.

Conventionally, there are three major access schemes used to share the available

bandwidth in a wireless communication. Nonetheless, they are known as the frequency

division multiple access (FDMA), time division multiple access (TDMA), and the code

division multiple access (CDMA).

As a result, there is a lot to debate about which schemes is better. However, the answer

to this depends on the combined techniques, such as the modulation scheme, anti-fading

techniques, forward error correction, and so on, as well as the requirements of services,

such as the coverage area, capacity, traffic, and types of information [11].


44

5.2 Frequency Division Multiple Access (FDMA)

Frequency division multiple access (FDMA) is the most widespread multiple-access

scheme for land mobile communication system due to its ability to discriminate

channels effortlessly by filters in the frequency domain. In FDMA, every subscriber is

allocated to an individual unique frequency band or channel.

Figure 5.2a shows the spectrum of a FDMA system. The allocated system bandwidth is

divided into bands with bandwidth of Wch and guard space between adjacent channels to

prevent spectrum overlapping that may be resulted from carrier frequency instability.

When a user sends a call request, the system will assign one of the available channels to

the user, in which, the channel is used exclusively by that user during a call. However,

the system will reassign this channel to a different user when the previous call is

terminated.

One of the most important advantages in FDMA system is there isn’t any need for

synchronization or timing control and therefore, the hardware is simple. In addition,

there is only a need for flat fading consideration as for anti-fading technique because the

bandwidth of each channel in the FDMA is sufficiently narrow.

Figure 5.2a Spectrum of FDMA systems


45

However, there are also various problems associated with FDMA systems and they are:

• Intermodulation interference increases with the number of carriers .

• Variable rate transmission is difficult because such a terminal has to prepare a lot of

modems. For the same reason, composite transmission of voice and non-voice data

is also difficult.

• High Q-value for the transmitter and receiver filters is required to guarantee high

channel selectivity [11].

5.3 Time Division Multiple Access (TDMA)

In the basic time division multiple access (TDMA) protocol, the transmission time axis

is divided into frames of equal duration, and each frame is divided into the same

number of time slots having equal duration. Each slot position within a frame is

allocated to a different user and this allocation stays the same over the sequence of

frames [12]. This means that a particular user may transmit during one particular slot in

every frame and thus, it has the entire channel bandwidth at its disposal during this slot.

Figure 5.3a illustrated the allocation in a basic TDMA frame with four time slots per

frame with the shaded areas representing the guard times in each slot in which

transmission is prohibited in this region. It is essential to have the guard times as it

prevents transmissions of different (spatially distributed) users from overlapping due to

transmission delay differences.

Figure 5.3a Frame and slot structure with basic TDMA


46

5.4 Code Division Multiple Access (CDMA)

In code division multiple access (CDMA) systems, the signal is multiplied by a very

large bandwidth signal called the spreading signal. The spreading signal is a pseudo-

noise code sequence that as a chip rate which is in orders of magnitudes greater than the

data rate of message [8].

Having its own pseudorandom codeword, all subscribers in a CDMA system use the

same carrier frequency and may transmit simultaneously. Figure 5.4a(i) displays the

spectrum of a CDMA system. The most distinct feature of CDMA system is that all the

terminals share the whole bandwidth, and each terminal signal is discriminated by the

code.

When each user sends a call request to the base station, the base station assigns on of

the spreading codes to the user. When five users initial and hold the calls as shown in

Figure 5.4(ii), time and frequency are occupied as shown in Figure 5.4(iii) [13].

Therefore, CDMA requires a larger bandwidth as compared to FDMA and TDMA.

Furthermore, there is also a need for code synchronization in CDMA system.


47

5.5 Space Division Multiple Access (SDMA)

In addition to these techniques, smart antennas provide a new method of multiple access

to the users, which is known as the space division multiple access (SDMA). The SDMA

(i)

(ii)

(iii)

Figure 5.4a Concept of a CDMA system: (i) spectrum of a CDMA system (ii) a call initiation and holding model for five-user case (iii) channel allocation to each user


48

scheme, which is commonly referred to space diversity, uses smart antenna to provide

control of space by providing virtual channels in an angle domain. With the use of this

approach, simultaneous calls in various different cells can be established at the same

carrier frequency.

The SDMA scheme is based upon the fact that a signal arriving from a distant source

reaches different antennas in an array at different times due to their spatial distribution,

and this delay is utilized to differentiate one or more users in one area from those in

another area [10].

This technique enables an effective transmission to take place in one cell without

affecting the transmission in another cell. Without the use of an array, this can be

accomplished by having a separate base station for each cell and keeping cell size

permanent, while the use of space diversity enables dynamic changes of cell shapes to

reflect the user movement.

Thus, an array of antennas constitutes to an extra dimension in this system by providing

dynamic control in space and needless to say, it leads to improved capacity and better

system performance.

Smart Antenna for Wireless Applications Chapter 6: Analysis of Array Antennas

49

Chapter 6

Analysis of Array Antennas

6.1 Aim and Procedures

Previous chapters had provided basic concept on antennas and smart antenna systems.

Thus, this will greatly contribute to further understanding the operation of smart antenna

systems. As a result, it would be appropriate to study the basic of antenna arrays, its

radiation pattern and performance.

This chapter will be covering the analysis of linear and planar arrays of microstrip patch

antennas. The design of microstrip patch antennas was studied and implemented before

carrying out simulations using software programs known as the Personal Computer

Antenna Aided Design (PCAAD) and MATLAB.

Various parameters were altered to study the effects that would be reflected on antenna

arrays. The simulated results achieved were tabulated. In addition, polar plots were also

generated to cater for a better visualization and analysis. Last but not least, the chapter

will conclude with some discussions on the results achieved.

6.2 Microstrip Patch Antenna Design

The microstrip rectangular patch antenna is by far the most widely used configuration.

Therefore, we will be designing the rectangular patch for the linear and planar array

simulations. Several factors contribute to the design of a microstrip rectangular patch

antenna. Figure 2.2b(i) shows some of the parameters constrain for the design, which


50

include the length and width of the antenna patch, the type of substrate used and the

substrate thickness.

In addition, the center/resonant frequency must also be determined. A resonant

frequency of 2GHz is chosen because in 1992, the World Administrative Radio

Commission (WARC) of the International Telecommunications Union (ITU)

formulated a plan to implement a global frequency band in the 2000 MHz range that

would be common to all countries for the universal wireless communication systems

[8].

The dimensions of a rectangular patch antenna can be determined using the following

equations:

Width, W = 2λ

2/1

2

)1( −

+rε (6.1)

Length, L = le

∆−

2

)*2( ελ

(6.2)

where the effective dielectric constant, εe and l∆ are given by:

Effective dielectric constant, εe = 2/112

12

12

1 −

+

−++

Wtrr εε

(6.3)

where t is the thickness of the substrate.

l∆ = (0.412t)( )

( )

+−

++

8.0258.0

264.03.0

tW

e

tW

e

ε

ε (6.4)

Patch size calculation:

Assuming a rectangular line-fed configuration.


51

Assuming resonant frequency, f = 2GHz

Assuming typical substrate of dielectric constant, εr = 2.2

Assuming substrate thickness, t = 0.5 cm

Wavelength, λ = C/f

= (3*108)/2GHz

= 0.15m

where C is the free space velocity of light.

Width, W = 2λ

2/1

2

)1( −

+rε

= 2/1

2)12.2(

215.0 −

+

= 0.0593 m

= 5.93 cm

Effective dielectric constant, εe = 2/112

12

12

1 −

+

−++

Wtrr εε

= 2/1

93.55.0*12

12

12.22

12.2 −

+

−++

= 2.02300444384

l∆ = (0.412t)( )

( )

+−

++

8.0258.0

264.03.0

tW

e

tW

e

ε

ε

= (0.412*0.5)

+−

++

8.05.093.5

)258.002.2(

264.05.093.5

)3.002.2(

= 0.2597


52

Length, L = le

∆−

2

)*2( ελ

= )2597.0*2(02.2*2(

100*15.0 −

= 4.75 cm

Nevertheless, after much testing, it was observed from PCAAD simulations that a

length of 4.75 cm (Figure 6.2a) does not produce a minimum voltage standing wave

ratio (VSWR)* compared to a length of 4.706 cm (Figure 6.2b) at 2GHz. Hence, the

new dimension of Length = 4.706 cm and Width = 5.93 cm is selected for applications

to the simulations.

*Note: The reflected waves from the interface between the source and the antenna

create, along with the travelling waves from the source towards the antenna,

constructive and destructive patterns, referred to as standing waves. Thus, when the

impedance of the antenna (load) to the characteristic impedance of the transmission line

matched, a desired minimum VSWR is achieved.

Figure 6.2a VSWR plot for length of 4.75 cm

VSWR ≈ 4.6


53

Figure 6.2c illustrated the radiation pattern of the single microstrip patch antenna with

simulated results of:

Bandwidth = 3.9%

Efficiency = 97.6%

Directivity = 7.2

Figure 6.2b VSWR plot for length of 4.706 cm

VSWR ≈ 4.4

Figure 6.2c Radiation pattern for single microstrip patch antenna

-30 -20 - 10 0

Note that the values here will be the same for all polar plots unless otherwise stated


54

6.3 Simulation on Linear Array Antenna

Linear array is the simplest and commonly used configuration. Therefore, it is essential

to investigate its performance. There are four basic factors influencing the performance

of the linear array antenna and this section will be examining a linear array of microstrip

patch antennas. The four influencing factors, which consists of the inter-element

spacing, number of elements in an array, the amplitude distribution and the phase

excitation, will be varied, and all observation will be monitored. The subsequent

simulations on linear array will be performed using the PCAAD program with the

following predefined parameters:

Microstrip antenna patch length, L = 4.706 cm

Microstrip antenna patch width, W = 5.93 cm

Substrate thickness, t = 0.5 cm

Dielectric constant = 2.2

Center frequency, f = 2GHz

Wavelength, λ = 15 cm

Assuming the element polarization is in the X-direction.

6.3.1 Effect of Varying Inter-element Spacing, d

The following assumptions are made:

• Phase shift = zero degree

• Amplitude distribution = uniform

• Number of elements in the array = 8

PCAAD simulations were carried out and the results were tabulated in Table 6.1. Figure

6.3a illustrated the radiation pattern for an inter-element spacing of ¼ wavelength and

Figure 6.3b displayed the pattern for an inter-element spacing of one wavelength.


55

Inter-element Spacing (cm)

Directivity 3 dB Beamwidth (degree)

Remarks

λ/8 = 1.875 10.2 46.5 1 main lobe λ/4 = 3.75 12.9 24.9 2 sidelobes (SLL = -15.1dB)

3λ/8 = 5.625 14.5 16.8 4 sidelobes (SLL = -13.8dB) λ/2 = 7.5 15.7 12.6 6 sidelobes (SLL = -13.4dB)

3λ/4 = 11.25 17.3 8.4 10 sidelobes (SLL = -13.1dB) λ = 15 16.3 6.3 14 sidelobes (SLL = -13.0dB)

and 2 grating lobes

Table 6.1

Figure 6.3a Radiation pattern of ¼ λλ inter-element spacing

Figure 6.3b Radiation pattern of λλ inter-element spacing


56

6.3.2 Effect of Varying Number of Elements, N




• Inter-element spacing = 2λ

= 7.5 cm


6.3c illustrated the radiation pattern for a 4-elemeents linear array while Figure 6.3d

displayed the radiation pattern for a 10-elemeents linear array.

Number of element (N)

Directivity 3 dB Beamwidth (degree)

Remarks

2 9.9 51.3 1 main lobe 3 11.5 34.0 2 sidelobes < 20 dB 4 12.7 25.4 2 sidelobes < 20 dB 6 14.4 16.9 4 sidelobes < 20 dB 8 15.7 12.6 6 sidelobes < 20 dB 10 16.6 10.1 8 sidelobes > 20 dB 20 19.6 4.9 18 sidelobes > 20 dB

Figure 6.3c Radiation pattern of a 4-elements linear array

Table 6.2


57

6.3.3 Effect of Varying Amplitude Distribution


• Number of elements = 8


= 7.5 cm

PCAAD simulations were carried out and the results were tabulated in Table 6.3.

Figure 6.3e illustrated the radiation pattern for an array with uniform distribution.

Figure 6.3f illustrated the radiation pattern for an array with Chebyshev distribution.

Figure 6.3g illustrated the radiation pattern for an array with Taylor distribution.

Amplitude Distribution Directivity 3 dB Beamwidth (degree)

Remarks

Uniform 15.7 12.6 6 sidelobes (SLL = -13.4dB) Chebyshev

(SLL = 20 dB) 15.4 14.1 6 sidelobes (SLL = -20.7dB)

Taylor (SLL = 20 dB)

14.9 16.1 6 sidelobes (SLL = -10.0dB)

Figure 6.3d Radiation pattern of a 10-elements linear array

Table 6.3


58

Figure 6.3e Radiation pattern of uniform distribution array

Figure 6.3f Radiation pattern of Chebyshev distribution array

Figure 6.3g Radiation pattern of Taylor distribution array


59

6.3.4 Effect of varying phase excitation, ββ



• Amplitude distribution = Taylor (SLL = 60 dB)


= 7.4 cm

PCAAD simulations were carried out and the results were tabulated in Table 6.4.

Figure 6.3h illustrated the radiation pattern for an array with phase excitation of 0°.

Figure 6.3i illustrated the radiation pattern for an array with phase excitation of 45°.

Figure 6.3j illustrated the radiation pattern for an array with phase excitation of 90°.

β (degree) Directivity 3 dB Beamwidth (degree)

Main beam angle (degree)

45 18.5 7.0 -15.0 90 18.1 7.8 -30.0 135 17.1 10.4 -49.0 180 15.9 - - 225 17.1 10.4 49.0 270 18.1 7.8 30.0 315 18.5 7.0 15.0 360 18.6 6.7 0

Table 6.4


60

Figure 6.3h Radiation pattern with phase excitation 0°°

Figure 6.3j Radiation pattern with phase excitation 90°°

Figure 6.3i Radiation pattern with phase excitation 45°°


61

6.4 Simulation on Planar Array Antenna A planar array provides more variables for controlling and modeling of beam patterns as

compared to the linear array. They are more flexible and can provide more symmetrical

patterns with lower sidelobes. In addition, they can be used to scan the main beam of

the antenna toward any point in space.

Therefore, this section will be exploring the radiation patterns of a planar array by

varying various parameters. The parameters include the inter-element spacing, number

of elements in the array and the amplitude distribution. The effect on beam steering of

the planar array will also be investigated. The subsequent simulations on planar array

will be performed using the PCAAD and MATLAB with the following predetermined

parameters:

Microstrip antenna patch length, L = 4.706 cm

Microstrip antenna patch width, W = 5.93 cm

Substrate thickness, t = 0.5 cm

Dielectric constant = 2.2

Center frequency, f = 2GHz

Wavelength, λ = 15 cm

Assuming the element polarization is in the X-direction.



• Number of elements = 5 x 5




62


6.4a illustrated the radiation pattern for a planar array with ½ wavelength inter-element

spacing in both X and Y directions while Figure 6.4b illustrated the radiation pattern for

a planar array with ¾ wavelength inter-element spacing in both X and Y directions.

Lastly, Figure 6.4c displayed the radiation pattern for a planar array with full

wavelength inter-element spacing in both X and Y directions.

X (cm) Y (cm) Directivity 3 dB Beamwidth (degree)

Comments

¼ λ ¼ λ 14.1 38.8 2 sidelobes (SLL = -19.1dB) ¼ λ ½ λ 16.6 38.8 2 sidelobes (SLL = -19.1dB) ¼ λ ¾ λ 18.2 38.8 2 sidelobes (SLL = -19.1dB)

¼ λ λ 18.7 38.8 2 sidelobes (SLL = -19.1dB) ½ λ ¼ λ 16.7 20.3 4 sidelobes (SLL = -13.5dB) ½ λ ½ λ 19.2 20.3 4 sidelobes (SLL = -13.5dB) ½ λ ¾ λ 20.8 20.3 4 sidelobes (SLL = -13.5dB) ½ λ λ 21.2 20.3 4 sidelobes (SLL = -13.5dB) ¾ λ ¼ λ 18.1 13.6 6 side lobes (SLL = -12.7dB) ¾ λ ½ λ 20.6 13.6 6 side lobes (SLL = -12.7dB) ¾ λ ¾ λ 22.2 13.6 6 side lobes (SLL = -12.7dB) ¾ λ λ 22.7 13.6 6 side lobes (SLL = -12.7dB) λ ¼ λ 16.4 10.2 6 side lobes (SLL = -12.4dB) and

2 grating lobes which beamwidth is greater than main lobe beamwidth

λ ½ λ 18.6 10.2 6 side lobes (SLL = -12.4dB) and 2 grating lobes which beamwidth is greater

than main lobe beamwidth λ ¾ λ 20.0 10.2 6 side lobes (SLL = -12.4dB) and

2 grating lobes which beamwidth is greater than main lobe beamwidth

λ λ 20.8 10.2 6 side lobes (SLL = -12.4dB) and 2 grating lobes which beamwidth is greater

than main lobe beamwidth

Table 6.5


63

Figure 6.4a Radiation pattern for inter-element spacing of: ½ λλ in X-direction & ½ λλ in Y-direction

Figure 6.4b Radiation pattern for inter-element spacing of: ¾ λλ in X-direction & ¾ λλ in Y-direction

Figure 6.4c Radiation pattern for inter-element spacing of: λλ in X-direction & λλ in Y-direction


64


From the previous simulated results, the inter-element spacing of ½ λ in both X-

direction and Y-direction is chosen for this simulation.





6.4d illustrated the radiation pattern for a 3x3 planar array while Figure 6.4e presented

the radiation pattern for a 5x5 planar array. The radiation pattern for an 8x8 planar array

is shown in Figure 6.4f.

Number of Element (X*Y)

Directivity 3 dB Beamwidth Comments

2 * 2 11.8 51.3 1 main lobe 2 * 3 13.4 51.3 1 main lobe 2 * 4 14.5 51.3 1 main lobe 2* 5 15.4 51.3 1 main lobe 3 * 2 13.4 34.0 2 side lobes > -20 dB 3 * 3 15.0 34.0 2 side lobes > -20 dB 3 * 4 16.1 34.0 2 side lobes > -20 dB 3 * 5 17.0 34.0 2 side lobes > -20 dB 4 * 2 14.7 25.4 2 side lobes > -20 dB 4 * 3 16.3 25.4 2 side lobes > -20 dB 4 * 4 17.4 25.4 2 side lobes > -20 dB 4* 5 18.3 25.4 2 side lobes > -20 dB 5 * 2 15.6 20.3 4 side lobes > -20 dB 5 * 3 17.2 20.3 4 side lobes > -20 dB 5 * 4 18.3 20.3 4 side lobes > -20 dB 5* 5 19.2 20.3 4 side lobes > -20 dB 6 * 6 20.8 16.9 4 side lobes > -20 dB 7 * 7 22.1 14.5 6 side lobes 8 * 8 23.2 12.6 6 side lobes

Table 6.6


65

Figure 6.4d Polar plot for a 3x3 planar array

Figure 6.4f Polar plot for a 8x8 planar array

Figure 6.4e Polar plot for a 5x5 planar array


66

6.4.3 Effect of Varying Amplitude Distribution

The simulations will be using the inter-element spacing of ½ λ in both X-direction and

Y-direction with the following assumptions:



PCAAD simulations were performance and the results achieved were tabulated in

Table 6.7.

Figure 6.4g and Figure 6.4h illustrated the radiation patterns for planar arrays with

uniform amplitude distribution and Chebyshev amplitude distribution respectively

whereas Figure 6.4i presented the radiation pattern for a planar array with Taylor

amplitude distribution.

Amplitude Distribution Directivity 3 dB Beamwidth (degree)

Remarks

Uniform 19.2 20.3 4 sidelobes (SLL = -13.5dB) Chebyshev

(SLL = 20 dB) 18.6 23.0 4 sidelobes (SLL = -21.8dB)

Taylor (SLL = 20 dB)

18.7 22.7 4 sidelobes (SLL = -21.2dB)

Table 6.7


67

Figure 6.4g Radiation pattern of uniform distribution array

Figure 6.4h Radiation pattern of Chebyshev distribution array

Figure 6.4i Radiation pattern of Taylor distribution array


68

6.4.4 Effect of Varying Phase Excitations, ββx and ββy

Radiation performance of a planar array will be examined by performing various

simulations. Changes will be monitored as the phase excitations, βx and βy, are varied.

The overall pattern, which is formed by combining the radiation pattern of a single

microstrip patch antenna and the array factor of the planar array, will be analyzed.

The overall pattern will be plotted and studied using the E-plane (x-z plane) and the H-

plane (y-z plane). The following assumptions are made for the simulations:


• Inter-element spacing = 8.3 cm in x-direction; 9 cm in y-direction

(The inter-element spacing were found to produce the best beam pattern after some

testing)

• Elements amplitude excitation = 1

MATLAB simulations were performance and the results achieved were tabulated in

Table 6.8.

Figure 6.4j and Figure 6.4k illustrated the radiation patterns for planar arrays with

different phase excitations using the E-plane (φ = 0°) and H-plane (φ = 90°).

Appendix A provides the MATLAB code for this simulation.


69

βx

(degree)

βy

(degree)

Amplitude of main beam

(decibels)

Sidelobe level

(decibels)

Main beam angle

(degree)

E-plane (φφ = 0°° )

0 0 12.04 -20.72 0

0 45 11.36 -20.73 0

0 90 9.03 -20.73 0

0 135 3.70 -20.77 0

0 180 Amplitude values are too small

45 45 11.19 -10.48 -10

90 45 10.69 -6.27 -20

135 45 9.83 -2.98 -30

H-plane (φφ = 90°° )

0 0 12.04 -25.39 0

0 45 11.15 -14.70 -9

0 90 11.23 -8.61 -17

0 135 10.14 -4.01 -25

45 45 11.15 -14.70 -9

90 45 8.83 -14.70 -9

135 45 3.49 -14.70 -9

180 45 Amplitude values are too small

Table 6.8


70

Radiation plots in E-plane (φ = 0°):

Figure 6.4j Radiation plots of an planar array in E-plane

(i) βx = 0°; βy = 0° (ii) βx = 0°; βy = 45°

(iii) βx = 45°; βy = 45° (iv) βx = 135°; βy = 45°


71

Polar plots in H-plane (φ = 90°):

Figure 6.4k Radiation plots of a planar array in H-plane

(i) βx = 0°; βy = 0° (ii) βx = 0°; βy = 45°

(iii) βx = 45°; βy = 45° (iv) βx = 90°; βy = 45°


72

6.5 Discussion

After the dimension of microstrip patch antenna was determined, it was employed in the

linear and planar arrays for our simulations.

(i) Linear Array

It was observed that an increase in inter-element spacing in a linear array would result

in higher directivity and a smaller 3dB beamwidth. Although this is a favorable

condition, but it was found that the number of undesirable sidelobes also increases with

increasing inter-element spading. It was also proven that an inter-element spacing of full

wavelength would cause the radiation pattern to have grating lobes and this could be

seen from Figure 6.3b.

Simulations results obtained had also proved that an increase in the number of elements

in a linear array would result in higher directivity and a smaller 3dB beamwidth, but

more sidelobes. However, on the other hand, non-uniform amplitude distribution

(Chebyshev and Taylor) linear array had shown expected results of lower sidelobes

level and a bigger 3dB beamwidth with lower directivity compared to uniform

amplitude distribution array. Lastly, the main beam was found to have the steering

capability as the phase excitation was varied with a suitable amplitude distribution and

inter-element spacing. This could be seen form Figure 6.3h, 6.3i, and 6.3j that the beam

rotated in the anti-clockwise direction as the phase excitation increases.

(ii) Planar Array

The element polarization was assumed to be in x-direction and it was found from the

simulation results that an increase of inter-element spacing in the x-direction would

produce a more focus main beam, but more sidelobes were generated. On the other

hand, it was found that the inter-element spacing in y–direction was directly

proportional to the directivity. Decreasing the inter-element spacing in the y-direction

would thus, cause a drop in directivity.


73

PCAAD simulations also showed that an increase in the number of elements in a planar

array would contribute to a more concentrated main beam with higher directivity, but at

the expense of generating more sidelobes. Therefore, there is always a compromise

between directivity and antenna size. Non-uniform amplitude distributions planar array

had confirmed that they would have a lower sidelobes level compare to uniform

amplitude array. Similar results were yield for linear array.

Finally, the overall radiation pattern, which is formed by combining the radiation

pattern of a single microstrip patch antenna and the array factor of the planar array, was

found to have the capability of beam steering when the phase excitation of βx was

varied in E-plane. This was due to the fact that it was in the x-z plane (E-plane). There

were only slight changes in the main beam amplitude but a significant change in

sidelobes level when βx changes. Variation in βy was found only to have effect on the

amplitude of the main beam.

However, when the patterns were plotted in H-plane, all conditions were found to have

an inverse effect. βy was in control of the main beam steering and would also caused

changes in the sidelobes level. Thus, variation in βx was discovered having the ability to

change the amplitude of the pattern as expected.

Smart Antenna for Wireless Applications Chapter 7: Antenna Synthesis Investigation

74

Chapter 7

Antenna Synthesis Investigation


Chapter 2 had covered the theory on antenna synthesis. In addition, it is important to

analyze the radiation patterns by using different systematic methods that may arrive at

an antenna configuration which will produce an acceptable approximates desired

pattern.

The two techniques, Woodward-Lawson Sampling Method and Dolph-Chebyshev

Method, which had been previously discussed, will be investigated in this chapter.

Firstly, the chapter will be covering on the Woodward-Lawson method. Simulations

will be carried out by varying the number of elements for synthesis on a sectored pattern

of a linear array. Following that, we will look into the area whereby the inter-element

spacing is varied for an 8 and 16 element linear array synthesizing.

The next section will be examining on the Dolph-Chebyshev method where all

observation is analyzed, in the event of changes in the number of elements or sidelobes

level for a linear array. Further investigation is performed by varying the inter-element

spacing for an 8 and 16 elements linear array. Finally, the chapter will conclude with

some discussions on the results achieved.


75

7.2 Woodward-Lawson Synthesis

This section explores the Woodward-Lawson method on linear array. The first part will

be analyzing the performance caused by variation in number of elements for synthesis

of a sectored pattern of a linear array while the next part will the analysis of varying

inter-element spacing for synthesizing an 8 and 20 element linear array.


The sector pattern will be defined as a 0dB between the angle of -30° and 30° with –

60dB elsewhere.


• Frequency = 2GHz

• Inter-element spacing = 0.5λ

Syntheses were carried out using PCAAD and the results achieved were tabulated in

Table 7.1.

Figure 7.2a illustrated the radiation patterns for 8 elements linear array.

A MATLAB code was also written to design a radiation pattern for 10 elements

uniform linear array for inter-element spacing of ½ wavelength. Refer to Appendix B

for the MATLAB code. Figure 7.2b illustrated the radiation pattern for this design.


76

Number of

elements

3dB Beamwidth

(degree)

Sidelobe level

(decibels)

Ripple, R

(decibels)

Transition width, T

(degree)

4 41.77 No sidelobes No ripple 46.8

8 50.17 -28.4 0.2 22.0

12 53.31 -29.6 0.3 14.8

16 54.93 -29.8 0.3 10.9

20 55.96 -30.0 0.3 8.7

40 57.96 -30.3 0.2 5.4

80 58.75 -45.5 0.2 2.4

160 59.04 -56.3 0.2 1.4

Table 7.1

Figure 7.2a Radiation pattern for 8 elements linear array

Figure 7.2b Radiation pattern for 10 element uniform linear array of ½ wavelength inter-element spacing


77


The inter-element spacing will be varied for synthesizing the 8 elements and 16

elements linear array. The radiation will be defined as 0dB at the angle of 0° for the

desired main beam and –60dB elsewhere. The frequency used will be 2GHz and the

wavelength is 15cm, which are the same for all other simulations that had been

performed.

Syntheses were carried out using PCAAD and the results achieved were tabulated in

Table 7.2.

Number of

elements

Inter-element spacing

(cm)

Sidelobe level

(decibels)

3dB Beamwidth

(degree)

Remarks

8 0.125λ No Sidelobe 52.9 -

8 0.25λ -12.8 25.73 2 sidelobes

8 0.375λ -12.9 17.04 4 sidelobes

8 0.5λ -12.8 12.74 6 sidelobes

8 0.625λ -12.9 10.2 8 sidelobes

8 0.75λ -12.9 8.46 10 sidelobes

8 0.875λ -12.9 7.21 12 sidelobes

8 λ - - Grating lobes occurs at

90° and -90°

16 0.125λ -13.2 25.59 2 sidelobes

16 0.25λ -13.2 12.68 6 sidelobes

16 0.375λ -13.2 8.42 10 sidelobes

16 0.5λ -13.3 6.29 14 sidelobes

16 0.625λ -13.3 4.95 18 sidelobes

16 0.75λ -13.2 4.17 22 sidelobes

16 0.875λ -13.2 3.5 26 sidelobes

16 λ -13.3 2.96 Grating lobes occurs at

90° and -90°

Table 7.2


78

Figure 7.2c and Figure 7.2d illustrated the radiation patterns of an 8 elements linear

array for an inter-element spacing of 0.25λ and 0.75λ respectively.

Figure 7.2c Radiation patterns of an 8 elements linear array for an inter-element spacing of 0.25λλ

Figure 7.2d Radiation patterns of an 8 elements linear array for an inter-element spacing of 0.75λλ


79

Figure 7.2e and Figure 7.2f displayed the radiation patterns of a 16 elements linear array

for an inter-element spacing of 0.25λ and 0.75λ respectively.

Figure 7.2f Radiation patterns of an 16 elements linear array for an inter-element spacing of 0.75λλ

Figure 7.2e Radiation patterns of an 16 elements linear array for an inter-element spacing of 0.25λλ


80

7.3 Dolph-Chebyshev Synthesis

This section studies the Dolph-Chebyshev method on linear array. Investigations are

carried out by varying the number of elements in the array and the sidelobe level of an 8

element linear array. Further observations are monitored by varying the inter-element

spacing of an 8 and 16 elements linear array.


The following assumptions are made for the investigation:

• Normalized inter-element spacing = 0.5

• Sidelobe level = 20dB

Syntheses were carried out using the MATLAB program. Appendix C provides the

MATLAB code for synthesis of N element linear array (2 ≤N ≤ 10) using the Dolph-

Chebyshev method. All results achieved were tabulated in Table 7.3. In addition, the

results obtained were compared with the Ensemble 5.1 program, which yields similar

details.

Number of elements

3 dB Beamwidth (degree)

Remarks

2 59.9° Main beam with no sidelobe

4 30.0° 2 sidelobes appear 6 20.0° 4 sidelobes appear 8 14.5° 6 sidelobes appear 10 11.0° 8 sidelobes appear 16 6.8° 14 sidelobes appear 22 5.0° 20 sidelobes appear 28 4.0° 26 sidelobes appear 34 3.0° 32 sidelobes appear 40 2.6° 38 sidelobes appear

Table 7.3


81

Using the Dolph-Chebyshev method, Figure 7.3a was generated and displayed the

radiation patterns for the 10 elements linear array. Figure 7.3a(i) illustrated the plot

generated from MATLAB while Figure 7.3a(ii) displayed one that was from Ensemble.

Both yielded the same results.

Figure 7.3a

150 100 50 0

0

-20

-30

-10

-40

(i) Radiation pattern for 10 elements array using MATLAB

(ii) Radiation pattern for 10 elements array using Ensemble


82

7.3.2 Effect of Varying Sidelobe Level

The following assumptions are made for the synthesis:

• Normalized inter-element spacing = 0.5


In this section, syntheses were also carried out using the MATLAB program and all

results achieved were compared with the Ensemble program. Likewise, both programs

generated similar results and the data obtained was tabulated in Table 7.4.

Sidelobe level (dB)


Remarks

5 10.0° 6 sidelobes appear 10 11.5° 6 sidelobes appear 15 12.0° 6 sidelobes appear 20 14.5° 6 sidelobes appear 25 15.5° 6 sidelobes appear 30 16.5° 6 sidelobes appear 40 18.0° 6 sidelobes appear 50 19.5° 6 sidelobes appear 60 20.1° 6 sidelobes appear 80 21.8° 6 sidelobes appear

Figure 7.3b was generated and displayed the radiation patterns for the 8 elements linear

array with a 25dB sidelobe level. Figure 7.3b(i) illustrated the plot generated from

MATLAB while Figure 7.3b(ii) displayed the radiation pattern generated by Ensemble.

Table 7.4


83

150 100 50 0

0

-20

-30

-10

-40

Figure 7.3b

(ii) Radiation pattern for 8 elements array with 25dB sidelobe level using Ensemble

(i) Radiation pattern for 8 elements array with 25dB sidelobe level using MATLAB


84


This section will be analyzing on the radiation pattern for various inter-element spacing

for 8 and 16 elements linear array.

First and foremost, the following assumption is made:

• Sidelobe level = 20dB

In addition to using the MATLAB program for all syntheses, Ensemble was also used to

verify the results achieved. Correspondingly, both programs produced comparable

results and the data obtained was tabulated in Table 7.5.

Number of elements

Inter-element spacing (Normalized)


Remarks

8 0.125 60.0° Main beam with no sidelobe

8 0.25 29.0° 4 sidelobes appear 8 0.375 19.0° 6 sidelobes appear 8 0.5 14.5° 6 sidelobes appear 8 0.625 11.5° 8 sidelobes appear 8 0.75 9.5° 10 sidelobes appear 8 0.825 8.0° 14 sidelobes appear 8 1 7.0° 2 grating lobes and

12 sidelobes appear 16 0.125 27.0° 4 sidelobes appear 16 0.25 13.5° 8 sidelobes appear 16 0.375 9.0° 12 sidelobes appear 16 0.5 6.8° 14 sidelobes appear 16 0.625 5.4° 18 sidelobes appear 16 0.75 4.5° 22 sidelobes appear 16 0.825 4.0° 26 sidelobes appear 16 1 3.2° 2 grating lobes and

28 sidelobes appear

Table 7.5


85

Figure 7.3c illustrated the radiation patterns for an 8 elements linear array with a

normalized inter-element spacing of 0.5. Figure 7.3c (i) displayed the linear plot

generated by MATLAB while Figure7.3c (ii) displayed the plot that was produced using

Ensemble.

150 100 50 0

0

-20

-30

-10

-40

(i) Radiation pattern for 8 element linear array with normalized inter-element spacing of 0.5 using MATLAB

(ii) Radiation pattern for 8 element linear array with normalized inter-element spacing of 0.5 using Ensemble

Figure 7.3c


86

Figure 7.3d illustrated the radiation patterns for 16 elements linear array with a

normalized inter-element spacing of 0.5. Figure 7.3d (i) displayed the linear plot

generated by MATLAB while Figure7.3d (ii) displayed the plot that was produced

using Ensemble.

150 100 50 0

0

-20

-30

-10

-40

(i) Radiation pattern for 16 element linear array with normalized inter-element spacing of 0.5 using MATLAB

(ii) Radiation pattern for 16 element linear array with normalized inter-element spacing of 0.5 using Ensemble

Figure 7.3d


87

7.4 Discussion

(i) Woodward-Lawson Method

Synthesis results proved that the ripple rate would be higher if there was an increase in

the number of elements in the linear array. It was also observed that the Woodward-

Lawson method had low sidelobes level, which is a positive sign for designers.

Although it could be seen that a very good transition width was achieved as the number

of elements in the array increases, but low beam ripple could also be obtained at some

sacrifice in transition width.

Furthermore, the investigated results illustrated that increment in the inter-element

spacing resulted in a desired smaller 3dB beamwidth but more sidelobes were

generated. However, the sidelobes level remained the same. Thus, this synthesis method

presented is most useful for shaping main beam of an antenna pattern as the sidelobe

level is at a satisfactory level.

(ii) Dolph-Chebyshev Method

The Dolph-Chebyshev method implemented showed that for a given sidelobe level, a

narrow 3dB beamwidth could be achieved by increasing the number of elements in the

array. Although the number of sidelobes increases with an increase in number of

elements, but the sidelobe level remained the same.

In addition, for a fix number of elements and inter-element spacing, it was found that

the 3dB beamwidth increases when the sidelobe level decreases but the number of

sidelobes did not change. Examining the tabulated results also illustrated that the 3dB

beamwidth decreases with an increasing inter-element spacing. However, the number of

sidelobes multiples. Grating lobes were also generated when an inter-element spacing

was equal to the wavelength. Last but not least, the result shows that this synthesis

technique can be applied for achieving a narrow beamwidth accompanied by low

sidelobes level.

Smart Antenna for Wireless Applications Chapter 8: Recursive Least Squares Algorithm Analysis

88

Chapter 8

Recursive Least Squares Algorithm

Analysis


After covering the basic concept of Recursive Least Squares algorithm in Chapter 4, the

objective of this chapter will be analyzing the radiation pattern of a uniform linear array

using the RLS approach. The MATLAB code for the RLS algorithm was formulated

and thus, compiling the codes on the computer will carry out the all the desired

simulations.

Refer to Appendix D for the MATLAB code.

8.2 Simulated Results

The following assumption are made for the simulations:

• Frequency = 2GHz

• Wavelength = 15cm

• Inter-element spacing = 7.5cm

• Forgetting factor = 0.95

• No noise in received data


89

The radiation patterns were presented in both linear and polar plots. Figure 8.2a

illustrated the patterns of a 4 element linear array at 0° and Figure 8.2b illustrated the

radiation pattern of a 4 element linear array at 45°.

Figure 8.2a Radiation pattern for 4 elements linear array at 0°°

(ii) Polar plot

(i) Linear plot


90

Figure 8.2b Radiation pattern for 4 element linear array at 45°°

(ii) Polar plot

(i) Linear plot


91

8.3 Discussion

Compiling the MATLAB code on Recursive Least Squares algorithm, the radiation

patterns of a 4 element linear array plotted were the consequences of the optimal weight

vector at the steady state multiply with the steering vector from the range of -90° to 90°.

Regardless of numerous signal sources, only the optimal weight vector obtained

provided the maximal radiation pattern for each individual desired signal source at the

desired angle.

Nevertheless, the simulations performed were based on a known steering direction

whereby an angle for the signal source was designated. The radiation patterns plotted

were at 0° and 45°. However, it must be noted that there may be some mismatch in the

time-variable signal environment as it requires to track the direction of the signal

source. Nevertheless, although the RLS algorithm was found to have a faster

convergence speed, but there is a greater computation complexity as shown in the

MATLAB code provided in Appendix D.

Smart Antenna for Wireless Applications Chapter 9: Conclusion and Future Developments

92

Chapter 9

Conclusion and Future Developments

9.1 Conclusion

This thesis had provided an introduction to basic antenna theory and a sound description

on the types of antennas that we would be using. Although the aim of thesis is the study

on smart antenna system, but the fundament antenna concept and the parameters of

antenna were examined. Thus, this had led to a better understanding on antennas.

Upon having a valuable knowledge on antenna, a detailed description on smart antenna

system was presented. That includes the benefits of smart antenna system, the

switching-beam array and adaptive array approaches, beam forming and the recursive

least squares algorithm.

In addition, the range of frequencies available for wireless communication technologies

can be utilized in various ways/schemes. Thus, the multiple access schemes, which

consist of the FDMA, TDMA, CDMA and SDMA, were introduced. It was also

discussed how channel capacity in wireless communication could be increased through

SDMA.

We had also investigated on the radiation pattern and performance of array antennas.

From the results of the simulations, it was seen that radiation patterns were related to

the number of elements in the array, the inter-element spacing, amplitude distribution

and the phase excitation. Thus, there is always a compromise between the influencing

parameters.

Smart Antenna for Wireless Applications Chapter 9: Conclusion and Future Developments

93

The next section had examined on antenna synthesis where investigations were carried

out using the Woodward-Lawson and Dolph-Chebyshev method. It was concluded that

different synthesis methods would have to be applied in order to yield different desired

radiation pattern. However, it was also possible for different methods to be integrated

together, thus forming an optimal desired pattern. Last but not least, an adaptive

algorithm known as the Recursive Least Squares algorithm was analyzed and had

shown that a smooth estimation optimal response could be obtained.

In conclusion, this thesis had met the objective of studying and analyzing on the

performance of the smart antenna system. It had also provided a sense of achievement

as significant amount of work had been accomplished. However, there are still other

important areas that require further work and they will be illustrated in the last section.

9.2 Future Developments

Although this thesis had provided significant study on the smart antenna system for the

wireless communication environment, but there are still other equally important areas

that require our attention. They include analysis on circular array in addition to an in-

depth investigation on planar array.

Further research can also be done on different methods of antenna synthesis as this

thesis had covered only the Woodward-Lawson and Dolph-Chebyshev methods. The

other techniques include the Schelkunoff Polynomial Method, Fourier Transform

Method and Taylor Line-Source (One-Parameter).

The implementation of the complex smart antenna system requires adaptive algorithms

for estimation of the optimal response and reducing the effects of noise in the time-

variable environment. Although recent evolution had made it feasible, there is always a

challenge to improve these algorithms for faster and more complex processing as the

world enters into the future of a wireless dimension.

References

1. K.F. Lee: “Principles of Antenna Theory,” John Wiley & Sons, New York,

1984.

2. G.T. Okamato: “Smart Antenna Systems and Wireless LANs,” Kluwer

Academic, Massachusettes, 1999.

3. C.A. Balanis: “Antenna Theory,” John Wiley & Sons, New York, 1997.

4. W.S. Strutzman and G.A. Thiele: “Antenna Theory and Design,” John Wiley &

Sons, New York, 1981.

5. M.T. Ma: “Theory and Application of Antenna Arrays,” John wiley & Sons,

New York, 1974.

6. T. Macnamara: “Handbook of Antennas for EMC,” Artech House, London,

1995.

7. P.H. Lehne and M. Pettersen, “An Overview of Smart Antenna Technology for

Mobil Communications System,” Surveys,

http://www.comsoc.org/pubs/surveys/4q99issue/lehne.html

8. J.C. Liberti Jr. and T.S. Rappaport: “Smart Antennas for Wireless

Communications: IS-95 and Third Generation CDMA Applications,” Prentice

Hall, Upper Saddle River, New Jersey, 1999.

9. I.E. Sutherland et al., “Experimental Evaluation of Smart Antenna System

Performance for Wireless Communications,” IEEE Transactions on Antennas

and Propagation, Vol. 46, No. 6, Jun. 1998, pp. 794-757.

10. L.C. Godara, “Applications of Antenna Arrays to Mobile Communication, Part

I: Performance, Improvement, Feasibility and Systems Considerations,”

Proceedings of the IEEE, Vol. 85, No. 7, Jul. 1997, pp. 1029-1060.

11. S. Sampei: “Applications of Digital Wireless Technologies to Global Wireless

Communications,” Prentice Hall, Upper Saddle River, New Jersey, 1997.

12. R. Prasad: “CDMA for Wireless Personal Communications,” Artech House,

Boston, 1996.

13. T.S. Rappaport: “Wireless Communications: Principles & Practice,” Prentice

Hall, Upper Saddle River, New Jersey, 1996.

14. S.Haykin: “Adaptive Filter Theory,” Prentice Hall, New Jersey, 1991.

Appendix A

% Planar Array teta = -90:1:90; theta = teta*pi/180; ph = 0; % E-plane, phi = 90 for H-plane phi = ph*pi/180; % Convert to radian bx = 0; % Phase shift in x-direction by = 0; % Phase shift in y-direction beta_x = (bx/180)*pi; % Convert to radian beta_y = (by/180)*pi; % Convert to radian x = 8.3; % Inter-element spacing in x-direction y = 9; % Inter-element spacing in y-direction k = (2*pi)/(3e10/2e9); % Wave number % Progreesive phase value in x-direction phix = k*x*sin(theta).*cos(phi) + beta_x; % Progreesive phase value in y-direction phiy = k*y*sin(theta).*sin(phi) + beta_y; ix1 = 1; % Excitation of each element ix2 = 1; iy1 = 1; iy2 = 1; % Array factor of array in the x-direction Sx = ix1+ix2*exp(j*phix); % Array factor of array in the y-direction Sy = iy1+iy2*exp(j*phiy); load A:\eplane.dat % load data of single element Edb = eplane(:,2); E = 10.^(Edb/20); % Covert to ratio subplot(2,2,1); % Define plot area % Plot radiation pattern of a Single microstrip element h = polar(theta',abs(E)); set(h,'color','red'); h = ylabel('Single Element'); set(h,'color','red');

subplot(2,2,2); % Define plot area AF = abs(Sx.*Sy); % Array factor of planar array % Plot radiation pattern of array factor of planar array h1 = polar(theta,AF); set(h1,'color','magenta'); h1 = ylabel('Array Factor'); set(h1,'color','magenta'); subplot(2,2,3); % Define plot area overall = abs(AF'.*E); % Pattern multiplication % Plot overall radiation pattern of planar array h2 = polar(theta',overall); set(h2,'color','blue'); h2 = ylabel('Overall pattern'); set(h2,'color','blue'); subplot(2,2,4); % Define plot area range_x = pi*(90/pi); range_x1 = -pi*(90/pi); theta = linspace(range_x1,range_x,181); h3 = plot(theta',overall); % Plot in rectangular pattern % Initialize y-axis for linear plot x_axis = pi*(90/pi); % Initialize y-axis for linear plot x_axis1 = -pi*(90/pi); axis([x_axis1 x_axis exp(-4) 5]); % Plot linear pattern set(h3,'color','green'); h3 = ylabel('Linear Plot'); set(h3,'color','green'); grid;

Appendix B

%This program uses the Woodward-Lawson synthesis, to design a %radiation pattern for a 10 elements uniform linear %array with an element spacing of one half the wavelength. t = 0:1:180; theta = t*pi/180; p5m = 1; n5m = -1; %cos(theta-m) p4m = 0.8; n4m = -0.8; p3m = 0.6; n3m = -0.6; p2m = 0.4; n2m = -0.4; p1m = 0.2; n1m = -0.2; p0m = 0; b5m = 0; nb5m = 0; %Excitation at the sample points b4m = 0; nb4m = 0; b3m = 1; nb3m = 1; b2m = 1; nb2m = 1; b1m = 1; nb1m = 1; b0m = 1; a5 = cos(theta) - p5m; %Pattern of each composing function AF5 = ((sin(5.*pi.*a5))./(sin((pi.*a5)./2)).*b5m)./10; a4 = cos(theta) - p4m; AF4 = ((sin(5.*pi.*a4))./(sin((pi.*a4)./2)).*b4m)./10; a3 = cos(theta) - p3m; AF3 = ((sin(5.*pi.*a3))./(sin((pi.*a3)./2)).*b3m)./10; a2 = cos(theta) - p2m; AF1 = ((sin(5.*pi.*a2))./(sin((pi.*a2)./2)).*b2m)./10; a1 = cos(theta) - p1m; AF2 = ((sin(5.*pi.*a1))./(sin((pi.*a1)./2)).*b1m)./10; a0 = cos(theta) - p0m; AF0 = ((sin(5.*pi.*a0))./(sin((pi.*a0)./2)).*b0m)./10; an1 = cos(theta) - n1m; AFn1 = ((sin(5.*pi.*an1))./(sin((pi.*an1)./2)).*nb1m)./10; an2 = cos(theta) - n2m; AFn2 = ((sin(5.*pi.*an2))./(sin((pi.*an2)./2)).*nb2m)./10;

an3 = cos(theta) - n3m; AFn3 = ((sin(5.*pi.*an3))./(sin((pi.*an3)./2)).*nb3m)./10; an4 = cos(theta) - n4m; AFn4 = ((sin(5.*pi.*an4))./(sin((pi.*an4)./2)).*nb4m)./10; an5 = cos(theta) - n5m; AFn5 = ((sin(5.*pi.*an5))./(sin((pi.*an5)./2)).*nb5m)./10; %Summation of composing functions total = AF5 + AF4 + AF3 + AF2 + AF1 + AF0 + AFn1 + AFn2 + AFn3 + AFn4 + AFn5; tot = abs(total); polar(theta,tot);%Plot polar pattern pause plot(t,tot); %Plot linear pattern xlabel('Theta (Degrees)'); ylabel('Normalized Magnitude'); grid;

Appendix C

clc; % Clear screen clear; % Clear all variables % Prompt user for number of elements in an array. disp(' ') disp('Please enter the number of elements in the array.') disp(' ') disp('Assuming that the array has at least 2 elements') disp('but not more than 10 elements.') disp(' ') N = input(['Number of elements in the array = ']); % Prompt user for the required Side Lobe Level. clc; disp(' ') disp('Please enter the required side lobe level in decibels.') disp(' ') SLL = input(['Side lobe level(dB) = ']); R = 10^(SLL/20); % Convert to ratio Zo = cosh((1/(N-1))*acosh(R)); % Determine Zo % Prompt user for the Normalised Inter-element Spacing. clc; disp(' ') disp('Please enter one of the following inter-element spacing (Normalised).') disp(' ') disp('Press "a" for 1/4 wavelength.') disp('Press "b" for 1/2 wavelength.') disp('Press "c" for 3/4 wavelength.') disp('Press "d" for full wavelength.') disp(' ') a=0.25; b=0.5; c=0.75; d=1; spacing = input(['Inter-element spacing (Normalised) = ']); t = 0:1:179; theta = t*pi/180; % Convert to radian u = pi*spacing*cos(theta); clc; disp(' ')

disp(['Number of elements = ' num2str(N)]) disp(['Side lobe level = ' num2str(SLL) ' dB']) disp(['Inter-element spacing (Normalised) = ' num2str(spacing)]) if N<=10 if N == 2; AFp = [1]; % Polynomial of excitation coefficient AFc = [1*Zo]; % Chebyshev polynomial X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(1,1); % Normalized with respect to the amplitude % of the elements at the edge AF = abs(Xo(1,1)*cos(u)); % Determine the array factor subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); % Setting maximum value of the % array factor to "max" AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta; subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum %values for X and Y scales grid % Turn grid on elseif N == 3; AFp = [0,2; 1,-1]; % Polynomial of excitation coefficient AFc = [2*Zo^2; % Chebyshev polynomial -1]; X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(2,1); % Normalized with respect to the amplitude % of the elements at the edge % Determine the array factor AF = abs(Xo(1,1)+Xo(2,1)*cos(2*u));

subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); % Setting maximum value of the % array factor to "max" AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta; subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum % values for X and Y scales grid % Turn grid on elseif N==4; AFp = [0,4; 1,-3]; % Polynomial of excitation coefficient AFc = [4*Zo^3; -3*Zo]; % Chebyshev polynomial X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(2,1); % Normalized with respect to the % amplitude of the elements at the edge % Determine the array factor AF = abs(Xo(1,1)*cos(u)+Xo(2,1)*cos(3*u)); subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); % Setting maximum value of the % array factor to "max" AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta; subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum % values for X and Y scales grid % Turn grid on elseif N == 5; AFp = [0,0,8; 0,2,-8; 1,-1,1]; % Polynomial of excitation coefficient

AFc = [8*Zo^4; -8*Zo^2; 1]; % Chebyshev polynomial X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(3,1); % Normalized with respect to the % amplitude of the elements at the edge % Determine the array factor AF = abs(Xo(1,1)+Xo(2,1)*cos(2*u)+Xo(3,1)*cos(4*u)); subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); % Setting maximum value of the % array factor to "max" AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta; subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum % values for X and Y scales grid % Turn grid on elseif N==6; AFp = [0,0,16; 0,4,-20; 1,-3,5,]; % Polynomial of excitation coefficient AFc = [16*Zo^5; -20*Zo^3; 5*Zo]; % Chebyshev polynomial X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(3,1); % Normalized with respect to the % amplitude of the elements at the edge % Determine the array factor AF = abs(Xo(1,1)*cos(u)+Xo(2,1)*cos(3*u)+Xo(3,1)*cos(5*u)); subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); % Setting maximum value of the % array factor to "max" AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta;

subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum % values for X and Y scales grid % Turn grid on elseif N == 7; AFp = [0,0,0,32; 0,0,8,-48; 0,2,-8,18 1,-1,1,-1]; % Polynomial of excitation coefficient AFc = [32*Zo^6; -48*Zo^4; 18*Zo^2; -1]; % Chebyshev polynomial X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(4,1); % Normalized with respect to the % amplitude of the elements at the edge % Determine the array factor AF = abs(Xo(1,1)+Xo(2,1)*cos(2*u)+Xo(3,1)*cos(4*u)+Xo(4,1)*cos(6*u)); subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); %Setting maximum value of the % array factor to "max" AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta; subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum % values for X and Y scales grid % Turn grid on elseif N==8; AFp = [0,0,0,64; 0,0,16,-112; 0,4,-20,56; 1,-3,5,-7,]; % Polynomial of excitation coefficient

AFc = [64*Zo^7; -112*Zo^5; 56*Zo^3; -7*Zo]; % Chebyshev polynomial X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(4,1); % Normalized with respect to the % amplitude of the elements at the edge % Determine the array factor AF = abs(Xo(1,1)*cos(u)+Xo(2,1)*cos(3*u)+Xo(3,1)*cos(5*u)+Xo(4,1)*cos(7*u)); subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); % Setting maximum value of the % array factor to "max" AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta; subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum % values for X and Y scales grid % Turn grid on elseif N == 9; AFp = [0,0,0,0,128; 0,0,0,32,-256; 0,0,8,-48,160; 0,2,-8,18,-32; 1,-1,1,-1,1]; % Polynomial of excitation coefficient AFc = [128*Zo^8; -256*Zo^6; 160*Zo^4; -32*Zo^2; 1]; % Chebyshev polynomial X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(5,1); % Normalized with respect to the % amplitude of the elements at the edge

% Determine the array factor AF = abs(Xo(1,1)+Xo(2,1)*cos(2*u)+Xo(3,1)*cos(4*u)+Xo(4,1)*cos(6*u)+Xo(5,1)*cos(8*u)); subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); % Setting maximum value of the % array factor to "max" AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta; subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum % values for X and Y scales grid % Turn grid on elseif N==10; AFp = [0,0,0,0,256; 0,0,0,64,-576; 0,0,16,-112,432; 0,4,-20,56,-120; 1,-3,5,-7,9]; % Polynomial of excitation coefficient AFc = [256*Zo^9; -576*Zo^7; 432*Zo^5; -120*Zo^3; 9*Zo]; % Chebyshev polynomial X = AFp\AFc; % Determine the excitation coefficient Xo = X/X(5,1); % Normalized with respect to the % amplitude of the elements at the edge % Determine the array factor AF = abs(Xo(1,1)*cos(u)+Xo(2,1)*cos(3*u)+Xo(3,1)*cos(5*u)+Xo(4,1)*cos(7*u)+Xo(5,1)*cos(9*u)); subplot(2,2,1); polar(theta,AF); % Generate polar plot AF1=20*log10(AF); % Convert to decibels max=max(AF1); % Setting maximum value of the % array factor to "max"

AF2=AF1-max; % Set values of array factor % with respect to maximum value theta1=(180/pi)*theta; subplot(2,2,2); plot(theta1,AF2); % Generate linear plot axis([0 180 -40 0]); % Set maximum and minimum values %for X and Y scales grid % Turn grid on end else disp(' ') disp(' ') disp(' ') disp(' ') disp(' ') disp(' ') disp(' ') disp(' ') disp(' ') disp(' ') disp('Invalid value !!!') disp(' ') disp('Press any key to exit........') pause end

Appendix D

%Number of element M = input(['Number of elements in array : ']); %Direction of desired signal a = input(['Steering angle in degrees : ']); x = a*pi/180; %Convert to radian % initializing the algorithm I = eye(M); %M X M identity matrix delta = 1e-6; %Small positive constant P0 = inv(delta)*I; %Initialize the algorithm w0 = (linspace(0,0,M))'; %Initial weight vector for n = 1:100 %Number of iterations B = steeringv(M,x); %Steering vector X = B'*n; wq = B'; dn = conj(wq)'*X; %Desired response vector un = X; %Input data vector forget = 0.95; %Forgetting factor pin = un'*P0; %Calculate pi(n) kn = forget + (pin*un); %Calculate k(n) Kn = (P0*un)/(kn); %Calculate K(n) an = dn - (conj(w0)'*un); %Calculate alpha(n) wn = w0 + (Kn*conj(an)); %Calculate w(n) Pn = (1/forget)*[P0 - [P0*un*un'*P0]/kn];%Calculate P(n) P0 = Pn; w0 = wn; end for ang = -90:1:90 %linear plot n = 91 + ang; angl(n) = ang; x = ang*pi/180; A = steeringv(M,x); out = (w0'*A'); %Multiply with steering vector output(n) = abs(out); output1 = output/max(output); %Normalize to unity xlabel('Angle in degree'); ylabel('Normalize array gain') plot(angl,output1); %Plot linear pattern axis tight;

xlabel('Angle (Degrees)'); ylabel('Normalized Array Gain (Ratio)'); grid; end pause ang = -90:1:90; y = ang*pi/180; polar(y,output1); %polar plot function S = steeringv(M,x); %define steering vector %free space wavelength of 15cm at resonant freq of 2GHz lamda = 0.15; d = lamda/2; %inter-element spacing K = 1:M; %x is DOA of the received signal S = exp((-2*pi*j*(K-1)*d*sin(x))/lamda);

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