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Analysis of Physical Parameters Influencing Beam Pattern of Uniform Linear Array of Antennas

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ANALYSIS OF THE PHYSICAL PARAMETERS INFLUENCING BEAM PATTERN OF A UNIFORM LINEAR ARRAY OF ANTENNAS

Final Year Project Report
Presented
by SAJID UR REHMAN CIIT/SP08-BET-090/ISB USMAN ULLAH ASIF CIIT/SP08-BET-121/ISB

In Partial Fulfillment
Of the Requirement for the Degree of

Bachelor of Science in Electrical (Telecommunication) Engineering DEPARTMENT OF ELECTRICAL ENGINEERING COMSATS INSTITUTE OF INFORMATION Technology, ISLAMABAD JAN 2012

Declaration We, hereby declare that this project neither as a whole nor as a part there of has been copied out from any source. It is further declared that we have developed this project and the accompanied report entirely on the basis of our personal efforts made under the sincere guidance of our supervisor. No portion of the work presented in this report has been submitted in the support of any other degree or qualification of this or any other University or Institute of learning, if found we shall stand responsible.

Signature:______________ Sajid Ur Rehman Signature:______________ UsmanUllah Asif COMSATS INSTITUTE OF INFORMATION Technology, ISLAMABAD JAN 2012 ANALYSIS OF THE PHYSICAL PARAMETERS INFLUENCING BEAM PATTERN OF A UNIFORM LINEAR ARRAY OF ANTENNAS An Undergraduate Final Year Project Report submitted to the Department of ELECTRICAL ENGINEERING

As a Partial Fulfillment for the award of Degree
Bachelor of Science in Electrical (Telecommunication) Engineering
By
Name | Registration Number | SAJID UR REHMAN | CIIT/SP08-BET-090/ISB | USMAN ULLAH ASIF | CIIT/SP08-BET-121/ISB |

| |

Supervised by DR SHURJEEL WYNE
Assistant Professor,
Department Of Electrical Engineering CIIT Islamabad

Final Approval This Project Titled ANALYSIS OF THE PHYSICAL PARAMETERS INFLUENCING BEAM PATTERN OF A UNIFORM LINEAR ARRAY OF ANTENNAS Submitted for the Degree of
Bachelor of Science in Electrical (Telecommunication) Engineering By Name | Registration Number | SAJID UR REHMAN | CIIT/SP08-BET-090/ISB | USMAN ULLAH ASIF | CIIT/SP08-BET-121/ISB | | | Has been approved for COMSATS INSTITUTE OF INFORMATION Technology, ISLAMABAD _____________________ Supervisor Dr Shurjeel Wyne Assistant Professor ______________________ ______________________ Internal Examiner-1 Internal Examiner-2 Dr Nadeem Javid Dr Safdar Bog Assistant Professor Assistant Professor

______________________ ______________________ External Examiner Hod Name, Name, Designation Designation

Dedication

This project is dedicated to our parents, who taught us that the best kind of knowledge to have is that which is learned for its own sake.
This work is also dedicated to our supervisor, without whose patience, understanding and support the completion of this work would not have been possible.

Acknowledgements

“I have learned that success is to be measured not so much by the position that one has reached in life as by the obstacles which he has had to overcome while trying to succeed”.

BookerT.Washington

We would like to thank our Gracious Allah Almighty, Who helped us overcome all the obstacles that came our way during the completion of our project. During our Project, we received encouragement, support and practical help from our teachers. It is pleasure to acknowledge their efforts and to show our gratitude.

We are highly obliged to our parents who supported us at each and every step and provided us with open moral and financial support. We would thank all our near and dear ones for being there through the temporary snags we came across.

We are greatly in debt to our project supervisors, Dr SHURJEEL WYNE for giving us remarkable suggestions, encouragements and moral support throughout the project. We express our sincere gratitude and appreciation to for his overall observation and guidance in the last two Semesters of our graduation that helped us to meet our goals. May God bless all our well-wishers with great pleasures and long life.

Table of Contents

Declaration…………………………………………………………………………………….ii
Acknowledgements…………………………………………………………………………...vi
Table of Contents…………………………………………………………………………….vii
List of Acronyms ………………………………………………………………..……………ix
List of Figures ………………………………………………………………………...………x
Abstract ………………………………………………………………………………………xi

1 Introduction
1.1 Need of Array Antenna …...……………………………………………………1
1.2 Smart Antenna System………………….………………………………………1
1.2.1 Phased Array Antenna……………………………………………..…1
1.3 Benefits of Smart Antenna……………………………………………………...2 1.4 Disadvantages of Smart Antenna………………………………………………3 1.5 Applications of Array Antenna…………………………………………………3 1.5.1 Radar…………………………………………………...…………….…3 1.5.2 Radio Astronomy..…………………………….…………………….…3 1.5.3 Sonar…………………………….……..…………………………….…3 1.5.4 Communications …………………………………………………….…4 1.5.5 Seismology………………………………………………..………….…4 1.6 Objectives……....…………………………………………………………............5
2 Linear Array of Antennas
2.1 Design of Array Antennas………………………….……………………………6
2.2 Uniform Linear Array of Antennas …………………..…………………………6
2.3 Broadside vs. end fire arrays……………………….……………………………7
2.4 Array Manifold Vector………………………………..…………………………7
2.5 Array Pattern…………………………………………………….………………9
2.6 Beam pattern parameters………………………….……………………………10 2.6.1 Main Lobe………………...…………………………………………10 2.6.2 Side lobe…………………………………………….……………….10 2.6.3 Grating Lobes……………….…………………….…………………11 2.6.4 Nulls…………………………………………………………………12 2.6.5 Beam width…………………………………….……………………13 2.6.6 Directivity and Gain……………………………...…………………13
3 Beamforming and Factors Effecting Uniform Linear Array of Antennas
3.1 Beamforming ………………………………………………………………..…14
3.1.1 Adaptive Beamforming………………………………………………14
3.2 Factors effecting beam pattern of linear array…………………………………15
3.2.1 Effect of number of elements……………………………………...…15
3.2.2 Effect of spacing between elements………………………………….17
4 Weighting Techniques
4.1 Uniform weightings……………………………………………………………21
4.2 Cosine weightings……………………………………………………………...22
4.3 Hamming weightings…………………………………………………………..24
4.4 Blackman weightings…………………………………………………………..25
4.5 Comparison of results…………………………………………………………26
5 Conclusions and Future Work
5.1 Conclusion………………………………………………………………..…….29
5.2 Future works……………………………………………………………..……..29

6 References…………………………………………………………………..………31

List of Acronyms

1-D One-Dimensional
2-D Two-Dimensional
BS Base Station
BWFN Beam Width between First Null
DSP Digital Signal Processing dB Decibels
MAV Manifold Array Vector
MS Mobile Station
SIR Signal to interference Ratio
SIRN Signal to Noise and Interference Ratio
SNR Signal to Noise Ratio
ULA Uniform Linear Array of Antenna

List of Figures

1.1 Switched beam system coverage patterns (a) and Adaptive array coverage (b). pg#
1.2 Submarine mounted hydrophone arrays …………………………..pg#
1.3 Seismic experiment ……………………………………..pg#
1.4 Caption……………………………………………………………………………..pg#
1.5 Caption……………………………………………………………………………..pg#
1.6 Caption……………………………………………………………………………..pg#
2.1 Uniform Linear Array with equal spacing between elements[1]
2.2 End fire array antenna ……………………..pg#
2.3 Caption……………………………………………………………………………..pg#
2.4 Main lobe with side lobes(In 3-D)………………………………………………………..pg#
2.5 Caption……………………………………………………………………………..pg#
2.6 Beam width of main lobe …………………………..pg#
3.1 Main beam steered at angle of 30 degree ……………………..pg#
3.2 No. of elements=5,spacing0.5 λ,targeted at an angle of 30 degree……………..pg#
3.3 No. of elements=10,spacing0 .5 λ, targeted at an angle of 30 degree ……..pg#
3.4 No. of elements=20,spacing0 .5 λ, targeted at an angle of 30 degree ………..pg#
3.5 No. of elements=50,spacing0 .5 λ, targeted at an angle of 30 degree ………..pg#
3.6 No. of elements=21,spacing0 .1 λ, targeted at an angle of 45 degree ……………..pg#
3.7 No. of elements=21,spacing0.3 λ,targeted at an angle of 45 degree ……………..pg#
3.8 No. of elements=21,spacing0 .5 λ,targeted at an angle of 45 degree ………..pg#
3.9 No. of elements=21, spacing1λ, targeted at an angle of 45 degree………………..pg#
3.10 No. of elements=21, spacing2 λ, targeted at an angle of 45 degree ………………..pg#
3.11 Caption……………………………………………………………………………..pg#
4.1 Caption……………………………………………………………………………..pg#
4.2 Caption……………………………………………………………………………..pg#

Abstract

In recent years, several smart antenna systems have been proposed and demonstrated at the base station (BS) of wireless communications systems, showing that significant system performance improvement is possible. A sensor array can be used to filter signals by using their spatial characteristics. This filtering is done by combining the outputs of the array sensors with complex gains that enhance or reject signals according to their spatial dependence. Beamforming is the combination of radio signals from a set of small non-directional antennas to simulate a large directional antenna. The simulated antenna can be steered electronically, even though the array is not moved physically. In communications, beamforming is used to point an antenna at the desired receiver to improve communication quality and to reduce interference to other receivers. The design of arrays to achieve certain performance criteria involves various considerations such as the array geometry and the complex weightings of the data at each sensor output, among other factors. In this project we will use the MATLAB® platform to investigate the physical Parameters of a uniform linear array of antennas that influence the beam Pattern of the array. In addition we will also investigate different strategies for weighting the antenna signals.

CHAPTER 01
Introduction

An antenna in a telecommunications system is the port through which radio frequency energy is transmitted from the transmitter to the outside world for transmission purposes, and in reverse, to the receiver from the outside world for reception purposes [1].
1.1 Need of Array Antenna
Dipole antenna has been playing a vital role in wireless communication since the early days of 20th century. A simple dipole antenna, receives and radiates signals in all directions. Now when signals are scattered in all directions, only a small percentage of energy reached the desired user. To overcome this limitation Omni- directional strategies simply boost the power of the signal. In the presence of a huge number of users and interferers, it becomes a worst situation as the signals which missed the desired user become interference for other neighboring users. Omni directional antennas do not offer any credential gain for the desired users, therefore desired users have to compete with interferers to receive signal energy. Also, that approach cannot reject undesired signals for specific users. Due to these limitations, there was a need for an evolution in the role and design of antenna in wireless communications.
1.2 Smart Antenna System
Array antenna is the type of antenna in which a single antenna is formed by connecting several antennas in a specific structure. A smart antenna use signal processing technique to combine multiple antenna elements. Due to that technique, its radiation becomes optimized and its radiation pattern is adjusted in accordance with the environment.
A smart antenna is a phased or adaptive array that adjusts to the environment. That is, for the adaptive array, the beam pattern changes as the desired user and the interference move, and for the phased array, the beam is steered or different beams are selected as the desired user moves [1].
1.2.1 Phased array
Phased array consists of either a number of fixed beams with one beam turned on towards the desired signal or a single beam (formed by phase adjustment only) that is steered towards the desired signal as shown in Fig. 1.1(a).
Adaptive array antenna is the type of array antenna in which multiple antenna elements are weighted and combined together to enhance signal to interference and noise ratio(SINR).Main beam of adaptive array antenna is placed in the direction of the desired signal and nulls are placed in the direction of the interference as shown in Fig. 1.1(b).

Figure- 1.1: Switched beam system coverage patterns (a) and Adaptive array coverage (b). 1.3 Benefits of Smart Antenna
The main cause for the up growing interest in smart antennas is the enhancement of capacity and better use of bandwidth. This will facilitate to reduce the interference from other users in heavily occupied areas.
Interference is the major source of performance degradation in the multiuser system. Or in other words we can say that the signal to interference ratio, SIR, is much larger than the signal to thermal noise ratio, SNR. Smart antennas enhance the level of received signal, decrease the interference level and hence increase the SIR. Particularly, the adaptive array provides significant improvement.
In rural areas and the areas which are sparsely populated, coverage of signals is more important than capacity. As smart antennas use array elements so they give narrow beam with increased gain as compared to traditional antennas system. Due to that increase in gain, range and coverage is also increased.
Smart antennas can be used to determine the location of users as they use targeted signals. By using that quality network providers can offer new services to users like guiding emergency services, location based games and locality information.
Smart antennas enhance security, because the signals are not scattered in all directions as in the case of Omni-directional antenna. The available bandwidth is also increased due to frequency reuse.

1.4 Drawbacks of Smart Antenna
The number of beams, gain, and beam width is a tradeoff of the price and size. The higher the number of antenna elements making up smart base station antenna array, the higher the available gain, the larger the size and higher the price [2]. Smart antennas are more complicated than traditional antennas. In other words we can say that faults or problems are harder to diagnose.
1.5 Applications of Array Antennas
Since 1939 Array antennas have numerous applications in everyday life. Satellite communication is a typical communication application. Now a days Array antennas are playing a vital role in our society; some of the applications are discussed below.
1.5.1 Radar
Radar technology uses array antenna. Multiple radar functions are performed due to ability of accurately and rapidly switching of beams. Antenna array is used for both reception and transmission of signals. Electronically steered array radar may track multiple targets; The size of the width of the beam (beam-width) determines the angular accuracy of the radar.
Ground- and-ship-based radar uses a model in which both the signal and interference are incident on the array as plane waves.
Recent radars systems use a planar array as it is electronically steerable and can be used as transmitter or receiver by using phase shifters.It can be integrated with the skin of the aircraft.

1.5.2 Radio Astronomy
Antenna arrays are widely used in the radio (or radar) astronomy.In radio astronomy system we detect celestial objects and determine their characteristics.These systems usually use arrays with very long baselines.These baselines range from tens of kilometers to thousands of kilometers.

1.5.3 Sonar
Sonar system also uses antenna arrays.A sonar transmits acoustic energy into the water and then processes the echoes received.Passive sonar system listen to incoming acoustic energy and use it to estimate the characteristics of observed signal field.Detection and tracking of submarines is the most important application of sonar system [3].

Figure- 1.2: Submarine mounted hydrophone arrays

1.5.4 Communications
Antenna arrays have a very important role in communication systems.Adaptive beamforming is used to maximize SINR of received signal by reducing the interference and increasing desired signal strength.As a base station serves many mobile stations, so it is cost-effective to insert the equipment to base station rather than to add it on mobile stations,which are physically of smaller size and low powered.However with the deployment of third generation systems and increased number of mobile users, there is greater need of capacity increase in cellular systems.Capacity can be increased by using adaptive antennas on the mobile stations.Besides advantage of increased capacity ,this may provide improve efficiency in the following fields [3] * Reduction of multipath fading * Suppression of interference signals * Improvements of call reliability * Increased data rates * Spectral efficiency.
1.5.5 Seismology
Array processing is playing an important role in two areas of seismology. First area is the detection and location of underground nuclear explosions.Second and the most important area is exploration seismology.In exploration process image of the subsurface is constructed in which structure and physical properties are described.
Acoustic energy is transmitted into the earth by a shot and a set of geophones are arranged in linear array to receive reflected energy.Arrays are used to measure reflections from differnt layers of earth.A typical seismology experiment is shown in Fig. 1.3 [3].

Figure-1.3: Seismic experiment
1.6 Objectives
Following are the objectives of our project * Understand basic concepts of Antenna Array Processing * Study and Understand Uniform linear arrays and there physical parameters * Mathematically quantify the influence of physical parameters * Investigate different complex weighting techniques * Verify the findings through Matlab Coding

CHAPTER 02
Array Antenna

2.1 Design of Array Antenna
There are two aspects of array design that determine the performance of the array as a spatial filter: * The array geometry establishes basic constraints upon the array operation. * The design of complex weights applied to signals at the antenna ports will determine the benefits that can be achieved with a given geometry.
The array geometry includes different geometries of array antenna like planar, rectangular, and circular. Linear arrays are those in which elements are arranged in a single line with identical inter element spacing, Planar arrays have array geometry arranged in some planar structure and Circular arrays are those in which elements are placed in a circular shape. These array structures have different specifications, but we will only discuss linear and specifically uniform linear array of antennas.
2.2 Uniform Linear Array of Antennas
A linear antenna array is the type of antenna in which array elements are arranged in a single line. The elements are located along a common axis. Now if the spacing between these elements is same then the resulting structure is known as uniform linear array of antennas. For simplicity of analysis we are considering that there are odd numbers of antenna elements and the middle of the array is located at the origin as shown in Fig.2.1. The location of elements is given as:

And

Figure- 2.1: Uniform Linear Array with equal spacing between elements[1]

2.3 Broadside vs. end fire arrays
Broadside array antenna is the antenna elements in which maximum radiation occurs at right angles to axis of the array antenna. In end fire array antenna maximum radiation occurs parallel to axis of the array antenna as shown in Fig.2.2.

Figure- 2.2: End fire array antenna

2.4 Array Manifold Vector

The Array manifold vector (AMV) is a function of the positions of the antennas in the array and the weights used. AMV depends on the number of elements, the element spacing, amplitude and phase of the applied signal to each element. The number of elements and the element spacing determine the surface area of the overall radiating structure.
AMV is given as

where Now by using the property i-e:

Equation (2.3) becomes

As

so by multiplying and dividing equation with -j we have:

In u-space (u=cosθ) it is given as:

In θ-space array manifold vector can be written as:

Where
N= Number of antenna element n=index of array antenna d=spacing between elements λ=wavelength θ=angle of arrival

2.5 Array Pattern
An array pattern can be described as variation of the power radiated by an antenna. This power variation as a function of the arrival angle is observed in the antenna's far field. The radiation pattern is a graphical demonstration of field strength received from or transmitted by an antenna. Radiation patterns of an antenna are taken at a single frequency. Array pattern is formed by the multiplication of array factor with weightings. The patterns are usually depicted in polar or rectilinear form with a dB scale.

Fig-2.3 Array Pattern with main lobe and grating lobe

For uniform linear array of antenna beam pattern can be written as:

In u-space beam pattern is given as:

Beam pattern is only defined over the region (-1≤u≤1), and that region is known as the visible region.
For ψ-space (ψ=kdcos(θ)) it can be written as:

2.6 Beam Pattern parameters
2.6.1 Main lobe.
The lobe which contains maximum power is known as main lobe. Main lobe is directed toward the desired user to give maximum gain to that specific user. Main lobe carries maximum power.

2.6.2 Side lobe

The side lobes are smaller beams that are away from the main beam. These side lobes are usually radiation in undesired directions .The maximum value of the side lobe is known as side lobe level.

Location of maxima of side lobes occurs when the numerator of equation (2.4) is maximum, i-e:

This condition holds when

In u-space it can be written as:

The peak of the first sidelobe occurs at ψ=±3π/N (2.13)

2.6.3 Grating lobes
Grating lobe is the lobe which absorbs equal power as that of main lobe. It is exactly behind the main lobe. Due to its power consumption it is not required .It occurs when both the numerator and denominator of equation (2.9b) equals 1.These appear at intervals

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Figure-2.5: Array pattern with side lobes and grating lobe

2.6.4 Nulls
Nulls are the points where amplitude of lobes is zero. The nulls occur when the numerator of equation (2.6) is zero and denominator is non-zero i-e:

This occur when

Thus first null occur at λ/Nd .

2.6.5 Beam width
Angular separation between two identical points on the opposite sides of radiation pattern is known as beam width. Beam width can be categorized as: * Half power beam width (HPBW) * First null beam width (FNBW)
HPBW is angular separation between points where power is half or where E-field level is 0.707 as shown in Fig-2.6. FNBW is the angular separation between first nulls.

Figure- 2.6: Beam width of main lobe

2.6.6 Directivity:
Directivity is a fundamental characteristic of an antenna. It tells us that how directional an antenna’s radiation pattern is. It is measured in dB scale. Now if an antenna radiates equally in all directions then its directivity would be 1(0dB). In other words we can say that directivity is the ability of the antenna to transmit at a particular direction and to receive from a specific direction.

Chapter 03
Beamforming and Factors Influencing Beam Pattern
3.1 Beamforming
In beamforming, an antenna is made directional by the combination of small non-directional antennas.
In communications, beamforming is used to steer an antenna at the signal source to lessen interference and thus get better quality in communication. In applications involving direction finding techniques, beamforming can be used to steer an antenna to find out the direction of the signal source.
The techniques of beamforming can generate multiple, simultaneously available beams. The beams can be controlled to have low side lobe levels and high gains. Directivity can be controlled by controlling beam width .The techniques of adaptive beam forming can automatically change the array pattern in accordance with optimized features of the received signal. In beam scanning, main beam of an array is steered and the direction can be changed. 3.1.1 Adaptive Beamforming

Antenna arrays that use techniques of adaptive beamforming reject the interfering signals which have a direction of arrival different from the direction of desired signal. Multi-polarized arrays can also reject interfering signals having different polarization states from the desired signal, even if the signals have the same direction of arrival. Beam pattern for the steered beam directed towards a user () is given as:

In u-space, array pattern is in the form:

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Figure-3.1: Main beam steered at angle of 30 degree

3.2 Factors Effecting Beam Pattern of Uniform Linear Array of Antennas
There are two basic factors which effect the beam pattern of uniform linear array of antennas. These are: * Number of antenna elements * Spacing between elements
Now we will discuss these factors briefly.

3.2.1 Number of elements

The array directivity increases with the number of elements. By increasing the number of elements the beam width of main lobe decreases and thus our main beam become more targeted. But as we increase the number of elements, side lobes also increases.

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Figure- 3.2: No. of elements=5, spacing0.5 targeted at an angle of 30 degree
Figure-3.3 : No. of elements=10,spacing0 .5 λ, targeted at an angle of 30 degree
Figure-3.3 : No. of elements=10,spacing0 .5 λ, targeted at an angle of 30 degree 0.2 0.4 0.6 0.8 1
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Figure-3.4: No. of elements=20,spacing0 .5 λ, targeted at an angle of 30 degree 0.2 0.4 0.6 0.8 1
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Figure- 3.5: No. of elements=50,spacing0 .5 λ, targeted at an angle of 30 degree

3.2.2 Spacing between Elements
The element spacing has a significant influence on the pattern of array antenna. By increasing the spacing between elements, beam become more directed (higher directivity).But as we increased the spacing, grating lobes occur, so the element spacing should be smaller than half-wavelength to evade grating lobes as discussed in section 2.6.3. 0.2 0.4 0.6 0.8 1
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Figure-3.6: No. of elements=21, spacing 0.1 λ, targeted at an angle of 45 degree

Figure- 3.7: no. of elements=21, spacing0.3 λ,targeted at an angle of 45 degree
Figure- 3.7: no. of elements=21, spacing0.3 λ,targeted at an angle of 45 degree 0.2 0.4 0.6 0.8 1
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Figure-3.8: no. of elements=21,spacing0 .5 λ,targeted at an angle of 45 degree
Figure-3.8: no. of elements=21,spacing0 .5 λ,targeted at an angle of 45 degree 0.2 0.4 0.6 0.8 1
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As we move towards 1,magnitude of grating lobe start increasing and at 1 grating lobe becomes equal to main lobe in magnitude.
Figure-3.9: No. of elements=21, spacing1λ, targeted at an angle of 45 degree
Figure-3.9: No. of elements=21, spacing1λ, targeted at an angle of 45 degree 0.2 0.4 0.6 0.8 1
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Element spacing beyond 1 create ambiguities and results in multiple unwanted grating lobes as shown in Figure-3.10.
Figure-3.10: No. of elements=21, spacing2 λ, targeted at an angle of 45 degree

Chapter 04
Weighting Techniques

4.1 Uniform Weightings
In uniform weightings no exponentials are involved. We will use uniform weight (1/N) and take it as a reference for other weightings. By putting the value of uniform weighting in equation-2.8b, we get the beam pattern as:

Now as we are dealing with uniform linear array antenna where spacing between elements is same so that equation 4.1 can be written as:

Figure-4.1: Beam pattern of uniform weighting

4.2 Cosine Weighting
We consider the scenario when there are odd number of elements,the cosine weighting is given as:

Now by writing above equation in exponential form we have

Now by putting that equation in array factor, beam pattern becomes

Figure-4.2: Beam pattern of Cosine Weightings

Array pattern for twenty one elements is shown in Figure 4.2.It is clear from the figure parameters that side lobe level is decreased with respect to uniform weightings, but on the other hand beam pattern becomes less directive i-e beamwidth of the main lobe increases as compared to that of uniform weightings.

4.3 Hamming Weighting
In Hamming weighting we place a null at the peak of the first sidelobe. The weighting function is given as:

The coefficients g0 and g1 are chosen to place a null at u=3/N

Beam pattern is the sum of three conventional beam patterns and is written as:

Array pattern for eleven elements is shown in the Figure-4.3.We have seen from the below matlab plot that the first zero occurs at u=4/N and the height of first non-zero side lobe is -39.5dB.
We have notices from matlab generated figure that the beamwidth of hamming weighting is smaller than that of the first two weightings and its first side lobe level is also low comparatively.It is clear that hamming weighting have higher directivity .

Figure-4.3: Beam pattern of Hamming Weightings
4.4 Blackmann-Harris Weighting
Blackmann-Harrris weighting is used when there are a large number of array elements. In that weigting scheme nulls are placed at the peaks of first two sidelobes.
As shown from Figure-4.4 that the main lobe of that weighting has is widest of all the weightings we have used previously, but its side lobe level is very low as compared to other weightings used.The extra beamwidth is usually worth the trade-off.

Figure-4.4: Beam pattern of blackman weighting

By comparing the parameters of weighting schemes and analyzing the figures (4.5 & 4.6), we have concluded the following facts :

* Uniform weightings have minimum beamwidth and its directivity is maximum. * Uniform weightings have highest sidelobe level. * Sidelobe level of cosine weightings is lower as compared to uniform weightings. * Cosine weightings do not depend on spacing between elements. * Cosine weightings have lower sidelobe levels than uniform and its sidelobe levels decreases drastically. * Beamwidth of hamming is smaller than blackmann * Spacing between elements have no effect on cosine weighting * Beamwidth of hamming weightings is larger than that of uniform and cosine, but level of its first two side lobes is very low as compared to previous ones. * Hamming weightings have no effect of number of elements and element spacing. * Main lobe of Blackman weighting is widest of all the weightings we have used . * Side lobe level of Blackman weightings is very low as compared to other weightings used.

Figure- 4.5: Comparison of all Weightings used

Chapter 05
Conclusions and Future Works
5.1 Conclusions
In this work we have discussed only uniform linear arrays, there beam pattern, spacing techniques and use of different weighting techniques to steer there beam pattern in a particular direction.
The ULA performance depends on its size which includes total number of antenna elements used and spacing between them (generally more elements yields better performance) and the weightings used.
Following conclusions summarize our study. * By increasing the number of elements, directivity increases and beam becomes more targeted. * If the element spacing between array elements is increased, the beam width decreases. * Increased element spacing results in a higher directivity. * For uniformly spaced arrays, half-wavelength is the optimum spacing to avoid grating lobes. * Increased element spacing beyond λ produces multiple unwanted grating lobes and sidelobe level also increases. * Uniform weightings have highest directivity and maximum gain in the desired direction although sidelobes level is highest among all the weightings used. So we can use uniform weighting in scenario where we need more directivity as in the case of radar. Its side lobes are also useful in radar system as they provide electronic warfare vulnerabilities. * Beamwidth between nulls is the smallest for Uniform Weighting, but it is the least effective with respect to sidelobe level.Hence, practically Hamming weighting is a better choice having lower side lobe level. * Smaller the directivity, the narrower the main lobe. In this sense, Blackman weighting is the best. * Blackman weightings have highest beam width and lowest side lobes level, so it can be used to cover greater area.
5.2 Future Works
This thesis work mainly focused on the performance of uniform linear array of elements i-e, array elements arranged in a collinear pattern and are equally spaced. The future work of our thesis can be carried to study of linear array elements with unequal spacing. Different techniques could be applied to move the null to our desired location and to control the beam width at specific side lobe levels .Our work can be further extended to study other structures of array antenna like planar, circular etc.

References

[1] Tsoulos,G.V.; ,"Smart antennas for mobile communication systems: benefits and challenges," Electronics & Communication Engineering Journal , vol.11 ,no.2, pp.84-94 , Apr 1999

[2] http://www.mtiwe.com/UserFiles/File/MTI/CPE%20White%20Paper.pdf

[3] Harry L. Van Trees, “Optimum Array Processing (Detection, Estimation, and Modulation Theory, Part IV)”, Wiley Interscience, New York, 2002

[4] Haynes,T , “A priemier of digital beamforming”,Spectrum Signal Processing,
March 26, 1998

[5] C. A. Balanis, Antenna Theory Analysis and Design. New York: Wiley, 1982, ch. ch. 12.

[6] J. D.Kraus, and R. J.Marhefka, Antennas : for all applications, 3rd ed.ˈNew York: McGraw-Hill, 2002.

[7] Durrani, S.; Bialkowski, M.E.; , "Effect of mutual coupling on the interference rejection capabilities of linear and circular arrays in CDMA systems," Antennas and Propagation, IEEE Transactions on , vol.52, no.4, pp. 1130- 1134, April 2004

[8] Durrani, S “Investigations into Smart Antennas for CDMA Wireless Systems”, Phd Thesis, The University of Queensland, Brisbane, Australia. August 2004

[9] http://en.wikipedia.org/wiki/Directivity

[10] Rappaport, “Wireless Communications-Principles and Practice” , ISBN-10: 0130422320

[11] http://en.wikipedia.org/wiki/Phased_array

[12] Durrani, S.; Bialkowski, M.E.; , "Corrections to “Effect of Mutual Coupling on the Interference Rejection Capabilities of Linear and Circular Arrays in CDMA Systems”," Antennas and Propagation, IEEE Transactions on , vol.53, no.5, pp. 1863, May 2005

[13] Thomas, T.A.; Desai, V.; Kepler, J.F.; , "Experimental MIMO Comparisons of a 4-Element Uniform Linear Array to an Array of Two Cross Polarized Antennas at 3.5 GHz," Vehicular Technology Conference Fall (VTC 2009-Fall), 2009 IEEE 70th , vol., no., pp.1-5, 20-23 Sept. 2009

[14] http://www.antenna-theory.com/arrays/main.php

[15] http://www.antenna-theory.com/intro/history.php

[16] John Litva and Titus Kwok-Yeung Lo, Digital Beamforming in Wireless Communications, Artech House
Norwood, MA, 1996.

[17] Warren L. Stutzman and Gary A. Thiele, Antenna Theory and Design, John Wiley & Sons, New York,
1981.

[18] Duan Ke-qing; Xie Wen-chong; Wang Yong-liang; , "Analysis and suppression for nonstationary clutter in airborne conformal array radar," Signal Processing (ICSP), 2010 IEEE 10th International Conference on , vol., no., pp.2087-2091, 24-28 Oct. 2010

[19] http://www.antenna-theory.com/arrays/weights/main.php…...

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