DESIGN AND ANALYSIS OF LARGE-SCALE ANTENNA ARRAYS FOR MASSIVE MIMO

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DESIGN AND ANALYSIS OF LARGE-SCALE ANTENNA ARRAYS FOR MASSIVE MIMO

APPLICATION

BY

NAIMUL MUKIT

A dissertation submitted in fulfilment of the requirement for the degree of Master of Science (Computer and Information

Engineering)

Kulliyyah of Engineering

International Islamic University Malaysia

APRIL 2019

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ii

ABSTRACT

Large-scale antenna arrays have a variety of applications including massive MIMO application for 5G technology. It offers high array and multiplexing gains which provide higher directivity that enhances the performance of link reliability and data rate. This thesis presents the design and analysis of large-scale antenna arrays. This project implements a simple and efficient technique of using sub-arrays for the development of large uniform arrays. Large arrays can be formed by repeating a small sub-arrays throughout the space of the large array. The use of sub-arrays simplifies the large array design by allowing the designer to concentrate on the smaller sub-array before constructing larger arrays. Thus, the performance and radiation characteristics of large arrays can be predicted through the investigation of sub-arrays. For this research, the array-factor for a planar and circular sub-array of 2x2 (4 elements) are analysed using MATLAB software and then large arrays are constructed by placing the 2x2 sub-array in a rectangular configurations to form 2x4 (8 elements), 4x4 (16 elements), 4x8 (32 elements) and up to 8x8 (64 elements) planar and circular arrays.

Thus, the array-factors, gains, directivities, 3dB HPBWs, number of side lobes and side lobe level of the constructed large arrays has been analysed and compared with the small sub-array. The results are utilized to develop a model of modular large array configuration. Computer Simulation Technology (CST) was used to simulate a similar patch antenna arrays for validation. Gains are found higher for both planar and circular array in simulation than calculation. Number of side lobes are also reduced significantly in simulation results. Performance of regular circular array is found better than planar array. A new concept with sub-array based circular array is introduced which showed better performance than regular circular array. Sub-array based circular array provides 3 dB higher gain than 16 elements regular circular array, while it is 6.5 dB higher than 4x4 planar array. Hence developing a large circular array using sub-array is proved practical and more likely suitable for massive MIMO applications.

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iii

ثحبلا ةصلاخ

لا تافوفصم تايئاوهلا

ةريبك قاطنلا اهيدل ةعومجم ةعونتم

نم تاقيبطتلا امب

يف كلذ ينقت ة

MIMO مخضلا

يذلا ربتعي نم تاينقتلا همهملا

لأ ةمظن ليجلا سماخلا

. 5G وهف رفوي

اًبسكم اًيلاع هفوفصمل لاسرلإا

ددعتملا امم

رفوي إ ةيهاجت ىلعأ لمعت ىلع زيزعت دلأا ءا نم ثيح

ةيقوثوم ا

لإ طابتر لدعمو تانايبلا

. مدقي هذه ثحبلا ميمصت ليلحتو ملا

تافوفص تايئاوهلا

ةريبك

قاطنلا . قبطي اذه عورشملا ةينقت

ةطيسب ةلاعفو لإ مادختس تافوفصملا

ةيعرفلا ريوطتل

فئافص

ةدحوم ةريبك

. نكمي ليكشت فئافص ةريبك

راركتب فيفص

يعرف ريغص يف ةيقب ةعومجملا

ةريبكلا . يدؤي إ مادختس تافوفصملا

ةيعرفلا ىلإ

طيسبت ميمصت فيفصلا

ريبكلا نع قيرط

حامسلا ممصملل

زيكرتلاب ىلع

ةفوفصملا ةيعرفلا

رغصلأا لبق

ءاشنإ فئافص . ربكأ

يلاتلابو

،

نكمي عقوت صئاصخ ءادلأا

عاعشلإاو نم

فئافصلا ةريبكلا

نم للاخ قيقحتلا و

إ فاشكتس ءادأ

تافوفصملا فلا

. ةيعر ةبسنلاب اذهل

ثحبلا

، مت ليلحت لماع ةفوفصملا ةفوفصملل

ةيعرفلا

هيوتسملا ةيرئادلاو

رصانعل

× 2 ) 2 وأ ( 4 مادختساب جمانرب

MATLAB مث

مت ءاشنإ فئافص

ةريبك نع قيرط عضو ةفوفصملا ةيعرفلا

× 2 2 يف تانيوكت ةليطتسم

ليكشتل

× 2 4 وأ ) 8

رصانع

، (

× 4 4 وأ ) ا ًرصنع 61

، (

× 4 8 وأ ) ا ًرصنع 22 امو (

لصي ىلإ

× 8 8 وأ ) 14

ا ًرصنع اًيوتسم (

تافوفصمو ةيرئاد

. يلاتلابو

، مت ليلحت لماوع ةفوفصملا

، بساكملاو

، و

لإا ةيهاجت

، و فصن ةوق ضرع عاعشلا

3dB دنع

، ددعو نم صوصفلا ةيبناجلا

ىوتسمو

صوصفلا ةيبناجلا

تافوفصملل ةريبكلا

ةينبملا هتنراقمو ا

عم ةفوفصملا ةيعرفلا

ةريغصلا .

مت

إ ادختس تم جئاتنلا ريوطتل جذومن

نم نيوكت ةعومجم ةريبك

مجحلا . مدختست ايجولونكت

ةاكاحملا

ةيبوساحلا (CST)

ةاكاحمل تافوفصم

ةلثامم يئاوهلل تبثتلل

نم اهتحص اهتيلعافو

. دجو نا يف

جئاتن ةاكاحملا بسك

ىلعأ لكل نم ةفوفصملا ةيوتسملا

لاو ةيرئاد نم جئاتن تاباسحلا .

كلذك دجو

نا ددع صوصفلا ةيبناجلا

صقانت لكشب ريبك يف جئاتن ةاكاحملا

ًًاضيا . دجو , نا ءادأ هفوفصملا

هيرئادلا ةيداعلا

لضفأ نم هفوفصملا ةيوتسملا

مت . ميدقت موهفم ديدج عم فيفص يرئاد

مئاق ىلع

فيفص يعرف

يذلاو رهظأ ءادأ لضفأ نم فيفصلا ادلا

يرئ يداعلا . رفوت فيفصلا يرئادلا

مئاقلا ىلع فيفص اًبسك يعرف

ىلعأ رادقمب 3dB نم 61 اًفيفص اًيرئاد اًمظتنم

، يف نيح هنأ

ىلعأ رادقمب dB 1.6

نم فيفصلا يوتسملا

4 × 4 نمو مث

، تبث نأ ريوطت ةفوفصم ةريبك

مادختساب فيفص

يوناث يلمع ةفوفصمو ةيرئاد

تاذ فيفص ةيعرف

حرتقم ة اًثيدح رثكأ ةمءلام

تاقيبطتل MIMO

ةمخضلا

.

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APPROVAL PAGE

I certify that I have supervised and read this study and that in my opinion, it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Master of Science (Computer and Information Engineering).

...

Md Rafiqul Islam Supervisor

...

Khaizuran Abdullah Co-Supervisor

...

Norun Farihah Abdul Malek Co-Supervisor

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Master of Science (Computer and Information Engineering).

...

Mohamed Hadi Habaebi Internal Examiner

...

Sarah Yasmin Bt. Mohamad Internal Examiner

This dissertation was submitted to the Department of Electrical and Computer Engineering and is accepted as a fulfilment of the requirement for the degree of Master of Science (Computer and Information Engineering).

...

Mohamed Hadi Habaebi

Head, Department of Electrical and Computer Engineering

This dissertation was submitted to the Kulliyyah of Engineering and is accepted as a fulfilment of the requirement for the degree of Master of Science (Computer and Information Engineering).

...

Ahmad Faris Ismail

Dean, Kulliyyah of Engineering

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DECLARATION

I hereby declare that this dissertation is the result of my own investigations, except where otherwise stated. I also declare that it has not been previously or concurrently submitted as a whole for any other degrees at IIUM or other institutions.

Naimul Mukit

Signature ... Date ...

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INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

DECLARATION OF COPYRIGHT AND AFFIRMATION OF FAIR USE OF UNPUBLISHED RESEARCH

DESIGN AND ANALYSIS OF LARGE-SCALE ANTENNA ARRAYS FOR MASSIVE MIMO APPLICATION

I declare that the copyright holders of this dissertation are jointly owned by the student and IIUM.

No part of this unpublished research may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without prior written permission of the copyright holder except as provided below

1. Any material contained in or derived from this unpublished research may be used by others in their writing with due acknowledgement.

2. IIUM or its library will have the right to make and transmit copies (print or electronic) for institutional and academic purposes.

3. The IIUM library will have the right to make, store in a retrieved system and supply copies of this unpublished research if requested by other universities and research libraries.

By signing this form, I acknowledged that I have read and understand the IIUM Intellectual Property Right and Commercialization policy.

Affirmed by Naimul Mukit

……..……….. ………..

Signature Date

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ACKNOWLEDGEMENTS

First and foremost I express my gratitude to Allah (SWT) for giving me the strength to complete the Master of Science thesis. This project helped me to build my research skills and it is a great experience for me.

It is my utmost pleasure to dedicate this work to my dear beloved parents, who granted me the gift of their unwavering belief in my ability to accomplish this goal:

thank you for your support and patience.

I would like to express my deepest gratitude to my respected supervisor Prof. Dr. Md.

Rafiqul Islam for his continuous support, useful critiques of this research work, great ideas, enthusiastic encouragement and patient guidance.

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LIST OF TABLES

Table 2.1 Comparison of Previous Work...23

Table 3.1 Comparison of Directivity, Gain, HPBW, Number of Sides Lobes and Side Lobe Level Variations (MATLAB) of Planar Arrays...32

Table 3.2 Comparison of Directivity, Gain, HPBW, Number of SidesLobes and Side Lobe Level Variations (MATLAB) of Circular Arrays...38

Table 4.1 TheValues of the Parameters Obtained in the Design (in mm)...46

Table 4.2 Comparison of Directivity, Realized Gain, 3dB Angular Width, Number of SidesLobes and Side Lobe Level Variations (CST) of Planar Array...53

Table 4.3 Comparison in Term of Directivity (d=0.7λ )... 55

Table 4.4 Comparison in Term of 2D Radiation Pattern(d= 0.7λ)... 55

Table 4.5 Comparison in Term of 2D Radiation Pattern (4 elements)...61

Table 4.6 Comparison of Directivity, Realized Gain, 3dB Angular Width, Number of Side Lobes and Side Lobe Level Variations (CST) of Circular Array...67

Table 4.7 Comparison in Term of Directivity for Circular Array...68

Table 4.8 Comparison in Term of 2D Radiation Pattern for Circular Array...69

Table 4.9 Comparison of Directivity, Realized Gain, 3dB Angular Width, Number of SidesLobes and Side Lobe Level Variations (CST)...72

Table 4.10 Comparison in Term of 2D Radiation Pattern...72

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LIST OF FIGURES

Figure 1.1 2x2 Planar Arrays Used in Mobile Handset 2

Figure 1.2 Flow-chart of Methodology 5

Figure 2.1 Linear Antenna Array of Isotropic Elements 9

Figure 2.2 Circular Array Geometry 10

Figure 2.3 Planar Array Geometry 10

Figure 2.4 3D Pattern of 5×5 Uniform Planar Array with dx=dy (a) λ/4 (b) λ/2 (c) λ 11

Figure 2.5 Array Synthesis when Using Sub-Array Concept 12

Figure 2.6 The Multiplication of Element Pattern, Sub-array Factor and Full-array Factor Produces the Final Array Factor 12

Figure 2.7 AEP Shaping Method 13

Figure 2.8 5×5 Small Sub-array to Build a 6×7 Element Large Planar Array 13 Figure 2.9 Two Finite 32-element Antenna Arrays: Dipoles (left) and Patches (right) 15

Figure 2.10 Maximal Gain Variation Between Two Elements in Terms of Direction of Incidence in the Azimuthal Plane of the 32-element Finite Array at 2.6GHz 15

Figure 2.11 S-parameter of the MIMO Antenna 16

Figure 2.12 Radiation Patterns of the MIMO Antenna 16

Figure 2.13 (a) Top View, (b) Side View or Layer Arrangement and of the Fabricated Prototype 17

Figure 2.14 Co-polarization Gain Patterns with Beam Steering Performance in θ=90º Cut Plane at 28 GHz 17

Figure 2.15 Optimized Coefficients Along the x-axis 18

Figure 2.16 Array Factor Patterns for Square Array Arrangements with d (a) 0.25 λ, (b) 0.5 λ and (c)0.6 λ 19

Figure 2.17 Simulated Return Loss of 56 Radiation Elements and 2× 2 MIMO Microstrip Antenna 20

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Figure 2.18 Relationship Between the Number of Outer Circular Array Elements and the Beamwidth (a) in the Horizontal Array

(b) in the Vertical Array 20

Figure 2.19 Radiation Patterns of E^tΔ 21

Figure 2.20 Radiation Patterns of E^tΩ 21

Figure 2.21 Simulated MIMO Full Antenna Array 22

Figure 3.1 Planar Array Arrangement (a) 2×2 (b) 4×4 (c) 8×8 (d) 16×16 26

Figure 3.2 Geometry of Beam Solid Angle 27

Figure 3.3 2D, Polar and Linear Plots of an Antenna Pattern with M×N Planar Arrays of Isotropic Radiators with a Spacing of dx =dy =0.7λ, and Equal Amplitude and Phase Excitations (a) 2×2 (b) 2×4 (c)4×4 (d)4×8 (e)8×8 (f)16×16 (g)32×32 (h)64×64 29

Figure 3.4 Variation of Directivity, Gain, 3dB Half-Power Beam Width, Number of Side Lobes and Side Lobe Level Vs Number of Elements of Circular Array 33

Figure 3.5 Spherical Coordinate System for Circular Array 35

Figure 3.6 2D, Polar and Linear Plots of an Antenna Pattern with N Circular Arrays of Isotropic Radiators with a Radius of 0.7λ a) 4 b) 8 c) 8 d)16 e)32 f)64 Elements 36

Figure 3.7 Variation of Directivity, Gain, 3dB Half-Power Beam Width, Number of Side Lobes and Side Lobe Level Vs Number of Elements of Circular Array 39

Figure 3.8 Comparison Between Planar and Circular Arrays (MATLAB) (a)Directivity(b)Gain(c)3dB HPBW(d)Number of Side Lobes (e)Side Lobe Level 39

Figure 4.1 Microstrip-Line Feed: (a) Top-View and (b) 3D-View 45

Figure 4.2 Single Planar Array Results; (a)Structure (b) Return Loss (c) 3D Pattern 46

Figure 4.3 2×2 Planar Array Results; (a)Structure (b)Return Losses (c)Mutual Coupling 48

Figure 4.4 2×4 Planar Array Results; (a)Structure (b) Return Losses (c)Mutual Coupling 49

Figure 4.5 4×4 Planar Array Results; (a)Structure (b) Return Losses (c)Mutual Coupling 50

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Figure 4.6 4×8 Planar Array Results; (a)Structure (b) Return Losses

(c)Mutual Coupling 51 Figure 4.7 8×8 Planar Array Results; (a)Structure (b) Return Losses

(c)Mutual Coupling 52 Figure 4.8 Variation of Directivity, Gain, 3dB Half-Power Beam Width, Number of Side Lobes and Side Lobe Level Vs Number of Elements of Planar Array 54 Figure 4.9 Comparison Between MATLAB and CST Simulation Results of Planar Arrays(a)Directivity (b)Gain (c)3dB HPBW

(d)Number of Side Lobes (e)Side Lobe Level 56 Figure 4.10 4 Elements Circular Array (Rectangular Arrangement) Results;

(a)Structure (b) Return Losses (c)Mutual Coupling 59 Figure 4.11 4 Elements Circular Array Results; (a)Structure (b)Return Losses (c)Mutual Coupling 60 Figure 4.12 8 Elements Circular Array Results; (a)Structure (b) Return Losses (c)Mutual Coupling 61 Figure 4.13 16 Elements Circular Array Results; (a)Structure (b)Return Losses (c)Mutual Coupling 62 Figure 4.14 16 Elements Circular Array Results; (a)Structure (b)Return Losses (c)Mutual Coupling 64 Figure 4.15 32 Elements circular Array Results; (a)Structure (b)Return Losses (c)Mutual coupling 65 Figure 4.16 64 Elements Circular Array Results; (a)Structure (b)Return Losses (c)Mutual Coupling 66 Figure 4.17 Variation of Directivity, Gain, 3dB Half-Power Beam Width, Number of Side Lobes and Side Lobe Level Vs Number of

Elements 68 Figure 4.18 Comparison Between MATLAB and CST Simulation Results of Circular Arrays (a)Directivity (b)Gain (c)3dB HPBW

(d)Number of Side Lobes (e)Side Lobe Level 70 Figure 4.19 Comparison Between CST Simulation Results of Planar Arrays and Circular Arrays (a)Directivity (b)Gain (c)3dB HPBW

(d)Number of Side Lobes (e)Side Lobe Level 73

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LIST OF SYMBOLS

N Number of Elements

2D Two Dimentional

3D Three Dimentional

HPBW Half Power Beam Width

β Progressive Phase Shift

AF Array Factor

AFn Normalized Array Factor

d Distance Between Array Elements

a Radius of Circular Array

θ Elevation Angle

ϕ Azimuth Angle

θo Elevetion Angle of Steering Direction

ϕo Azimuth Angle of Steering Direction

k Wave Vector

λ Wavelength

ψ Phase Deviation

D Directivity

dB Decibel

ϵr Dielectric Constant of Substrate

c Speed of Light

Bw Bandwidth

Z0 Input Impedance

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CHAPTER ONE INTRODUCTION

1.1 BACKGROUND

In wireless communication research areas, Large-Scale Antenna Array Systems (also called Hyper MIMO or Massive MIMO) is a vital concept that indicates the significance of 5^th generation (5G) technology network architectures. In multiple input multiple output (MIMO), huge antenna array elements which are at the base stations and those functioned equivalently to direct the signals into tighter space. Furthermore, Improvement of energy efficiency and throughput can be achieved by using multiple antennas in user devices. Large antenna array can be placed in different linear, circular, planar, cylindrical etc. array orientation in very tiny space because they resonated in millimetre wave frequency ranges (Noor Hidayah, et al, 2016).

In any massive MIMO system performance depends on various parameters such as orientation of array, number of array elements, spacing between array elements, individual radiation pattern and mutual coupling of array elements. Types of antennas used for massive MIMO are patch, horn or dipoles antennas and commonly used frequency ranges are 3-6 GHz, 27-28GHz and 60-70 GHz. Figure 1.1 shows, a 2×2 planar antenna array orientation used in smartphones. Large planar or circular arrays such as 2×4, 4×4, 4×8, 8×8 or 4, 8, 16, 32 and 64 elements can be fitted at the base stations in less than one square meter. Both planar and circular arrays can be extremely directional in the preferred directions with fewer side lobes and high gains.

Besides, the array factor directivity and gain of antennas can be simply calculated.

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2

Figure 1.1 2×2 planar arrays used in mobile handset

Thus, planar and circular arrays with very huge number of individual elements is very essential for investigating and implementing any massive MIMO system with mm Wave frequencies ranges (Yaacoub. E, et al, 2016).

Massive MIMO is the currently most compelling sub-6 GHz physical-layer technology for future wireless access. The main concept is to use large antenna arrays at base stations to simultaneously serve many autonomous terminals. Excellent spectral efficiency, achieved by spatial multiplexing of many terminals in the same time-frequency resource. Efficient multiplexing requires channels to different terminals to be sufficiently different, which has been shown to hold, theoretically and experimentally, in diverse propagation environments. Specifically, it is known that Massive MIMO works as well in line-of-sight as in rich scattering. Superior energy efficiency, by virtue of the array gain, that permits a reduction of radiated power.

Moreover, the ability to achieve excellent performance while operating with low- accuracy signals and linear processing further enables considerable savings (Erik G.

Larsson, et al, 2017).

To study the behavior and characteristics of large antenna arrays, there are numerous approaches used by different the researchers. One of the common methods is the concept of sub-arrays which is also used in this dissertation. With this concept, Sub-arrays are elements in large array. This offers simpler analysis for designers to concentrate on small sub-array design and construct large arrays by placing those sub-

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arrays all over the entire large array. From the multiplication of the array factor and individual element pattern, the overall pattern of an array can be found. Using sub- arrays, the overall pattern can be found from the sub-array factor, the product of element pattern and the full array factor determined by the amplitude of excitation, inter elements spacing as well as phasing between sub-arrays (Noor Hidayah, et al, 2017).

1.2 PROBLEM STATEMENT

Most of large antennas are designed using planar array for massive MIMO applications. However, there are still some challenges like the compactness of antenna, the surface area required, low gain, return loss, low bandwidth and efficiency using planar array for massive MIMO applications. Very few research has been done regarding circular array for massive MIMO applications. After the comparison of both planar and circular arrays, it is possible to overcome all challenges by designing a circular array approach for massive MIMO application.

Currently, there are several numerical approaches used when designing and predicting the radiation characteristics of large-scale antenna arrays as discussed in the literature review chapter. With the advancement of those numerical computational methods, array analysis and design of large array have become possible. However, this methods are highly computer-intensive and costly, since they require the use of expensive commercial codes. Moreover, they involve a complex computations which can consume large memory space, long time and effort. Therefore, this dissertation proposes an efficient method of using sub-arrays for developing large uniform antenna arrays. This concept of sub-arrays simplifies the analysis and saves cost, memory, time and effort in the design of large array.

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4 1.3 RESEARCH OBJECTIVES

The specific research objectives are:

1. To design and analyze the performance of planar and circular array performance using sub-array concept for massive MIMO applications.

2. To evaluate and validate the performance of the developed arrays using numerical and simulation models.

1.4 RESEARCH METHODOLOGY

To design antenna arrays requires some calculation on parameters. This research consists of the following steps:

1. Analyse planar array antennas: Analyse of 2×2, 2×4, 4×4, 4×8, 8×8 planar Antenna arrays numerically using MATLAB software.

2. Analyse circular array antennas: Analyse of 4, 8, 16, 32, 64 elements circular Antenna arrays numerically using MATLAB software.

3. Compare results: Comparison of MATLAB numerical results of planar array and circular array antennas.

4. Design and simulate a single patch antenna: Design and simulation of a single 6GHz patch antenna using CST software.

5. Design and simulate planar array of patch antennas: Design and simulation of 2×2, 2×4, 4×4, 4×8, 8×8 planar Antenna arrays using CST software with 2×2 arrays as base sub-array unit and then scale it up to 8×8 planar antenna arrays.

6. Design and simulate circular array of patch antennas: Design and simulation of 4, 8, 16, 32, 64 elements circular antenna arrays using CST

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5

software with 4 elements arrays as base sub-array unit and then scale it up to 64 elements circular antenna arrays.

7. Validate results: Comparison of CST simulation of planar array and circular array antennas.

Finally, by analysing the results a model to predict the radiation pattern of large-scale antenna arrays will be proposed. Figure 1.2 shows flow-chart of this work.

Figure 1.2 Flow-chart of methodology START

Literature review

MATLAB Design and Analysis

CST Simulation and Comparison of results

Recommendation of array

END Validation

of Results No

No

Sub-array modularity modelling Yes

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6 1.5 DISSERTATION OUTLINE

This project is organized into five chapters:

Chapter 1: A basic introduction about large-scale antenna arrays (Massive MIMO) applications, design methodologies and project objectives.

Chapter 2: This chapter covers the literature review done on the design of large antenna arrays, their types, the methods used for finding the radiation pattern from large arrays, applications as well as formulation of array factors.

Chapter 3: Discussion on the design of large isotropic planar and circular array antennas using sub-array in MATLAB and simulation of planar and circular array antennas in CST.

Chapter 4: This chapter analyses the theoretical calculated MATLAB results and validate the results with CST simulation results.

Chapter 5: This chapter includes conclusion and future Recommendation.

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CHAPTER TWO LITERATURE REVIEW

2.1 INTRODUCTION

The fundamental target of 5G is focused towards improving the limits of the system with better coverage at a much lower cost. The most crucial target is the "capacity" as it directly related to speed and information rates. The innovation is being researched to encounter these high information rate goals is the massive MIMO (Shorbagyl, M.

E. et al, 2016; Nurul, N.H. et al, 2011).

For large array antennas, a very convenient technique is proposed by using sub-arrays when it comes to the design. Actually, sub-arrays simplify the design of large array by letting the designer to focus on the minimum sub-array design first and then use that sub-array as a base element for larger array. Rather than complex large array study, this methodology implements the sub-array to design the large array.

Therefore, by reducing large array into small sub-array could save lots of CPU time besides requirement of more memory. Commonly, radiation characteristics of any large array can be easily projected if the mutual coupling between the elements of array antenna are not taken into consideration. The radiation characteristics and performance of an array could be achieved by pattern multiplication approach of the array factor as well as the radiation pattern of single element.

There are various mathematical methods existing for large array investigation.

Some of the investigations are based on infinite-array method along with the periodicity of the array structure however others use the size of actual array.

Therefore, this chapter summarizes the various techniques used when designing large- scale antenna arrays such as sub-array approaches as well as numerical methods. The

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most popular numerical methods involve in the design of large arrays are Method of Moments, Finite element method and finite difference time domain method which are introduced in this chapter (Noor Hidayah, et al, 2016).

2.2 ANTENNA ARRAYS

Antenna array can be defined as a multiple antennas placed in different geometrical arrangements to achieve a highly directive antenna patterns. In order to achieve such directive patterns, the total field of the entire array could be determined by simply combining all the individual element radiations. According to (George. V, et al., 2008), it’s found that the individual element radiation fields add constructively in certain directions and cancel out in others. To simplify the analysis, it is generally assumed that all the arrays elements are identical with same radiation patterns.

Antenna arrays are preferred over a single antenna element due to their scanning ability (phased arrays) where the main lobe is scanned to any desired direction.

Moreover, arrays produce a very high gains with reasonable side lobes which is necessary for distance communications.

Array factor for antenna arrays has a particular interest as it shows the radiation characteristics for any antenna configurations. Array factor can be obtained by using Maxwell’s equations. Every array produces its unique array factor. Most importantly when calculating the array factor, two things are taken into the consideration which are firstly the geometry that elements are arranged and the impact of varying phase shift. One of the approaches used when finding the radiation pattern of an array antenna is called pattern multiplication. In the coming sections, the array factors for different antenna arrangements are presented. There are five considerations that contribute to the performance of an antenna arrays (Atef. Z, et al, 2014):

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9 1) Geometry (linear, planar, circular, etc.) 2) Inter element spacing

3) Amplitude excitation 4) Phase current excitation

5) Overall radiation pattern of elements

2.2.1 Linear Arrays

A linear array is a configuration of antenna elements placed along a line where the orientation of all the elements are in the same direction. The elements are arranged in a way that the radiation fields from the individual elements interfere constructively to produce the preferred pattern. Figure. 2.1 shows a linear array of isotropic elements with equal spacing‘d’ placed in z-direction (Ram, et al, 2015; Atef. Z, et al, 2014).

Figure 2.1 Linear Antenna Array of Isotropic elements

2.2.2 Circular Array

Circular array is formed when the elements are arranged in a circular configuration as shown in Figure 2.2. Circular array has wide applications including radar, space navigation, sonar and many more systems. In addition, circular arrays are recently proposed for smart antennas and wireless communications.