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Department Of Electronic & Electrical Engineering
Direction Dependent Antenna Modulation using a Butler Matrix & a
Four Element Array
By
Bhavishya Sehgal
April 2015
A thesis submitted in partial fulfillment of the requirements for the degree of
Bachelors Of Engineering in Electronic & Communications with a Year in
Industry.
Word Count: 7250
30/04/2015 00:07
Page 1 of 2https://foe-coversheet.group.shef.ac.uk/index.php
EEE360-003
110232799
Individual Assessed Work Coversheet
Assessment Code: EEE360/3
Description: Final Report
Staff Member Responsible: Mr Neil
Powell
Due Date: 30-04-2015 16:00:00
Student Registration Number:
110232799
Assessment Code:
EEE360-003
Word Count: 7250
I certify that the attached is all my own
work, except where specifically stated and
confirm that I have read and understood
the University's rules relating to
plagiarism.
I understand that the Department reserves
the right to run spot checks on all
coursework using plagiarism software.
I
CHAPTER 0
Abstract
Direction Dependent Antenna Modulation aims to provide enhanced wireless data
communications (physical layer) security by carrying out modulation at the antenna
level to achieve M-level modulation as a function of transmission angle. This enables
the transmitter to transmit a certain M-ary constellation in the desired receiver
location, however corrupt the same in both power and shape in other undesired
directions. An effective way to achieve it is by providing progressive phase shifts to
the elements of an antenna array at each symbol transmission during a single
transmission period to obtain a radiation pattern, which is a function of the
transmission angle. This concept is similar to that of phased arrays but different in the
sense that these progressive phase shifts are varied at each symbol transmission. The
work carried out in this thesis aims to implement directional modulation using an
alternative unique transmitter system consisting of a beam-forming network, the 4x4
Butler Matrix, which provides four outputs out of phase with each other for every
excited input port or a combination of input ports. These phased outputs excite the
four elements of a linear dipole antenna array and produce a varied radiation pattern at
each symbol transmission, thus achieving the aim, i.e. M-Level modulation as a
function of transmission angle.
This thesis initially aims to provide a thorough theoretical background to the reader on
the Butler Matrix, the antenna array and the concept of directional modulation (DM).
Further, it details the design and simulations of the 4x4 Butler Matrix and the Dipole
Antenna Array using Computer Simulation Technology. Using the theoretical
background, the thesis firstly details the MATLAB simulations of Array Factor and
then that of Constellation diagrams showing M-ary modulation schemes achieved
using a Butler Matrix, which are direction dependent and improve data
communications security. Finally, along with a brief conclusion, important results are
thoroughly discussed and important recommendations are provided for future research
and development of directional modulation transmitter systems.
The 4x4 Butler Matrix is implemented in copper microstrip on a FR4 substrate, a
design considerably cheaper than an n-bit phase shifter. The S-Parameter simulations
of its magnitude and phase show desirable but imperfect results. The Four Element
Linear Dipole Antenna Array is implemented in λ/2 copper wires. Its farfield
simulation, compared with a single antenna element, shows a higher directivity, gain
and reduced sidelobe levels. More importantly, its farfield shows the effect of phase
shifts on the variation of its radiation pattern as well. Moreover, the Array Factor
simulations of the antenna array show the considerable effect of amplitude excitations
and phase shifts to the variation of its radiation pattern. Finally, assuming the input RF
signal from the Voltage Crystal Oscillator (VCO) has a constant amplitude (1) and
phase (0°) at every symbol transmission, a 14-ary modulation scheme was achieved
using all the possible input port combinations of a 4x4 Butler Matrix. The best
constellation was achieved at -60° from boresight, with further simulations showing
the change of this constellation, in both power level and shape, with change in the
transmission angle. These simulations also intuitively show a higher error rate in the
undesired directions as compared to a conventional system when subject to Additive
White Gaussian Noise (AWGN). This proved the fact that directional modulation can
be achieved using a Butler Matrix and that these DM constellations achieved have an
ability to improve wireless data communications security.
II
List Of Figures
Figure 1: 4x4 Butler Matrix Block Diagram
Figure 2: 90 Degree Hybrid Coupler Structure
Figure 3: 0dB Crossover Structure
Figure 4: 4 Element Linear Antenna Array
Figure 5: Conventional Transmitter Block Diagram
Figure 6: Conventional Transmission Scheme
Figure 7: Directional Modulation Transmitter Block Diagram
Figure 8: Directional Modulation Transmission Scheme
Figure 9: Conventional QPSK in Desired Receiver Direction (left) & in
Eavesdropper Direction (Right) with AWGN
Figure 10: Directional Modulation QPSK in Desired Receiver Direction (left) &
Eavesdropper Direction (right) with AWGN
Figure 11: Ideal Directional Modulation Error Rate Curve as a Function of
Transmission Angle
Figure 12: 90 Degree/3dB Hybrid Coupler CST Design with Multipin Waveguide
Ports
Figure 13: Hybrid Coupler S-Parameter Magnitude Simulation
Figure 14: Hybrid Coupler S-Parameter Phase Simulation
Figure 15: Hybrid Coupler Power Flow Simulation
Figure 16: 0dB Crossover CST Design with Waveguide Ports
Figure 17: Crossover S-Parameter Magnitude Simulation
Figure 18: Crossover Power Flow Simulation
Figure 19: -45 Degree Phase Shifter CST Design
Figure 20: Phase Shifter S-Parameter Phase Simulation
Figure 21: 4x4 Butler Matrix CST Design with Multipin Waveguide Ports
Figure 22: Butler Matrix S-Parameter Magnitude Simulation for Input Port 3
Excitation
Figure 23: Butler Matrix S-Parameter Phase Simulation for Input Port 3 Excitation
Figure 24: Butler Matrix Power Flow Simulation for All Input Ports Excitation
Figure 25: Four Element Linear Dipole Antenna Array CST Design
Figure 26: Dipole Antenna Farfield Simulation
Figure 27: Linear Dipole Antenna Array Farfield (left) & 2-D Polar Plot (right)
Simulation without Phase Shifts
Figure 28: Linear Dipole Antenna Array Farfield (left) & 2-D Polar Plot (right)
Simulation with Progressive Phase Shifts
Figure 29: Array Factor Simulation with Constant Amplitude Excitations and Phase
Shifts
Figure 30: Array Factor Simulation with Varying Amplitude Excitations and
Constant Phase Shifts
Figure 31: Array Factor Simulation with Constant Amplitude Excitations and
Progressive Phase Shifts
Figure 32: Array Factor Simulation (left) & Constellation Point at Boresight
Simulation (right) to prove Model Validity
Figure 33: Directional Modulation Transmitter System using a 4x4 Butler Matrix
Figure 34: 14-ary Constellation Simulation at -60 Degrees from Boresight (Desired
Receiver Direction)
III
Figure 35: 14-ary Constellation Simulation at -30 Degrees from Boresight
(Eavesdropper Direction)
Figure 36: 14-ary Constellation Simulation in Desired Direction with AWGN &
SNR=10
Figure 37: 14-ary Constellation Simulation in Desired Direction with AWGN &
SNR=20
Figure 38: 4-ary Constellation Simulation at -70 Degrees from Boresight (Desired
Receiver Direction)
Figure 39: 4-ary Constellation Simulation at -40 Degrees from Boresight
(Eavesdropper Direction) showing change in Shape of Constellation
Figure 40: Constellation Point Simulation from -90 Degrees from Boresight to
Boresight
Figure 41: 4-ary Constellation Simulation at Desired Direction with AWGN &
SNR=10
Figure 42: 4-ary Constellation Simulation at Eavesdropper Direction with AWGN &
SNR=10
Figure 43: 4-ary Conventional Constellation Simulation at Boresight (Desired
Receiver Direction)
Figure 44: 4-ary Conventional Constellation Simulation at 20 Degrees from
Boresight (Eavesdropper Direction) showing Change in only Power Level & Phase of
Constellation
Figure 45: 4-ary Conventional Constellation Simulation at Desired Direction with
AWGN & SNR=10
Figure 46: 4-ary Conventional Constellation Simulation at Eavesdropper Direction
with AWGN & SNR=10
Figure 47: 8-ary Constellation Simulation at -70 Degrees from Boresight (Desired
Receiver Direction)
Figure 48: 8-ary Constellation Simulation at -40 Degrees from Boresight
(Eavesdropper Direction)
Figure 49: 8-ary Constellation Simulation at Desired Direction with AWGN &
SNR=15
Figure 50: 8-ary Constellation Simulation at Eavesdropper Direction with AWGN &
SNR=15
Figure 51: Recommended Horizontal Crossover Design with Wider Central Stripline
Figure 52: Modified Directional Modulation Transmitter System using a 4x4 Butler
Matrix with a Control Unit for VCO Signal
Figure 53: Butler Matrix S-Parameter Magnitude Simulation for Input Port 1
Excitation
Figure 54: Butler Matrix S-Parameter Magnitude Simulation for Input Port 2
Excitation
Figure 55: Butler Matrix S-Parameter Magnitude Simulation for Input Port 4
Excitation
Figure 56: Butler Matrix S-Parameter Phase Simulation for Input Port 1 Excitation
Figure 57: Butler Matrix S-Parameter Phase Simulation for Input Port 2 Excitation
Figure 58: Butler Matrix S-Parameter Phase Simulation for Input Port 4 Excitation
Figure 59: Dipole Antenna Array S-Parameter Simulation
Figure 60: Dipole Antenna CST Design
Figure 61: Dipole Antenna S-Parameter Simulation
IV
List Of Tables
Table 1: Gantt Chart
Table 2: Progressive Phase Shifts with each Excited Input Port of a 4x4 Butler
Matrix
Table 3: Microstrip Parameter Dimensions
Table 4: Return Loss & Insertion Loss for Each Excited Input Port of a 4x4 Butler
Matrix
Table 5: Output Port Phases for each Excited Input Port of a 4x4 Butler Matrix
Table 6: Phase Difference b/w Consecutive Output Ports for each Excited Input Port
of a 4x4
Butler Matrix. Error in the Progressive Phase Shifts compared with the Theoretical
Target
Table 7: Dipole Antenna Array Parameter Dimensions
Table 8: Theoretical Output Phases & Amplitude Excitations for each or
combination of Excited Input Ports of a 4x4 Butler Matrix
Table 9: Best 8 Input Port Combinations of a 4x4 Butler Matrix
Table 10: Best 4 Input Port Combinations of a 4x4 Butler Matrix
Table 11: Phase of 4-ary Constellation Points (from Desired Receiver Direction at -
70 Degrees from Boresight)
V
TABLE OF CONTENTS
CHAPTER 0
Abstract………………………………………………………………………….I
List Of Figures………………………………………………………………….II
List Of Tables.....................................................................................................IV
CHAPTER 1
I. Introduction……………………………………………………………..1
II. Literature Review……………………………………………………….2
III. Aims & Specifications…………………………………………………..3
CHAPTER 2
IV. Theoretical Background………………………………………………..5
i. The Butler Matrix………………………………………………5
ii. Antenna Array…………………………………………………..7
iii. Direction Dependent Antenna Modulation……………………8
CHAPTER 3
V. CST Design & Simulations……………………………………………13
i. 4x4 Butler Matrix……………………………………………...13
ii. Four Element Linear Dipole Array…………………………..21
VI. MATLAB Simulations………………………………………………...23
i. Array Factor…………………………………………………...24
ii. M-ary Constellations…………………………………………..25
CHAPTER 4
VII. Discussion……………………………………………………………....37
VIII. Conclusion……………………………………………………………...38
IX. Recommendations……………………………………………………..38
CHAPTER 5
X. Bibliography…………………………………………………………...40
XI. Appendices………………………………………………………………i
i. Appendix A: MATLAB Code…………………………………..i
ii. Appendix B: Miscellaneous……………………………………vi
iii. Interim Report………………………………………………….xi
1
CHAPTER 1
I. Introduction
With the advent of wireless communications technology and with it the immense need
for data security because of its broadcast nature, there is an on-going extensive
research and development of transmitter systems that are/would be capable of
providing secure data communications between the transmitter and the desired
receiver.
Direction dependent antenna modulation or directional modulation or direct antenna
modulation has proved to be a significant concept to achieve wireless data
communications security at the physical level, i.e. physical layer security. The basic
principle behind directional modulation is that while ensuring modulation is taking
place at the antenna level, not the baseband, a certain constellation with a low error rate
is achieved in the desired receiver direction, however it aims to scramble the same
constellation with a high error rate in all other undesired directions. This is highly
achievable if an M-ary constellation is obtained, which is a function of transmission
angle. [1] – [4]
Since the late 2000’s, some methods to achieve this have been proposed and a few of
them that have been briefly discussed in the literature review section of this chapter.
One such useful method proposes the use of an antenna array with phase shifters to
achieve a varied radiation pattern at each symbol transmission, i.e. providing different
progressive phase shifts to the elements of an antenna array at every symbol
transmission, while ensuring that the RF signal is fed directly to these phase shifters,
which in turn modulate the signal at the antenna level. [3]
This is in contrast to conventional transmitter systems, where modulation takes place at
the baseband, which is then converted to RF and transmitted over a fixed radiation
pattern at each symbol transmission. This design does not allow any angular
dependency and only the power level of the constellation reduces at a direction away
from the desired receiver location, which can be easily detected by a sensitive receiver.
The methodology to achieve directional modulation proposed in this thesis works on
the same principle as above, however, instead of using n-bit IC phase shifters, which
cost approximately £2-4k each and have an exhaustive design process, the aim is to
achieve the same with the use of a beam forming network, i.e. a 4x4 Butler Matrix,
which can be easily implemented in microstrip on a substrate, which in turn costs the
same as that of a printed circuit board.
The structure of this thesis has been designed in such a way to provide a thorough
understanding of this topic to the reader. In addition to the literature reviewed by the
author, the latter of this chapter details the aims and specifications of the work included
in this thesis. Chapter 2 solely explains the theoretical background required to
implement directional modulation using a Butler Matrix and a four-element array.
Furthermore, chapter 3 focuses on the design and simulations of the above essential
components of this transmitter system using state-of-the-art CAD software, Computer
Simulation Technology. Moreover, MATLAB is used for signal processing and
simulating M-ary constellations, which are essential to prove that directional
modulation can be achieved using a 4x4 Butler Matrix.
2
Finally, chapter 4 provides the reader with a detailed discussion of the observations
made by the author over the period of this project, a brief conclusion and a few
recommendations for future work that could be carried out for further research and
development in directional modulation transmitter systems.
II. Literature Review
Directional Modulation
i. [1] This paper introduces the concept of Near Field Direct Antenna Modulation
(NFDAM), where, the reflectors of an antenna array are excited in the near field of the
radiating dipole antenna. The RF signal is then modulated at the antenna level using
different combinations of switches or varactors, implemented on the reflectors, at every
symbol transmission. This allowed obtaining varying signal radiation patterns, which
were dependent on the transmission angle, thus improving data security and
contributing to the start of extensive research in directional modulation.
ii. [2] In this paper, using the concept of phased arrays, it is shown that by shifting the
phase of the elements of an antenna array at every symbol transmission, QPSK
constellations can be corrupted in undesired directions. Also, optimisation or genetic
algorithms were used to decide the best combination of phase shifts that would provide
a high error rate in the undesired directions and a low error rate in the desired receiver
direction. This directional modulation transmitter system was compared with a
conventional transmitter system to show the improvement in wireless data
communications security achieved with directional modulation.
iii. [3] This paper utilizes the same concept as in ii, however the phase shifts have been
provided using 2-bit phase shifters for a two-element array directional modulation
transmitter system. However, due to the high level of difficulty in implementing
optimisation algorithms, phase shift assumptions were made here to simulate a 16-ary
constellation, which is a function of the transmission angle. Also, a high error rate was
observed at directions away from the desired receiver direction while a low error rate
at the desired receiver direction providing a narrow error rate curve, which is a
function of transmission angle.
iv. [4] In this paper, published recently in 2015, directional modulation has been
experimentally achieved by using a 13x13 Fourier Rotman Lens and a 13 Element
Patch Antenna Array.
The work carried out in this thesis takes inspiration from all of the above research in
directional modulation. It aims to provide directional modulation using the concept of
phased arrays, however, instead of using n-bit phase shifters, the work in this thesis
aims to implement the same by using different input port combinations of a 4x4 Butler
Matrix to provide with a different set of phase shifts and amplitude excitations, at each
symbol transmission, to the elements of a linear dipole antenna array.
3
Butler Matrix
[5] In this paper, a 4x4 Butler Matrix operating at 5.2GHz has been designed (in
microstrip and FR4 substrate) and simulated using CAD software SONNET for
WLAN applications due to its beam steering capability, easy design and cost
effectiveness. A thorough theoretical background on the Butler Matrix and its
components has been provided along with essential set of equations to design the
Hybrid Coupler, Crossover and the Phase Shifter. Finally, the design has been
simulated to show the desired performance.
Although, further review [6] [7] was carried out to understand the concept, design and
use of a Butler Matrix, the above paper was sufficient to design and simulate the 4x4
Butler Matrix.
III. Aims & Specifications
The aim of the work carried out in this thesis is to achieve M-Level modulation as a
function of the transmission angle, i.e. Direction Dependent Antenna Modulation using
a 4x4 Butler Matrix and a 4 Element Linear Dipole Antenna Array.
MATLAB Simulations
i. To simulate the Array Factor, as a function of the transmission angle, of the
four element linear array. This is required to observe the variation in the Array
Factor, hence, a variation in the radiation pattern of the array as a function of
the transmission angle, with the change in phase shifts and amplitude
excitations to the elements of an antenna array.
ii. To simulate the varying radiated signals as symbols on the Constellation
Diagrams, i.e. to achieve M-ary Constellations using a 4x4 Butler Matrix. This
is essential to further observe the direction dependency of the transmitted
symbols on the constellation diagram and thus, prove direction dependent
antenna modulation can be achieved using a 4x4 Butler Matrix.
iii. To further observe this system’s enhanced data communications security in
comparison with conventional systems, with a high error rate in undesired
directions and a low error rate in the desired receiver direction when subject to
AWGN.
CST Design & Simulations
i. CAD software: Computer Simulation Technology (CST).
ii. System operating at 2.45GHz.
iii. Copper Microstrip for 4x4 Butler Matrix with thickness, Mt=0.1mm and λ/2
Copper Wire for Linear Dipole Antenna Array.
iv. FR4 Substrate for Butler Matrix with thickness, h=1.6mm and Dielectric
constant, !!=4.3.
4
v. To design and simulate individual components of a 4x4 Butler Matrix, i.e. the
90° Hybrid Coupler, the 0dB Crossover and the -45° Phase Shifter. Then,
combine these components for the final design of a 4x4 Butler Matrix and carry
out the required S-Parameter and Power Flow simulations.
vi. To design and simulate a λ/2 Dipole Antenna. Then, combine four of these
antennas at a distance of λ/2 to complete the design of a Four Element Linear
Dipole Antenna Array and carry out its Farfield and S-Parameter simulations.
Gantt Chart
A | Literature Review
B | Research
C | Array Factor Simulation using MATLAB
D | Computer Simulation Technology (CST) Tutorial
E | Design & Simulation Of Butler Matrix Components & Dipole Antenna using CST
F | Complete Design & Simulations of a 4x4 Butler Matrix and Linear Dipole Antenna Array using CST
G | M-ary Constellation Simulation using MATLAB
H | Prepare Presentation
I | Prepare Thesis
Table 1: Gantt Chart
Component 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
A
B
C
D
E
F
G
H
I
5
CHAPTER 2
IV. Theoretical Background
i. The Butler Matrix
A Butler Matrix is a NxN passive beam-forming network, which performs a Fast
Fourier Transform (FFT) on its input to produce N outputs [6], which, for each excited
input port, has a linear progressive phase shift as shown in Table 2 [7]. The N outputs
then excite a N-element antenna array to produce N overlapping orthogonal beams.
This enables the Butler Matrix to electronically steer the beams for which it is widely
used in the communications industry. [5] [7] However, in context to this thesis, since
the Butler Matrix has this great ability to provide varying phase shifts to the elements
of an antenna array, it can essentially be used for providing directional modulation,
which has been further discussed and proved in the latter part of chapter 3.
Table 2: Progressive Phase Shifts with each Excited Input Port of a 4x4 Butler Matrix
Excited Input Port Progressive Phase Shift
1 -45°
2 +135°
3 -135°
4 +45°
A NxN Butler Matrix consists of !
2 !"#!! 90°/3dB Hybrid Couplers, !
2 (!"#!! −
1) Phase Shifters & a few 0dB Crossovers. [5] Hence, as shown in Figure 1 below, the
4x4 Butler Matrix consists of four Hybrid Couplers, two -45° Phase Shifters and two
Crossovers. These components are essential as it allows it to excite the elements of an
antenna array with the progressive phase shifts. Moreover, Figure 1 shows the process
by which the 4x4 Butler Matrix can achieve 4 outputs out of phase with each other for
every excited input port. Assuming that the first input port of the Butler Matrix is
excited with a signal of amplitude 1 and phase 0°, then it provides four output signals,
which are out of phase with each other by -45° and have an attenuated amplitude. To
further understand how this is achieved, the individual components of a Butler Matrix
have been described in detail.
Figure 1: 4x4 Butler Matrix Block Diagram
6
a. Hybrid Coupler
Figure 2: 90 Degree Hybrid Coupler Structure
The 90° Hybrid Coupler, implemented in microstrip of length λ/4 and constructed
using two striplines with characteristic impedance,!!!=50Ω & two striplines with
!!/ 2=35.4Ω, has four ports as shown Figure 2 with Port 1 or 4 being for the input. It
is generally used due to its ability to generate two equi-power output signals (with 3dB
attenuation) at Port 2 & Port 3 (coupled) with 90° phase difference between them. Port
4 or 1 is isolated (no power) depending on which Port is excited. [5]
b. Crossover
Figure 3: 0dB Crossover Structure
The Crossover, implemented in microstrip of length λ/4 and constructed using
striplines with characteristic impedance,!!!=50Ω, has four ports as shown in Figure 3,
It is used to transfer the signal from Port 1 or 4 to Port 3 or 2 respectively without any
change in the power level or the phase of the signal. [5]
c. Phase Shifter
The Phase Shifter, implemented in microstrip of length, ! =!
!∗!
!!
where ! is the value
of phase shift required. [5]
The design and simulation of the 4x4 Butler Matrix and its components using CST has
been further discussed in chapter 3.
7
ii. Antenna Array
This thesis is concerned with the concept of only linear or 1-D antenna arrays. These
arrays consist of N antenna elements, spaced at a distance d as shown in Figure 4. [9]
Figure 4: 4 Element Linear Antenna Array
Antenna arrays are used as they provide a higher directivity, gain and reduced sidelobe
levels as compared to a single element. These characteristics have been shown and
discussed in chapter 3. The main lobe can be steered depending on the phase shifts
provided to the array, thus forming a phased array, which in turn forms an essential
concept in directional modulation, where, these phase shifts are varied as well but at
every symbol transmission to obtain a direction dependent M-ary constellation.
The overall farfield of the array is the summation of each element’s field and assuming
all elements are identical and isotropic, it can be also calculated by multiplying the
field of a single element with the Array Factor, a property of the array, which depends
on its geometry. [9]
The Array Factor of a N element linear antenna array is given by [9],
!" ! = !!!![ !!! !"#$%&!!!]!
!!! (1), where,
!: Elevation Angle
!!: Amplitude Excitation
N: Number of Elements
k: Propagation Constant = 2π/λ
d: Spacing between Elements
!!: Phase Shift
With respect to this thesis, the number of elements of the antenna array has been set to,
N=4 as a 4x4 Butler Matrix is being used to excite it. Also, the spacing between
elements has been set to λ/2 as it sufficiently provides a narrow main beam and
reduced sidelobe levels.
8
The Array factor can be re-written as,
!" ! = !!!![ !!! !"#$%!!!]!
!!! (2)
The Array Factor provides a method to visualize the change in the variation of
radiation pattern as a function of transmission angle by providing different
combinations of amplitude excitations and phase shifts to the elements of the array.
These simulations have been further discussed in chapter 3.
Furthermore, in order to synthesize the complex radiation pattern of a transmitted
signal as a complex digital symbol with magnitude and phase, which in turn can be
observed as a complex constellation point on the constellation diagram (or the real-
imaginary coordinate system), assuming a line-of-sight (LOS) communications exists
between the transmitter and m receivers in m directions, this digital symbol, x(t), is
obtained in m directions at a specific time t, using the following equation [2],
!!!
!
⋮
!!!
!
=
!!!
, 1 ⋯ !!!
, !
⋮ ⋱ ⋮
!!!
, 1 ⋯ !!!
, !
∗!
!! !
⋮
!! !
(3), where,
!!!
! : Symbol in direction m
!!!
, !: Field of element n in direction m
!! ! : Signal excitation of element n, given by,
!! ! = !!!!!! (4), where, [2]
!!: Amplitude excitation
!!: Phase shift
iii. Direction Dependent Antenna Modulation
Direction Dependent Antenna Modulation is a M-Level modulation, which is direction
dependent as the modulation has been implemented at the antenna level, not the
baseband. The best way to introduce the concept of a directional modulation
transmitter system is by comparing it with a conventional modulation transmitter
system.
In a conventional transmitter system as shown in Figure 5, data modulation takes place
at the baseband level, thus, a modulated signal is first converted into RF and then
transmitted in all directions with a fixed radiation pattern. This results in the same data
or constellation being transmitted in all directions with a lower power levels in
unwanted directions, which can still be detected by a sensitive receiver. [1] – [3]
9
Figure 5: Conventional Transmitter Block Diagram
This conventional transmission scheme can be better understood from Figure 6, where
a QPSK constellation is transmitted with a fixed radiation pattern, which in turn
provides with the same constellation in all directions but with reduced power levels.
Figure 6: Conventional Transmission Scheme
10
On the other hand, in a directional modulation transmitter system as shown in Figure 7,
modulation is imparted at the antenna level by providing varying phase shifts to the
elements of an array at each symbol transmission. This results in the modulation being
dependent on the transmission angle as the signal is transmitted with a time varying
radiation field at each symbol transmission. Thus, data can be transmitted in the correct
direction with a low error rate, and can be corrupted in any undesired direction in both
power level and shape with a high error rate. This makes it a very difficult job for
sensitive receivers in unwanted directions to detect the signal and sometimes even
impossible. [2] [3] The directional modulation scheme shown in Figure 8 provides a
better understanding to the same.
Figure 7: Directional Modulation Transmitter Block Diagram
Figure 8: Directional Modulation Transmission Scheme
11
A high error rate in unwanted directions can be achieved by obtaining a constellation
point on the constellation, which moves a considerable distance in directions away
from the desired receiver direction. In doing so, with the constellation changing in both
shape and power levels, when subject to Additive White Gaussian Noise (AWGN), a
received signal has a high probability to be detected as an error. [3]
Comparing Figure 9 and Figure 10, it can be inferred that both conventional and DM
transmitter systems provide a low error rate in the desired directions, however, in the
undesired direction, the error rate provided by the conventional transmitter is lower
than the error rate provided by the directional transmitter due to its change in shape,
which in turn is due to the fact that the constellation is direction dependent. [2] [3]
Figure 9: Conventional QPSK in Desired Receiver Direction (left) & in Eavesdropper Direction
(Right) with AWGN
Figure10: Directional Modulation QPSK in Desired Receiver Direction (left) & Eavesdropper
Direction (right) with AWGN
12
Figure 11 shows the ideal error rate curve as a function of transmission angle. With
directional modulation, this narrow error rate curve can be achieved, with a low error
rate in the undesired direction and a high error rate elsewhere. [2] [3]
Figure 11: Ideal Directional Modulation Error Rate Curve as a Function of Transmission Angle
To determine the probability of a received constellation point is an error, an algorithm
based on minimum distance decoding can be implemented. [3] Here, firstly, the
Euclidean distance is calculated between any received constellation point and the
points on the transmitted constellation. Then, this received constellation point is
decoded as a constellation point to which it is closest to and compared with the
constellation point that was originally transmitted. Finally, if these two points don't
correlate then it can be inferred that the receiver has detected a signal with error. [8]
To simulate the error rate as shown in Figure 11, using minimum distance decoding,
the following equation for the symbol error rate [8] could be taken into account as
well.
!! = !!"#$!!(
!!"#
!!!
) (5), where,
!!"#$ is the largest number of nearest neighbours, !!"# is the minimum Euclidean
distance in the constellation, Q (x) is the complimentary Gaussian function and !! is
the noise power spectral density.
13
CHAPTER 3
V. CST Design & Simulations
Computer Simulation Technology (CST) was used to design a 4x4 Butler Matrix (in
copper microstrip). Thereafter, Waveguide ports were implemented to the design to
carry out its S-Parameter and Power Flow simulations. Moreover, a Four Element
Linear Dipole Antenna Array was designed using copper wire. Discrete ports were
then implemented to the design to simulate the array for its Farfield and S-Parameters.
i. 4X4 Butler Matrix
The Butler Matrix, as described in chapter 2 was designed using state-of-the-art CAD
software, Computer Simulation Technology. The 4X4 Butler Matrix was implemented
in copper (annealed) microstrip on a FR4 substrate operating at 2.45 GHz. Initially, the
individual components that form a Butler Matrix i.e. the 90°/3dB Hybrid Coupler, the
0dB Crossover and the -45° Phase Shifter were individually designed and simulated.
Finally, these components were cascaded together to design and simulate the 4x4
Butler Matrix.
a. 90°/3dB Hybrid Coupler
Design
The 90° Hybrid Coupler was constructed with two !! (50Ω) and two !!/ 2 (35.4Ω)
transmission lines of length λ/4 shunt together as shown in Figure 12. [5]
Figure 12: 90 Degree/3dB Hybrid Coupler CST Design with Multipin Waveguide Ports
The width, W, of the two transmission lines was calculated using the following
equations [5],
!/ℎ =
!
!
{! − 1 − log 2! − 1 +
!!!!
!!!
log ! − 1 + 0.39 −
!.!"
!!
} (6)
! =
!"!!
!! !!
(7), where, h=1.6mm is the thickness of the FR4 substrate and !! = 4.3 is
the dielectric constant of the FR4 substrate.
14
The length, L of the transmission lines was then calculated using the equation [5],
! = !
(4 ∗ ! ∗ !!"##)
(8), where, c is the speed of light, f=2.45GHz is the operating
frequency and !!"## is the effective dielectric constant. The derivation of the above
equation for length, L, and the equation to calculate !!"## has been described in
Appendix B.
Using these equations, the values obtained for the above parameters are shown in
Table 3.
Table 3: Microstrip Parameter Dimensions
Parameter Dimension
Width, W, of 50Ω Stripline 4.1mm
Width, W, of 35.4Ω Stripline 6.52mm
!!"## (50Ω) 3.34
!!"## (35.4Ω) 3.48
Length, L of 50Ω Stripline 16.75mm
Length, L of 50Ω Stripline 16.41mm
Simulation
The S-Parameters and the Power Flow of the Hybrid Coupler were simulated to
observe desired results and proper functioning.
The S-Parameter magnitude simulation in Figure 13 shows a high return loss of -
28.16dB and the two output ports have an insertion loss close to -3dB as desired.
Figure 62: Hybrid Coupler S-Parameter Magnitude Simulation
15
The S-Parameter phase simulation in Figure 14 shows the difference in phase between
its output ports is 53.77°-(-33.85) = 87.62°, which is very close to the desired phase
difference of 90°.
Figure 14: Hybrid Coupler S-Parameter Phase Simulation
Figure 15: Hybrid Coupler Power Flow Simulation
Finally, the Power Flow simulation in Figure 15 shows that attenuated power has been
equally distributed between its output ports.
16
b. 0 dB Crossover
Design
Figure 16: 0dB Crossover CST Design with Waveguide Ports
The 0dB Crossover was constructed only with 50Ω striplines using the same set of
equations for length and width as for the Hybrid Coupler.
Simulation
The S-Parameter magnitude simulation in Figure 17 shows that the output port has a
very low insertion loss of -2.43dB, which is in turn very close to the ideal value of
0dB.
Figure 17: Crossover S-Parameter Magnitude Simulation
17
Figure 18: Crossover Power Flow Simulation
Again, the Power Flow simulation in Figure 18 shows that most of the power has been
transferred diagonally from Port 1 to Port 3 with very little attenuation.
c. 45° Phase Shifter
Design
Figure 19: -45 Degree Phase Shifter CST Design
The Phase Shifter was constructed using a single 50Ω transmission line of length, L,
using the following equation [5],
! = !
(8 ∗ ! ∗ !!"##)
(9)
The derivation of the above equation is described in Appendix B.
18
Simulation
The S-Parameter phase simulation in Figure 20 shows that a phase of -40.43° has been
achieved, which is very close to the ideal phase requirement of -45°.
Figure 20: Phase Shifter S-Parameter Phase Simulation
d. 4x4 Butler Matrix
Design
Finally, the above components were then cascaded together to complete the design of
the 4x4 Butler Matrix as shown in Figure 21.
Figure 21: 4x4 Butler Matrix CST Design with Multipin Waveguide Ports
19
Simulation
The S-Parameter magnitude and phase simulations for the 4x4 Butler Matrix have been
shown in Figure 22 and 23 respectively, for when input port 3 is excited. The
simulations for other input port excitations are provided in Appendix B.
Figure 22: Butler Matrix S-Parameter Magnitude Simulation for Input Port 3 Excitation
Figure 23: Butler Matrix S-Parameter Phase Simulation for Input Port 3 Excitation
The output ports tend to show a low insertion loss and the input port shows a high
return loss, however, the simulated results are not perfect and vary for every input and
output port. The results for the S-Parameter magnitude simulations have been provided
in Table 4, with undesired results highlighted. Similarly, the phase difference between
the output ports shows a considerable error compared with the theoretical values [7] as
can be seen in Table 6. Again, the S-Parameter phase simulation results have been
provided in Table 5.
20
Table 4: Return Loss & Insertion Loss for Each Excited Input Port of a 4x4 Butler Matrix
Excited
Input Port
Return
Loss (dB)
Insertion
Loss o/p
Port 1
(dB)
Insertion
Loss o/p
Port 2
(dB)
Insertion
Loss
o/p Port 3
(dB)
Insertion
Loss o/p
Port 4
(dB)
1 -11.22 -16.80 -25.86 -2.67 -6.97
2 -25.76 -3.35 -6.92 -14.71 -8.01
3 -26.32 -8.02 -14.85 -6.94 -3.31
4 -11.13 -6.94 -2.67 -26.01 -17.29
Table 5: Output Port Phases for each Excited Input Port of a 4x4 Butler Matrix
Excited
Input Port
Output Port
1 Phase (°)
Output Port
2 Phase (°)
Output Port
3 Phase (°)
Output Port
4 Phase (°)
1 -100.44 -162.85 126.40 79.94
2 -112.48 124.42 3.19 165.19
3 164.32 5.25 124.83 -112.31
4 79.92 126.90 -155.58 -99.69
Table 6: Phase Difference b/w Consecutive Output Ports for each Excited Input Port of a 4x4
Butler Matrix. Error in the Progressive Phase Shifts compared with the Theoretical Target
Excited
Input
Port
Port 2-
1(°)
Port 3-
2(°)
Port 4-
3(°)
Achieved
Target (°)
(Average)
Theoretical
Target (°)
Error (°)
1 -62.41 -70.75 -46.46 -59.87 -45 14.87
2 236.9 238.77 162 212.56 +135 77.56
3 -159.07 -240.42 -237.14 -212.21 - 135 77.21
4 46.98 77.52 55.89 60.13 +45 15.13
In order to reduce the error in magnitude and phase of the Butler Matrix, a couple of
recommendations for future implementation have been provided in chapter 5.
However, as this design is not being implemented experimentally, what is more
important is that from these results it can be inferred that for every excited input port a
NxN Butler Matrix provides N outputs out of phase with each other.
21
Figure 24: Butler Matrix Power Flow Simulation for All Input Ports Excitation
The Power Flow simulation in Figure 24 shows the power flow in a Butler Matrix
when all input ports are excited.
ii. Four Element Linear Antenna Array
Initially, a λ/2 dipole antenna was designed using CST. The design and S-Parameter
simulation is provided in Appendix B. Then four of these antennas were put together at
a distance of λ/2 as specified earlier. This linear dipole antenna array was then
simulated to observe its Farfield.
Design
Figure 25: Four Element Linear Dipole Antenna Array CST Design
The 4 Element Linear Dipole Antenna shown in Figure 25 was designed by combining
four Half-Wave Dipole Antennas. The dipole antenna operating at 2.45GHz was
22
designed using copper wires and the following equations [9] were used to calculate the
parameters of the antenna.
Length of antenna (half-wavelength), L= λ/2 = c/(2*f) (10), where c is the speed of
light and f is the operating frequency.
Radius of antenna, R= λ/1000 (11).
Feeding gap of antenna, g= λ/400 (12).
Using these equations, the antenna was designed with the parameters shown in Table 7.
Table 7: Dipole Antenna Array Parameters
Parameter Dimension (mm)
Length 58.2
Radius 0.1225
Feeding Gap 0.29
These antennas were then used to form the linear array and were placed at distance, d=
λ/2 from each other.
Discrete ports were implemented to this array design, which was simulated to observe
its S-Parameters and Farfield.
Simulation
A comparison has been carried out between a single antenna element and an antenna
array using the Farfield simulations of the Dipole Antenna and the Linear Dipole
Antenna Array. The Farfield of the single dipole antenna in Figure 26 shows a lower
directivity and gain (2.18dB) as compared with the Farfield of the dipole antenna array
in Figure 27, which shows a higher directivity and gain (9.4dB). Thus, the simulations
prove that a higher directivity, gain and reduced sidelobe levels are obtained with
antenna array.
Figure 26: Dipole Antenna Farfield Simulation
23
Figure 27: Linear Dipole Antenna Array Farfield (left) & 2-D Polar Plot (right) Simulation
without Phase Shifts
Figure 28 shows the Farfield of an antenna array, which has been subject to
progressive phase shifts unlike the Farfield in Figure 27. From the Farfield simulations
it can be inferred that a variation in the radiation pattern is achieved by providing these
phase shifts to the elements of an array, which can be observed more clearly from the
Polar plots of the array’s farfields.
Figure 28: Linear Dipole Antenna Array Farfield (left) & 2-D Polar Plot (right) Simulation with
Progressive Phase Shifts
V. MATLAB Simulations
To visualise the effect of different sets of amplitude excitations and phase shifts on the
radiation pattern of a 4-element linear antenna array, the Array Factor was simulated.
Furthermore, digital symbols were simulated for different combination of amplitudes
and phase shifts obtained from different input port combinations of a 4x4 Butler Matrix
and represented as constellation points on the complex I-Q diagram to achieve M-ary
modulation constellations, which are dependent on the transmission angle and thus,
improve data communications security.
24
i. Array Factor
The array factor of a 4-element linear array with each element spaced at a distance of
λ/2 was simulated using MATLAB. Simulations were carried out for different
combinations of amplitude excitations and phase shifts to observe the change brought
in by these different combinations to the radiation pattern. These can be visualised for
the three different cases shown below in Figures 29, 30 and 31.
Case 1: Amplitude Excitations: 1, 1, 1, 1; Phase Shifts: 0, 0, 0, 0
Figure 29: Array Factor Simulation with Constant Amplitude Excitations and Phase Shifts
Case 2: Amplitude Excitations: 0.5, 1, 1, 0.5; Phase Shifts: 0, 0, 0, 0
Figure 30: Array Factor Simulation with Varying Amplitude Excitations and Constant Phase
Shifts
25
Case 3: Amplitude Excitations: 1, 1, 1, 1; Phase Shifts: 0, -45, -90, -135
Figure 31: Array Factor Simulation with Constant Amplitude Excitations and Progressive Phase
Shifts
ii. M-ary Constellations
Before simulating the M-ary constellations, it was important to prove the validity of
the model implemented using MATLAB to simulate complex symbols as constellation
points on the complex constellation diagram. To prove this, for a set of amplitude
excitations and phase shifts, the magnitude of the normalised constellation simulated
was compared with the magnitude of the normalised array factor at boresight. Figure
32 shows the same, where the magnitude of the normalised array factor at boresight is
equal to 0.6533, which in turn is equal to the magnitude of the simulated normalised
constellation point, which is (−0.25)! + (−0.6036)! = 0.6533.
Figure 32: Array Factor Simulation (left) & Constellation Point at Boresight Simulation (right) to
prove Model Validity
26
Using different port combinations of a 4x4 Butler Matrix, which in turn provide a
different set of amplitude excitations and phase shifts to the elements of an antenna
array, M-ary constellations were simulated to prove that M-Level modulation as a
function of transmission angle can be achieved using a Butler Matrix Directional
Modulation Transmitter System, which is shown in Figure 33. Here, keeping the
amplitude and phase of the signal generated from the Voltage Crystal Oscillator
constant, at each symbol transmission, the signal is modulated at the antenna level
using a certain combination of input ports, which provide a set of amplitude excitations
and phase shifts to the elements of the antenna array.
Figure 33: Directional Modulation Transmitter System using a 4x4 Butler Matrix
Table 8 shows that for a constant input signal from the VCO, with amplitude 1 and
phase 0°, for a combination of excited input ports of a 4x4 Butler Matrix, a set of
amplitudes and phase shifts are obtained at the four output ports.
Table 8: Theoretical Output Phases & Amplitude Excitations for each or combination of Excited
Input Ports of a 4x4 Butler Matrix
Excited
i/p Port(s)
o/p Port
1 Phase
(°)
o/p Port
2 Phase
(°)
o/p Port
3 Phase
(°)
o/p Port
4 Phase
(°)
Progressive
Phase Shift
(°)
o/p
Amplitude
Excitation
1 -45 -90 -135 -180 -45 0.5
2 -135 0 +135 -90 +135 0.5
3 -90 +135 0 -135 -135 0.5
4 -180 -135 -90 -45 +45 0.5
1 & 2 -180 -90 0 +90 +90 1
1 & 3 -135 +45 -135 +45 -180 1
1 & 4 +135 +135 +135 +135 0 1
2 & 3 +135 +135 +135 +135 0 1
2 & 4 +45 -135 +45 -135 +180 1
3 & 4 +90 0 -90 -180 -90 1
1, 2 & 3 +90 +45 0 -45 -45 1.5
1, 2 & 4 0 +135 -90 +45 +135 1.5
1, 3 & 4 +45 -90 +135 0 -135 1.5
2, 3 & 4 -45 0 +45 +90 +45 1.5
1, 2, 3 & 4 -90 -90 -90 -90 0 2
27
Now, using all of these port combinations, i.e. modulating one signal using one port
combination and then changing the input port combination at every symbol
transmission, a 14-ary constellation was simulated at -60° from Boresight shown in
Figure 34. If the transmitter system is modified in such a way that the input signal
phase and amplitude can be changed at every symbol transmission than ideally an ∞-
ary constellation can be achieved and this has been discussed briefly in chapter 4.
Figure 34: 14-ary Constellation Simulation at -60 Degrees from Boresight (Desired Receiver
Direction)
Figure 35 shows the 14-ary constellation at -30° from Boresight. The constellation
shows how the each constellation point from the desired receiver direction in Figure 34
has moved across the constellation, which has resulted in the change in shape of the
constellation. Moreover, only 7 constellation points have been received at this
undesired direction. This is an exciting result as these two 14-ary constellations at
different directions have proved that the M-ary constellations achieved from a 4x4
Butler Matrix are direction dependent, i.e. M-Level Modulation has been achieved
using a 4x4 Butler Matrix and more importantly, the loss of constellation points at the
undesired direction makes it impossible for the eavesdropper to detect a signal.
Figure 35: 14-ary Constellation Simulation at -30 Degrees from Boresight (Eavesdropper
Direction)
28
Communication channels add Additive White Gaussian Noise (AWGN) to the
transmitted signal and thus the received constellation is actually received with noise.
The 14-ary constellation shown before has been subject to AWGN in Figure 36 with
the Signal to Noise Ratio (SNR) set to 10. As can be seen from this figure, this addition
of noise to the constellation has a negative impact on the error rate at the desired
direction, as there is a high probability that the receiver may detect a received signal as
another transmitted signal, which would result in an error.
Figure 36: 14-ary Constellation Simulation in Desired Direction with AWGN & SNR=10
One way to improve the error rate at the desired direction would be to increase the
value of SNR to 20 as shown in Figure 37, however, the simulated constellation
anyways has few constellation points very close to each other, which would still result
in an error with improved SNR.
Figure 37: 14-ary Constellation Simulation in Desired Direction with AWGN & SNR=20
29
If this 14-ary scheme is not considered ideal for experimental work, alternative 8-ary
and 4-ary constellations, which are used widely in industry, have been simulated using
the best eight and four input port combinations of the 4x4 Butler Matrix respectively
shown in Table 9 and 10 respectively.
Table 9: Best 8 Input Port Combinations of a 4x4 Butler Matrix
Excited
i/p Port(s)
o/p Port
1 Phase
(°)
o/p Port
2 Phase
(°)
o/p Port
3 Phase
(°)
o/p Port
4 Phase
(°)
Progressive
Phase Shift
(°)
o/p
Amplitude
Excitation
1 & 3 -135 +45 -135 +45 -180 1
2 & 4 +45 -135 +45 -135 +180 1
3 & 4 +90 0 -90 -180 -90 1
1, 2 & 3 +90 +45 0 -45 -45 1.5
1, 2 & 4 0 +135 -90 +45 +135 1.5
1, 3 & 4 +45 -90 +135 0 -135 1.5
2, 3 & 4 -45 0 +45 +90 +45 1.5
1, 2, 3 & 4 -90 -90 -90 -90 0 2
Table 10: Best 4 Input Port Combinations of a 4x4 Butler Matrix
Excited
i/p Port(s)
o/p Port
1 Phase
(°)
o/p Port
2 Phase
(°)
o/p Port
3 Phase
(°)
o/p Port
4 Phase
(°)
Progressive
Phase Shift
(°)
o/p
Amplitude
Excitation
1 & 3 -135 +45 -135 +45 -180 1
2 & 4 +45 -135 +45 -135 +180 1
1, 2 & 4 0 +135 -90 +45 +135 1.5
1, 3 & 4 +45 -90 +135 0 -135 1.5
30
The desired 4-ary constellation shown in Figure 38 was achieved at a direction that is -
70° from boresight. The constellation points are further apart from each other as
desired to provide low error rate at this direction.
Figure 38: 4-ary Constellation Simulation at -70 Degrees from Boresight (Desired Receiver
Direction)
Figure 39 shows the 4-ary constellation at -40° from boresight, which is an undesired
direction. Here, again, the constellation shows that the constellation points have moved
(from the desired direction shown in Figure 38 previously) in such a way that the
constellation has changed in both power level and shape. This would make detection
by an eavesdropper a much harder prospect. Moreover, three points have moved much
closer to each other, which would in turn provide with a higher error rate.
Figure 39: 4-ary Constellation Simulation at -40 Degrees from Boresight (Eavesdropper Direction)
showing change in Shape of Constellation
31
To further prove the direction dependency of this constellation, a single constellation
point was simulated from a direction that is -90° from boresight to the boresight
direction in increments of 10° as shown in Figure 40. The figure shows that the
constellation point moves a considerable distance from the desired direction, which in
turn scrambles the constellation, thus making it very difficult for an eavesdropper to
detect the signal.
Figure 40: Constellation Point Simulation from -90 Degrees from Boresight to Boresight
As discussed before, the 4-ary constellation has been subject to AWGN as shown in
Figure 41. With the constellation points being further apart from each other, the
probability of a received signal being detected as another transmitted signal is
negligible and thus this constellation provides a low error rate in the desired receiver
direction.
Figure 41: 4-ary Constellation Simulation at Desired Direction with AWGN & SNR=10
32
Since, the constellation at -40° from boresight had three points close to each other,
when subjected to AWGN as shown in Figure 42, the error rate at this undesired
direction would be very high. This is exactly what is desired and thus the 4-ary
constellation achieved using a 4x4 Butler Matrix can easily be implemented
experimentally to enhance wireless data communications security.
Figure 42: 4-ary Constellation Simulation at Eavesdropper Direction with AWGN & SNR=10
To prove the fact that a directional modulation transmitter system provides enhanced
security as compared to a conventional transmitter, the phases of the constellation
points in Figure 38 (4-ary directional modulation constellation at desired receiver
direction) were calculated as shown in Table 11 and used to modulate the signal at
baseband, remembering the fact that the radiation pattern is now kept constant at every
symbol transmission. This provided with a 4-ary conventional constellation as shown
in Figure 43 in the desired Boresight direction. It can be inferred from this figure that
the constellation obtained at the desired receiver direction for the conventional
transmitter has a higher power level compared to that of a directional modulation
transmitter in Figure 38, with all the constellation points further apart from each other.
Table 11: Phase of 4-ary Constellation Points (from Desired Receiver Direction at -70 Degrees
from Boresight)
Constellation Point Phase (°)
-0.1285 + j1.18 96.2
0.8574 + j0.4698 28.7
0.08056 – j0.7395 276.2
-0.8574 – j0.4698 208.7
33
Figure 43: 4-ary Conventional Constellation Simulation at Boresight (Desired Receiver Direction)
However, Figure 44, which shows the conventional constellation at an undesired
direction at 20°, it can be seen that only the power level and phase of constellation has
changed but the shape of the constellation has remained the same. Thus a sensitive
receiver in an undesired direction would be easily able to detect the signal.
Figure 44: 4-ary Conventional Constellation Simulation at 20 Degrees from Boresight
(Eavesdropper Direction) showing Change in only Power Level & Phase of Constellation
34
Again, subjecting the constellation to AWGN, in the desired direction as shown in
Figure 45, a low error rate would be obtained. However, at an undesired direction, as
shown in Figure 46, the constellation has not changed sufficiently enough to have a
high error rate. This result is in total contrast to that of directional modulation, where a
narrow error rate can be obtained with a high error rate in all undesired directions, as
explained before in chapter 2.
Figure 45: 4-ary Conventional Constellation Simulation at Desired Direction with AWGN &
SNR=10
Figure 46: 4-ary Conventional Constellation Simulation at Eavesdropper Direction with AWGN &
SNR=10
35
Finally, the 8-ary constellation was simulated as shown in Figure 47. The desired
constellation was achieved at -70° from boresight, where the constellation points were
furthest away from each other.
Figure 47: 8-ary Constellation Simulation at -70 Degrees from Boresight (Desired Receiver
Direction)
Again, as shown in Figure 48 below, at an undesired direction, the constellation points
have moved in a way that the entire constellation has scrambled due to change in both
power level and shape. This would make signal detection a very hard prospect for the
eavesdropper.
Figure 48: 8-ary Constellation Simulation at -40 Degrees from Boresight (Eavesdropper Direction)
36
Finally, subjecting the constellation to AWGN, it is observed in Figures 49 and 50 that
the error rate in the desired direction would considerably be lower to that in the
undesired direction due to the movement of constellation points across the
constellation such that they scramble the constellation and move very close to each
other.
Figure 49: 8-ary Constellation Simulation at Desired Direction with AWGN & SNR=15
Figure 50: 8-ary Constellation Simulation at Eavesdropper Direction with AWGN & SNR=15
37
CHAPTER 4
VII. Discussion
A 4x4 Butler Matrix has been easily implemented in copper microstrip on a FR4
substrate using state-of-the-art CAD software CST, thus being an efficient and cheap
alternative to n-bit phase shifters for use in a directional modulation transmitter
systems. Although the simulated S-Parameters obtained were not ideal, they did
provide sufficient knowledge about the performance of a 4x4 Butler Matrix. Such
imperfections in microwave designs can be easily corrected or tweaked for use of this
design in future experiments.
Also, the 4 Element Linear Dipole Antenna was designed using copper wires (again a
cheap, reliable and efficient component of the system) and simulated to observe its
farfield. Firstly, its farfield, as compared to that of a single antenna element, showed a
higher directivity, gain and reduced levels of sidelobes. More importantly, the farfield
of this array showed a variation with change in phase shifts to its elements. Thus, all
these properties of the antenna array make it an ideal and essential component for use
in directional modulation.
Moving on to the theoretical Array Factor simulations of an antenna array, it has been
clearly shown that by providing different amplitude excitations and phase shifts to the
antenna array, a time varying radiation pattern, which is dependent on the transmission
angle is obtained. Thus, this proves that by changing the phase shifts of the elements at
every signal synthesis or symbol transmission, an M-ary constellation of direction
dependent symbols can be achieved.
The final work carried out in this thesis proves that directional modulation can be and
has been achieved using a 4x4 Butler Matrix, i.e. the M-ary constellations obtained
using the different amplitude excitations and phase shifts from different port
combinations of a Butler Matrix are direction dependent and the constellation points
move sufficiently across the constellation as a function of transmission angle. This
direction dependency of the constellation essentially provides with a certain
constellation in the desired receiver direction with a low error rate, but provides a
scrambled constellation in other undesired directions with a high error rate, again due
to change in the shape of the constellation.
It has been assumed that the input signal amplitude and phase to the power divider is
kept constant at every symbol transmission. This provides with a maximum of a 14-ary
constellation (best constellation at -60° from boresight), achieved using all the possible
port combinations of a 4x4 Butler Matrix. This 14-ary constellation has been further
proved to be direction dependent, changing in both power level and shape with
transmission angle, thus providing a high error rate in the undesired directions when
subject to AWGN. However, since the 14-ary constellation does seem to provide error
at the desired receiver direction as well, the best 8 input port combinations of the
Butler Matrix were used to provide with an 8-ary constellation at -70° from boresight.
Similarly, the best 4 input port combinations were used to provide with a 4-ary
constellation, which was then compared with a conventional 4-ary constellation, which
in turn showed that a directional modulation transmitter provides enhanced wireless
data security compared to a conventional transmitter. This direction dependency of the
M-ary constellations was obtained, which proves that the 4x4 Butler Matrix is capable
38
of providing directional modulation to enhance wireless date communications security
at the physical level.
VIII. Conclusion
Conclusively, a unique transmitter system, which provides M-level modulation as a
function of transmission angle, i.e. Direction Dependent Antenna Modulation for
physical layer security has been proposed in this thesis. The CST design and
simulations of the most important components of this system, i.e. the 4x4 Butler
Matrix and the 4 Element Linear Dipole Antenna Array have been carried out. The
effect of amplitude excitations and phase shifts to the elements of a 4-element antenna
array has been discussed with the theoretical concept of Array Factor. Finally, using
different input port combinations of a 4x4 Butler Matrix at each symbol transmission,
different M-ary constellations were simulated, which were then proved to be direction
dependent i.e. changing in both power level and shape with the transmission angle,
providing a high error rate in undesired directions and a low error rate in desired
receiver direction.
IX. Future Recommendations
i. Firstly, the design of the 0dB Crossover of the 4x4 Butler Matrix implemented in this
thesis should be replaced with the suggested one as shown in Figure 51. This design
has a wider central stripline, which should decrease the error in the phase differences
of the output ports. Also, further tweaking of the microwave design should be carried
out to get near to perfect S-Parameter simulations. This is important if this design
needs be implemented to carry out an experiment for directional modulation.
Figure 51: Recommended Horizontal Crossover Design with Wider Central Stripline
ii. Secondly, for the suggested input port combinations of the 4x4 Butler Matrix, which
provided with direction dependent 14-ary, 8-ary and 4-ary constellations, an
experiment with the directional modulation transmitter system design mentioned in this
thesis should be carried out to prove directional modulation using a 4x4 Butler Matrix.
iii. Thirdly, the error rate, as a function of transmission angle, as discussed in chapter
2, should be simulated using MATLAB for the suggested M-ary constellations when
subject to AWGN. The idea behind this has been thoroughly discussed in this thesis
and the direction dependence of the M-ary constellations intuitively shows that a low
39
error rate can be achieved at the desired receiver location and a high error rate in the
undesired directions.
iii. Finally, the directional modulation transmitter system design should be modified
(as shown below) such that, the phase of the VCO should be varied at each symbol
transmission. In an ideal case, this would provide an infinite M-ary constellation in a
single transmission period, thus, an optimised or genetic algorithm [2] needs to
implemented, which would chose the best input port combinations as well as the best
sets of amplitudes and phase of the input signal in order to propose the best M-ary
constellations that provide a high error rate in all unwanted directions and a low error
rate in the desired receiver direction.
Figure 52: Modified Directional Modulation Transmitter System using a 4x4 Butler Matrix with a
Control Unit for VCO Signal
40
CHAPTER 5
X. Bibliography
[1] A. Babakhani, D. B. Rutledge, and A. Hajimiri “Transmitter Architectures Based
on Near-Field Direct Antenna Modulation,” IEEE JOURNAL OF SOLID-STATE
CIRCUITS, vol. 43, no. 12, pp. 2674-2692, 2008
[2] M. P. Daly, and J. T. Bernhard, “Directional Modulation Technique for Phased
Arrays,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol. 57, no. 9,
pp. 2633-2640, September 2009.
[3] H. Shi, A. Tennant: ‘Direction Dependent Antenna Modulation Using a Two
Element Array’, Proceedings of the 5th European Conference on Antennas and
Propagation (EUCAP), Rome, Italy, pp. 812-815, 2011.
[4] Y. Ding, Y. Zhang, and V. Fusco, “Fourier Rotman Lens Enabled Directional
Modulation Transmitter,” International Journal of Antennas and Propagation, vol.
2015, Article ID 285986, pp. 1-13, 2015.
[5] W. Bhowmik and S. Srivastava, “Optimum Design of a 4x4 Planar Butler Matrix
Array for WLAN Application,” JOURNAL OF TELECOMMUNICATIONS, vol. 2,
ISSUE 1, pp. 68-74, April 2010.
[6] M. UENO, “A Systematic Design Formulation for Butler Matrix Applied FFT
Algorithm,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol. AP-
29, no. 3, pp. 496-501, 1981.
[7] S. Z. Ibrahim, M. K. A. Rahim: ‘Switched Beam Antenna using Omnidirectional
Antenna Array’, In 2007 ASIA-PACIFIC CONFERENCE ON APPLIED
ELECTROMAGNETICS PROCEEDINGS. Melaka, MALAYSIA, December 4-6,
2007, IEEE, pp. 1-4.
[8] A. Goldsmith, “Wireless Communications”, 1st edition. New York, NY:
Cambridge University Press. 2005.
[9] C. A. Balanis, “Antenna Theory: Analysis and Design”, 3rd edition. New Jersey:
John Wiley & Sons, INC. 2005.
[10] Prof. Tzong-Lin Wu. Microwave Filter Design. [ONLINE] Available at:
http://ntuemc.tw/upload/file/2011021716275842131.pdf. [Accessed 28 April 15].
i
XI. Appendices
Appendix A: MATLAB Code
Array Factor Code
clc;
N=4; %Number Of Elements
j=sqrt(-1);
An=ones(1,N);
Ph=zeros(1,N);
A=zeros(1,N);
%Amplitude Excitations
An(1,2)=1;
An(1,3)=1;
An(1,4)=1;
An(1,5)=1;
%Phase Shifts
Ph(1,2)=0;
Ph(1,3)=-45;
Ph(1,4)=-90;
Ph(1,5)=-135;
for n=2:N+1
A(1,n)=An(1,n)*exp(j*(Ph(1,n)*pi/180));
End
%Array Factor Simulation (as a function of Elevation Angle)
AF=zeros(181,N);
i=0;
for theta=-90:90
i=i+1;
for n=2:N+1
af(i,n)=A(1,n)*(exp(-j*(n-1)*pi*sin((theta)*pi/180))); [Equation (2)]
af(i,n)=af(i,n) + af(i,n-1);
end
AF(i,n)=abs(af(i,n));
End
%Plot of Normalised Array Factor with Elevation Angle
figure;
theta=-90:90;
plot(theta,AF/N);
xlabel('Elevation Angle');
ylabel('Normalised Array Factor');
title('Array Factor vs Elevation Angle');
grid on;
hold on;
ii
M-ary Constellation Code
clc;
N=4; %Number Of Elements
j=sqrt(-1);
bits = 1000; %Number of Bits
b=(randn(1,bits)>0.5); % Generating 0,1 with Equal Probability
An=ones(1,N);
Pn=zeros(1,N);
A=zeros(1,N);
for n=1:N
A(1,n)=An(1,n)*exp(j*Pn(1,n)*pi/180);
end
s=zeros(N,length(b)/4);
%4 Bits Transmitted as 1 Symbol
for k=1:length(b)/4
a=b(4*k);
c=b(4*k-1);
d=b(4*k-2);
e=b(4*k-3);
%14-ary Constellation using 4x4 Butler Matrix Input Port Combinations
%Varying Element Excitation using formula, sn=An*exp(j*Pn) at each symbol
transmission [Equation (4)]
%Port1
if (a==0)&&(c==0)&&(d==0)&&(e==0)
s(1,k)=0.5*exp(j*((-45)*pi/180));
s(2,k)=0.5*exp(j*((-90)*pi/180));
s(3,k)=0.5*exp(j*((-135)*pi/180));
s(4,k)=0.5*exp(j*((-180)*pi/180));
end
%Port2
if (a==0)&&(c==0)&&(d==0)&&(e==1)
s(1,k)=0.5*exp(j*((-135)*pi/180));
s(2,k)=0.5*exp(j*((0)*pi/180));
s(3,k)=0.5*exp(j*((135)*pi/180));
s(4,k)=0.5*exp(j*((270)*pi/180));
end
%Port3
if (a==0)&&(c==0)&&(d==1)&&(e==0)
s(1,k)=0.5*exp(j*((-90)*pi/180));
s(2,k)=0.5*exp(j*((-225)*pi/180));
s(3,k)=0.5*exp(j*((0)*pi/180));
s(4,k)=0.5*exp(j*((-135)*pi/180));
end
iii
%Port4
if (a==0)&&(c==0)&&(d==1)&&(e==1)
s(1,k)=0.5*exp(j*((-180)*pi/180));
s(2,k)=0.5*exp(j*((-135)*pi/180));
s(3,k)=0.5*exp(j*((-90)*pi/180));
s(4,k)=0.5*exp(j*((-45)*pi/180));
end
%Port1&2
if (a==0)&&(c==1)&&(d==0)&&(e==0)
s(1,k)=1*exp(j*((-180)*pi/180));
s(2,k)=1*exp(j*((-90)*pi/180));
s(3,k)=1*exp(j*((0)*pi/180));
s(4,k)=1*exp(j*((90)*pi/180));
end
%Port1&3
if (a==0)&&(c==1)&&(d==0)&&(e==1)
s(1,k)=1*exp(j*((-135)*pi/180));
s(2,k)=1*exp(j*((-315)*pi/180));
s(3,k)=1*exp(j*((-135)*pi/180));
s(4,k)=1*exp(j*((+45)*pi/180));
end
%Port1&4
if (a==0)&&(c==1)&&(d==1)&&(e==0)
s(1,k)=1*exp(j*((135)*pi/180));
s(2,k)=1*exp(j*((135)*pi/180));
s(3,k)=1*exp(j*((135)*pi/180));
s(4,k)=1*exp(j*((135)*pi/180));
end
%Port2&3
if (a==0)&&(c==1)&&(d==1)&&(e==1)
s(1,k)=1*exp(j*((-225)*pi/180));
s(2,k)=1*exp(j*((-225)*pi/180));
s(3,k)=1*exp(j*((-225)*pi/180));
s(4,k)=1*exp(j*((-225)*pi/180));
end
%Port2&4
if (a==1)&&(c==0)&&(d==0)&&(e==0)
s(1,k)=1*exp(j*((-315)*pi/180));
s(2,k)=1*exp(j*((-135)*pi/180));
s(3,k)=1*exp(j*((45)*pi/180));
s(4,k)=1*exp(j*((-135)*pi/180));
end
%Port3&4
if (a==1)&&(c==0)&&(d==0)&&(e==1)
s(1,k)=1*exp(j*((-270)*pi/180));
s(2,k)=1*exp(j*((0)*pi/180));
s(3,k)=1*exp(j*((-90)*pi/180));
s(4,k)=1*exp(j*((-180)*pi/180));
end
iv
%Port1,2&3
if (a==1)&&(c==0)&&(d==1)&&(e==0)
s(1,k)=1.5*exp(j*((-270)*pi/180));
s(2,k)=1.5*exp(j*((-315)*pi/180));
s(3,k)=1.5*exp(j*((0)*pi/180));
s(4,k)=1.5*exp(j*((-45)*pi/180));
end
%Port1,2&4
if (a==1)&&(c==0)&&(d==1)&&(e==1)
s(1,k)=1.5*exp(j*((0)*pi/180));
s(2,k)=1.5*exp(j*((135)*pi/180));
s(3,k)=1.5*exp(j*((270)*pi/180));
s(4,k)=1.5*exp(j*((315)*pi/180));
end
%Port1,3&4
if (a==1)&&(c==1)&&(d==0)&&(e==0)
s(1,k)=1.5*exp(j*((45)*pi/180));
s(2,k)=1.5*exp(j*((-90)*pi/180));
s(3,k)=1.5*exp(j*((135)*pi/180));
s(4,k)=1.5*exp(j*((90)*pi/180));
end
%Port2,3&4
if (a==1)&&(c==1)&&(d==0)&&(e==1)
s(1,k)=1.5*exp(j*((-45)*pi/180));
s(2,k)=1.5*exp(j*((0)*pi/180));
s(3,k)=1.5*exp(j*((45)*pi/180));
s(4,k)=1.5*exp(j*((90)*pi/180));
end
%Port1,2,3&4
if (a==1)&&(c==1)&&(d==1)&&(e==0)
s(1,k)=2*exp(j*((-90)*pi/180));
s(2,k)=2*exp(j*((-90)*pi/180));
s(3,k)=2*exp(j*((-90)*pi/180));
s(4,k)=2*exp(j*((-90)*pi/180));
end
end
af=zeros(181,N);
i=0;
for theta=-90:90
i=i+1;
for n=1:N
af(i,n)=af(i,n)+ A(1,n)*exp(-j*(n-1)*pi*sin((theta)*pi/180));
end
end
v
i=0;
AFn=zeros(181,N);
SNR=10; %Signal To Noise Ratio
for theta=-90:90
i=i+1;
AFn(i,:)=af(i,:)/N;
x=AFn*s; %Received Symbols at Each Value of Theta [Equation (3)]
y=awgn(x,SNR, 'measured'); %Adding AWGN
end
q=31; %Value of Theta
%Scatter Plot
figure; % M-ary Constellation at Direction q
X=real(x(q,:));
Y=imag(x(q,:));
scatter(X,Y,'k','filled');
hold on;
X=real(y(q,:));
Y=imag(y(q,:));
scatter(X,Y,'y','filled');
hold on;
axis([-1 1 -1 1]);
grid on;
xlabel('Real');
ylabel('Imaginary');
legend('Original Constellation', 'Noisy Data Points');
title('M-ary Constellation');
vi
Appendix B: Miscellaneous
Microstrip Equations and their Derivations
i. The effective dielectric constant, !!"##, was calculated using the equation [10],
!!"##!
!!!!
!
+
!!!!
!
(1 + 12
!
!
)!!.!
, where, !! is the dielectric constant of the FR4
substrate, h is the thickness of the FR4 substrate and W is the width of the microstrip.
ii. Length, L, of microstrip for Hybrid Coupler and Crossover was calculated using the
following equation [5],
Length, ! = !!/4, where,
!! = !/ !!"## & λ = c/f, hence,
! = !
(4 ∗ ! ∗ !!"##)
iii. Length, L, of microstrip for 45 Degree Phase Shifter was calculated using the
following equations [5],
Φ =
2π
!!
∗ !
!! = !/ !!"## , λ = c/f, Φ =
!
!
hence,
! = !
(8 ∗ ! ∗ !!"##)
vii
Butler Matrix S-Parameter Magnitude & Phase Simulations
Figure 53: Butler Matrix S-Parameter Amplitude Simulation for Input Port 1 Excitation
Figure 54: Butler Matrix S-Parameter Magnitude Simulation for Input Port 2 Excitation
viii
Figure 55: Butler Matrix S-Parameter Magnitude Simulation for Input Port 4 Excitation
Figure 56: Butler Matrix S-Parameter Phase Simulation for Input Port 1 Excitation
ix
Figure 57: Butler Matrix S-Parameter Phase Simulation for Input Port 2 Excitation
Figure 58: Butler Matrix S-Parameter Phase Simulation for Input Port 4 Excitation
x
Linear Antenna Array S-Parameter Simulation & Dipole Antenna Design
Figure 59: Dipole Antenna Array S-Parameter Simulation
Figure 60: Dipole Antenna CST Design
Figure 61: Dipole Antenna S-Parameter Simulation
EEE"360" Interim"Report"
1"
THE UNIVERSITY OF SHEFFIELD
Department of Electronic and Electrical Engineering
BEng Final Year Individual Design Project
Student Bhavishya Sehgal
Registration
Number & Course
110232799
BEng (Hons) Electronic & Communications with a Year in Industry
Project Title Direction Dependent Antenna Modulation using a Butler Matrix and a Four
Element Array
Supervisor Dr. Alan Tennant Second Marker Dr. Xiaoli Chu
EEE"360" Interim"Report"
2"
Direction Dependent Antenna Modulation using a
Butler Matrix and a Four Element Array
Introduction
This design project aims to achieve enhanced data security due to the advent in wireless data
communications technology over the last few years. One of the suggested methods to achieve this
high level of security is the concept of Directional Modulation, for which, a few techniques and ideas
have been researched into and provided with. Similarly, this project aims to provide with a different
approach to directional modulation using a unique system, as shown in Figure 1 below, of a 4x4
Butler Matrix and a four-element linear antenna array.
Figure 1: Transmitter system to achieve Directional Dependent Antenna Modulation
In conventional transmitter systems, data is only modulated at the baseband level and is transmitted
by an antenna system that has a fixed radiation pattern. Although, the system provides a variation in
signal power in different directions, sensitive receivers located in undesired directions can still
demodulate this signal as the signal has the same characteristics in every direction. On the other
hand, with directional modulation, modulation is implemented at the antenna level as well. In the
context of this project, directional modulation would be achieved by using a 4x4 Butler Matrix,
which provides the linear antenna array with four progressive phase shifts for each of the four input
signals. This linear phased array would then provide with a variable radiation pattern for each of the
excited inputs, thus, scrambling the signal characteristics in the undesired directions and retaining
them in the desired boresight direction.
EEE"360" Interim"Report"
3"
This difference in signal modulation characteristics in desired and undesired directions for a
directionally modulated antenna array can be shown below in Figure 2, using Constellation or I-Q
diagrams.
Figure 2: Constellation diagram visualising the effect of directional modulation
Aims & Specification
The aim of this project is to achieve m-level modulation as a function of the transmission angle, i.e.
direction dependent antenna modulation using the unique system discussed and presented in the
previous section of this report.
MATLAB Simulations
1) To simulate the Array Factor, as a function of the transmission angle, of the four element linear
array. This is required to observe the change in the Array Factor, as a function of the transmission
angle, with the change in progressive phase shifts and amplitudes of the output signals from the
Butler Matrix.
2) To simulate the modulated signals as symbols on the Constellation diagram, using modulation
techniques such as M-PSK or QAM. This is required to observe the movement of symbols on the
constellation diagram with change in the transmission angle and thus, prove the direction dependency
of the system. To further prove the system’s direction dependency and enhanced security with the
concept of Bit Error Rate (BER), i.e. to observe a higher BER in undesired directions and a lower
BER in the desired boresight direction.
System Design & Simulations
- Design & Simulation Software: Computer Simulation Technology (CST)
- System Operating/Resonant Frequency: 2.45GHz
- Materials:
- Copper (annealed): for Microstrip (thickness = 0.1mm) and Dipole Antenna Array
- FR4 (lossy): for Substrate (thickness = 1.6mm)
- Teflon (PTFE) (lossy): for Connector
EEE"360" Interim"Report"
4"
1) To design and simulate individual components of a Butler Matrix, i.e. the Hybrid Coupler, the
Crossover and the Phase Shifter.
Then, combine these components for the final design of a 4x4 Butler Matrix and carry out the
required S-parameter simulations. The Butler Matrix would provide the necessary progressive phase
shifts and beam forming.
2) To design and simulate a half wave dipole antenna. Then, combine four of these dipoles to form a
four element antenna array and carry out its farfield simulations.
3) To design a Power Divider and carry out the required S-parameter simulations. The Power Divider
would switch the input signal phase to the Butler Matrix.
Finally, combine all the individual designs for the design of the transmitter system as shown in
Figure 1 previously and carry out the required simulations. Finally, input the data from those
simulations into the MATLAB programs and carry out the comparisons between the experimental
and the CST design simulations to confirm that the system actually provides directional modulation
and enhanced wireless data security.
Progress
1) Completed the literature review of many topics relevant to this project including directional
modulation, Butler Matrix, microstrip technology, half wave dipole, array factor, phased arrays,
antenna radiation theory, M-Ary signalling etc.
2) Mastered the use of MATLAB for the simulations required in this project and of Computer
Simulation Technology (CST) software required for the design and simulation of the transmitter
system.
3) Wrote a MATLAB program to simulate the Array Factor of a four element linear array. A change
in the array factor is observed, as a function of the transmission angle, when the elements are
provided with progressive phase shifts, as shown below in Figures 3 and 4.
0 20 40 60 80 100 120 140 160 180
0
0.5
1
1.5
2
2.5
3
3.5
4
Figure 3: Array Factor (Theta) - No Progressive Phase Shifts
EEE"360" Interim"Report"
5"
0 20 40 60 80 100 120 140 160 180
0
0.5
1
1.5
2
2.5
Figure 4: Array Factor (Theta) - Progressive Phase Shifts: 0,90,0,90
0 20 40 60 80 100 120 140 160 180
0
0.5
1
1.5
2
2.5
3
3.5
4
Figure 5: Array Factor (Theta) - for all four excited inputs of Butler Matrix - Different Phase Shifts & Amplitude
Excitations
4) Undertook the design and simulation of the Half Wave Dipole antenna as shown below in Figures
6, 7 & 8. Four of these dipoles will be combined in the future to produce a design of the four element
linear array.
Figure 6: CST design of a Half Wave Dipole Antenna with a Discrete Port
EEE"360" Interim"Report"
6"
Figure 7: Return Loss S-Parameter showing the antenna operation at 2.45GHz
Figure 8: Farfield Simulation of Antenna with Directivity = 2.176 dBi
5) Undertook the design and simulation of the components of a Butler Matrix. These components
will be combined in the future to produce a final design of a 4x4 Butler Matrix.
i) 90 Degree Hybrid Coupler
A Hybrid coupler is used to generate two signals at its two outputs, which are ideally 90 degrees out
of phase with each other and this is shown, with the difference in phases between the two ports at
2.45GHz to be approximately (54 – (-32)) = 86 Degrees, in Figures 10 and 11 on the next page. Also,
the power applied to its input port is equally distributed between its two output ports, which can be
shown in Figure 12 on page 8.
EEE"360" Interim"Report"
7"
Figure 9: CST Design of a 90 Degree Hybrid Coupler
Figure 10: Port 2 Phase at 2.45GHz = 54 Degrees
Figure 11: Port 3 Phase at 2.45GHz = -32 Degrees
EEE"360" Interim"Report"
8"
Figure 12: Power from Input Port 1(1) equally distributed between two Output Ports 2(1) & 2(2)
(Two Multipin Ports shown here)
ii) -45 Degrees Phase Shifter
This was implemented using a microstrip line as shown below in Figure 13.
Figure 13: CST design of a -45 Degree Phase Shifter
iii) 0dB Crossover
The Crossover provides an approximately -2dB gain at Port 3 (ideal 0dB), which is as shown in
Figure 15 on the next page.
EEE"360" Interim"Report"
9"
Figure 14: CST design of a Crossover
Figure 15: -2dB gain at Port 3
Figure 16: Power flow from Port 1 to Port 3
EEE"360" Interim"Report"
10"
Revised Gantt Chart
A | Literature Review
B | Research
C | Array Factor Simulation Using MATLAB
D | Learning Computer Simulation Technology (CST)
E | Design & Simulation Of Butler Matrix Components & Dipole Antenna
F | Complete Design & Simulation Of Transmitter System
G | Constellation Diagram & Bit Error Rate Simulation Using MATLAB
H | Improve Design & Carry Out Further Simulations
I | Evaluate Theoretical & CST Simulations
Component 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A
B
C
D
E
F
G
H
I

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110232799-Final Year Thesis

  • 1. Department Of Electronic & Electrical Engineering Direction Dependent Antenna Modulation using a Butler Matrix & a Four Element Array By Bhavishya Sehgal April 2015 A thesis submitted in partial fulfillment of the requirements for the degree of Bachelors Of Engineering in Electronic & Communications with a Year in Industry. Word Count: 7250
  • 2. 30/04/2015 00:07 Page 1 of 2https://foe-coversheet.group.shef.ac.uk/index.php EEE360-003 110232799 Individual Assessed Work Coversheet Assessment Code: EEE360/3 Description: Final Report Staff Member Responsible: Mr Neil Powell Due Date: 30-04-2015 16:00:00 Student Registration Number: 110232799 Assessment Code: EEE360-003 Word Count: 7250 I certify that the attached is all my own work, except where specifically stated and confirm that I have read and understood the University's rules relating to plagiarism. I understand that the Department reserves the right to run spot checks on all coursework using plagiarism software.
  • 3. I CHAPTER 0 Abstract Direction Dependent Antenna Modulation aims to provide enhanced wireless data communications (physical layer) security by carrying out modulation at the antenna level to achieve M-level modulation as a function of transmission angle. This enables the transmitter to transmit a certain M-ary constellation in the desired receiver location, however corrupt the same in both power and shape in other undesired directions. An effective way to achieve it is by providing progressive phase shifts to the elements of an antenna array at each symbol transmission during a single transmission period to obtain a radiation pattern, which is a function of the transmission angle. This concept is similar to that of phased arrays but different in the sense that these progressive phase shifts are varied at each symbol transmission. The work carried out in this thesis aims to implement directional modulation using an alternative unique transmitter system consisting of a beam-forming network, the 4x4 Butler Matrix, which provides four outputs out of phase with each other for every excited input port or a combination of input ports. These phased outputs excite the four elements of a linear dipole antenna array and produce a varied radiation pattern at each symbol transmission, thus achieving the aim, i.e. M-Level modulation as a function of transmission angle. This thesis initially aims to provide a thorough theoretical background to the reader on the Butler Matrix, the antenna array and the concept of directional modulation (DM). Further, it details the design and simulations of the 4x4 Butler Matrix and the Dipole Antenna Array using Computer Simulation Technology. Using the theoretical background, the thesis firstly details the MATLAB simulations of Array Factor and then that of Constellation diagrams showing M-ary modulation schemes achieved using a Butler Matrix, which are direction dependent and improve data communications security. Finally, along with a brief conclusion, important results are thoroughly discussed and important recommendations are provided for future research and development of directional modulation transmitter systems. The 4x4 Butler Matrix is implemented in copper microstrip on a FR4 substrate, a design considerably cheaper than an n-bit phase shifter. The S-Parameter simulations of its magnitude and phase show desirable but imperfect results. The Four Element Linear Dipole Antenna Array is implemented in λ/2 copper wires. Its farfield simulation, compared with a single antenna element, shows a higher directivity, gain and reduced sidelobe levels. More importantly, its farfield shows the effect of phase shifts on the variation of its radiation pattern as well. Moreover, the Array Factor simulations of the antenna array show the considerable effect of amplitude excitations and phase shifts to the variation of its radiation pattern. Finally, assuming the input RF signal from the Voltage Crystal Oscillator (VCO) has a constant amplitude (1) and phase (0°) at every symbol transmission, a 14-ary modulation scheme was achieved using all the possible input port combinations of a 4x4 Butler Matrix. The best constellation was achieved at -60° from boresight, with further simulations showing the change of this constellation, in both power level and shape, with change in the transmission angle. These simulations also intuitively show a higher error rate in the undesired directions as compared to a conventional system when subject to Additive White Gaussian Noise (AWGN). This proved the fact that directional modulation can be achieved using a Butler Matrix and that these DM constellations achieved have an ability to improve wireless data communications security.
  • 4. II List Of Figures Figure 1: 4x4 Butler Matrix Block Diagram Figure 2: 90 Degree Hybrid Coupler Structure Figure 3: 0dB Crossover Structure Figure 4: 4 Element Linear Antenna Array Figure 5: Conventional Transmitter Block Diagram Figure 6: Conventional Transmission Scheme Figure 7: Directional Modulation Transmitter Block Diagram Figure 8: Directional Modulation Transmission Scheme Figure 9: Conventional QPSK in Desired Receiver Direction (left) & in Eavesdropper Direction (Right) with AWGN Figure 10: Directional Modulation QPSK in Desired Receiver Direction (left) & Eavesdropper Direction (right) with AWGN Figure 11: Ideal Directional Modulation Error Rate Curve as a Function of Transmission Angle Figure 12: 90 Degree/3dB Hybrid Coupler CST Design with Multipin Waveguide Ports Figure 13: Hybrid Coupler S-Parameter Magnitude Simulation Figure 14: Hybrid Coupler S-Parameter Phase Simulation Figure 15: Hybrid Coupler Power Flow Simulation Figure 16: 0dB Crossover CST Design with Waveguide Ports Figure 17: Crossover S-Parameter Magnitude Simulation Figure 18: Crossover Power Flow Simulation Figure 19: -45 Degree Phase Shifter CST Design Figure 20: Phase Shifter S-Parameter Phase Simulation Figure 21: 4x4 Butler Matrix CST Design with Multipin Waveguide Ports Figure 22: Butler Matrix S-Parameter Magnitude Simulation for Input Port 3 Excitation Figure 23: Butler Matrix S-Parameter Phase Simulation for Input Port 3 Excitation Figure 24: Butler Matrix Power Flow Simulation for All Input Ports Excitation Figure 25: Four Element Linear Dipole Antenna Array CST Design Figure 26: Dipole Antenna Farfield Simulation Figure 27: Linear Dipole Antenna Array Farfield (left) & 2-D Polar Plot (right) Simulation without Phase Shifts Figure 28: Linear Dipole Antenna Array Farfield (left) & 2-D Polar Plot (right) Simulation with Progressive Phase Shifts Figure 29: Array Factor Simulation with Constant Amplitude Excitations and Phase Shifts Figure 30: Array Factor Simulation with Varying Amplitude Excitations and Constant Phase Shifts Figure 31: Array Factor Simulation with Constant Amplitude Excitations and Progressive Phase Shifts Figure 32: Array Factor Simulation (left) & Constellation Point at Boresight Simulation (right) to prove Model Validity Figure 33: Directional Modulation Transmitter System using a 4x4 Butler Matrix Figure 34: 14-ary Constellation Simulation at -60 Degrees from Boresight (Desired Receiver Direction)
  • 5. III Figure 35: 14-ary Constellation Simulation at -30 Degrees from Boresight (Eavesdropper Direction) Figure 36: 14-ary Constellation Simulation in Desired Direction with AWGN & SNR=10 Figure 37: 14-ary Constellation Simulation in Desired Direction with AWGN & SNR=20 Figure 38: 4-ary Constellation Simulation at -70 Degrees from Boresight (Desired Receiver Direction) Figure 39: 4-ary Constellation Simulation at -40 Degrees from Boresight (Eavesdropper Direction) showing change in Shape of Constellation Figure 40: Constellation Point Simulation from -90 Degrees from Boresight to Boresight Figure 41: 4-ary Constellation Simulation at Desired Direction with AWGN & SNR=10 Figure 42: 4-ary Constellation Simulation at Eavesdropper Direction with AWGN & SNR=10 Figure 43: 4-ary Conventional Constellation Simulation at Boresight (Desired Receiver Direction) Figure 44: 4-ary Conventional Constellation Simulation at 20 Degrees from Boresight (Eavesdropper Direction) showing Change in only Power Level & Phase of Constellation Figure 45: 4-ary Conventional Constellation Simulation at Desired Direction with AWGN & SNR=10 Figure 46: 4-ary Conventional Constellation Simulation at Eavesdropper Direction with AWGN & SNR=10 Figure 47: 8-ary Constellation Simulation at -70 Degrees from Boresight (Desired Receiver Direction) Figure 48: 8-ary Constellation Simulation at -40 Degrees from Boresight (Eavesdropper Direction) Figure 49: 8-ary Constellation Simulation at Desired Direction with AWGN & SNR=15 Figure 50: 8-ary Constellation Simulation at Eavesdropper Direction with AWGN & SNR=15 Figure 51: Recommended Horizontal Crossover Design with Wider Central Stripline Figure 52: Modified Directional Modulation Transmitter System using a 4x4 Butler Matrix with a Control Unit for VCO Signal Figure 53: Butler Matrix S-Parameter Magnitude Simulation for Input Port 1 Excitation Figure 54: Butler Matrix S-Parameter Magnitude Simulation for Input Port 2 Excitation Figure 55: Butler Matrix S-Parameter Magnitude Simulation for Input Port 4 Excitation Figure 56: Butler Matrix S-Parameter Phase Simulation for Input Port 1 Excitation Figure 57: Butler Matrix S-Parameter Phase Simulation for Input Port 2 Excitation Figure 58: Butler Matrix S-Parameter Phase Simulation for Input Port 4 Excitation Figure 59: Dipole Antenna Array S-Parameter Simulation Figure 60: Dipole Antenna CST Design Figure 61: Dipole Antenna S-Parameter Simulation
  • 6. IV List Of Tables Table 1: Gantt Chart Table 2: Progressive Phase Shifts with each Excited Input Port of a 4x4 Butler Matrix Table 3: Microstrip Parameter Dimensions Table 4: Return Loss & Insertion Loss for Each Excited Input Port of a 4x4 Butler Matrix Table 5: Output Port Phases for each Excited Input Port of a 4x4 Butler Matrix Table 6: Phase Difference b/w Consecutive Output Ports for each Excited Input Port of a 4x4 Butler Matrix. Error in the Progressive Phase Shifts compared with the Theoretical Target Table 7: Dipole Antenna Array Parameter Dimensions Table 8: Theoretical Output Phases & Amplitude Excitations for each or combination of Excited Input Ports of a 4x4 Butler Matrix Table 9: Best 8 Input Port Combinations of a 4x4 Butler Matrix Table 10: Best 4 Input Port Combinations of a 4x4 Butler Matrix Table 11: Phase of 4-ary Constellation Points (from Desired Receiver Direction at - 70 Degrees from Boresight)
  • 7. V TABLE OF CONTENTS CHAPTER 0 Abstract………………………………………………………………………….I List Of Figures………………………………………………………………….II List Of Tables.....................................................................................................IV CHAPTER 1 I. Introduction……………………………………………………………..1 II. Literature Review……………………………………………………….2 III. Aims & Specifications…………………………………………………..3 CHAPTER 2 IV. Theoretical Background………………………………………………..5 i. The Butler Matrix………………………………………………5 ii. Antenna Array…………………………………………………..7 iii. Direction Dependent Antenna Modulation……………………8 CHAPTER 3 V. CST Design & Simulations……………………………………………13 i. 4x4 Butler Matrix……………………………………………...13 ii. Four Element Linear Dipole Array…………………………..21 VI. MATLAB Simulations………………………………………………...23 i. Array Factor…………………………………………………...24 ii. M-ary Constellations…………………………………………..25 CHAPTER 4 VII. Discussion……………………………………………………………....37 VIII. Conclusion……………………………………………………………...38 IX. Recommendations……………………………………………………..38 CHAPTER 5 X. Bibliography…………………………………………………………...40 XI. Appendices………………………………………………………………i i. Appendix A: MATLAB Code…………………………………..i ii. Appendix B: Miscellaneous……………………………………vi iii. Interim Report………………………………………………….xi
  • 8. 1 CHAPTER 1 I. Introduction With the advent of wireless communications technology and with it the immense need for data security because of its broadcast nature, there is an on-going extensive research and development of transmitter systems that are/would be capable of providing secure data communications between the transmitter and the desired receiver. Direction dependent antenna modulation or directional modulation or direct antenna modulation has proved to be a significant concept to achieve wireless data communications security at the physical level, i.e. physical layer security. The basic principle behind directional modulation is that while ensuring modulation is taking place at the antenna level, not the baseband, a certain constellation with a low error rate is achieved in the desired receiver direction, however it aims to scramble the same constellation with a high error rate in all other undesired directions. This is highly achievable if an M-ary constellation is obtained, which is a function of transmission angle. [1] – [4] Since the late 2000’s, some methods to achieve this have been proposed and a few of them that have been briefly discussed in the literature review section of this chapter. One such useful method proposes the use of an antenna array with phase shifters to achieve a varied radiation pattern at each symbol transmission, i.e. providing different progressive phase shifts to the elements of an antenna array at every symbol transmission, while ensuring that the RF signal is fed directly to these phase shifters, which in turn modulate the signal at the antenna level. [3] This is in contrast to conventional transmitter systems, where modulation takes place at the baseband, which is then converted to RF and transmitted over a fixed radiation pattern at each symbol transmission. This design does not allow any angular dependency and only the power level of the constellation reduces at a direction away from the desired receiver location, which can be easily detected by a sensitive receiver. The methodology to achieve directional modulation proposed in this thesis works on the same principle as above, however, instead of using n-bit IC phase shifters, which cost approximately £2-4k each and have an exhaustive design process, the aim is to achieve the same with the use of a beam forming network, i.e. a 4x4 Butler Matrix, which can be easily implemented in microstrip on a substrate, which in turn costs the same as that of a printed circuit board. The structure of this thesis has been designed in such a way to provide a thorough understanding of this topic to the reader. In addition to the literature reviewed by the author, the latter of this chapter details the aims and specifications of the work included in this thesis. Chapter 2 solely explains the theoretical background required to implement directional modulation using a Butler Matrix and a four-element array. Furthermore, chapter 3 focuses on the design and simulations of the above essential components of this transmitter system using state-of-the-art CAD software, Computer Simulation Technology. Moreover, MATLAB is used for signal processing and simulating M-ary constellations, which are essential to prove that directional modulation can be achieved using a 4x4 Butler Matrix.
  • 9. 2 Finally, chapter 4 provides the reader with a detailed discussion of the observations made by the author over the period of this project, a brief conclusion and a few recommendations for future work that could be carried out for further research and development in directional modulation transmitter systems. II. Literature Review Directional Modulation i. [1] This paper introduces the concept of Near Field Direct Antenna Modulation (NFDAM), where, the reflectors of an antenna array are excited in the near field of the radiating dipole antenna. The RF signal is then modulated at the antenna level using different combinations of switches or varactors, implemented on the reflectors, at every symbol transmission. This allowed obtaining varying signal radiation patterns, which were dependent on the transmission angle, thus improving data security and contributing to the start of extensive research in directional modulation. ii. [2] In this paper, using the concept of phased arrays, it is shown that by shifting the phase of the elements of an antenna array at every symbol transmission, QPSK constellations can be corrupted in undesired directions. Also, optimisation or genetic algorithms were used to decide the best combination of phase shifts that would provide a high error rate in the undesired directions and a low error rate in the desired receiver direction. This directional modulation transmitter system was compared with a conventional transmitter system to show the improvement in wireless data communications security achieved with directional modulation. iii. [3] This paper utilizes the same concept as in ii, however the phase shifts have been provided using 2-bit phase shifters for a two-element array directional modulation transmitter system. However, due to the high level of difficulty in implementing optimisation algorithms, phase shift assumptions were made here to simulate a 16-ary constellation, which is a function of the transmission angle. Also, a high error rate was observed at directions away from the desired receiver direction while a low error rate at the desired receiver direction providing a narrow error rate curve, which is a function of transmission angle. iv. [4] In this paper, published recently in 2015, directional modulation has been experimentally achieved by using a 13x13 Fourier Rotman Lens and a 13 Element Patch Antenna Array. The work carried out in this thesis takes inspiration from all of the above research in directional modulation. It aims to provide directional modulation using the concept of phased arrays, however, instead of using n-bit phase shifters, the work in this thesis aims to implement the same by using different input port combinations of a 4x4 Butler Matrix to provide with a different set of phase shifts and amplitude excitations, at each symbol transmission, to the elements of a linear dipole antenna array.
  • 10. 3 Butler Matrix [5] In this paper, a 4x4 Butler Matrix operating at 5.2GHz has been designed (in microstrip and FR4 substrate) and simulated using CAD software SONNET for WLAN applications due to its beam steering capability, easy design and cost effectiveness. A thorough theoretical background on the Butler Matrix and its components has been provided along with essential set of equations to design the Hybrid Coupler, Crossover and the Phase Shifter. Finally, the design has been simulated to show the desired performance. Although, further review [6] [7] was carried out to understand the concept, design and use of a Butler Matrix, the above paper was sufficient to design and simulate the 4x4 Butler Matrix. III. Aims & Specifications The aim of the work carried out in this thesis is to achieve M-Level modulation as a function of the transmission angle, i.e. Direction Dependent Antenna Modulation using a 4x4 Butler Matrix and a 4 Element Linear Dipole Antenna Array. MATLAB Simulations i. To simulate the Array Factor, as a function of the transmission angle, of the four element linear array. This is required to observe the variation in the Array Factor, hence, a variation in the radiation pattern of the array as a function of the transmission angle, with the change in phase shifts and amplitude excitations to the elements of an antenna array. ii. To simulate the varying radiated signals as symbols on the Constellation Diagrams, i.e. to achieve M-ary Constellations using a 4x4 Butler Matrix. This is essential to further observe the direction dependency of the transmitted symbols on the constellation diagram and thus, prove direction dependent antenna modulation can be achieved using a 4x4 Butler Matrix. iii. To further observe this system’s enhanced data communications security in comparison with conventional systems, with a high error rate in undesired directions and a low error rate in the desired receiver direction when subject to AWGN. CST Design & Simulations i. CAD software: Computer Simulation Technology (CST). ii. System operating at 2.45GHz. iii. Copper Microstrip for 4x4 Butler Matrix with thickness, Mt=0.1mm and λ/2 Copper Wire for Linear Dipole Antenna Array. iv. FR4 Substrate for Butler Matrix with thickness, h=1.6mm and Dielectric constant, !!=4.3.
  • 11. 4 v. To design and simulate individual components of a 4x4 Butler Matrix, i.e. the 90° Hybrid Coupler, the 0dB Crossover and the -45° Phase Shifter. Then, combine these components for the final design of a 4x4 Butler Matrix and carry out the required S-Parameter and Power Flow simulations. vi. To design and simulate a λ/2 Dipole Antenna. Then, combine four of these antennas at a distance of λ/2 to complete the design of a Four Element Linear Dipole Antenna Array and carry out its Farfield and S-Parameter simulations. Gantt Chart A | Literature Review B | Research C | Array Factor Simulation using MATLAB D | Computer Simulation Technology (CST) Tutorial E | Design & Simulation Of Butler Matrix Components & Dipole Antenna using CST F | Complete Design & Simulations of a 4x4 Butler Matrix and Linear Dipole Antenna Array using CST G | M-ary Constellation Simulation using MATLAB H | Prepare Presentation I | Prepare Thesis Table 1: Gantt Chart Component 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 A B C D E F G H I
  • 12. 5 CHAPTER 2 IV. Theoretical Background i. The Butler Matrix A Butler Matrix is a NxN passive beam-forming network, which performs a Fast Fourier Transform (FFT) on its input to produce N outputs [6], which, for each excited input port, has a linear progressive phase shift as shown in Table 2 [7]. The N outputs then excite a N-element antenna array to produce N overlapping orthogonal beams. This enables the Butler Matrix to electronically steer the beams for which it is widely used in the communications industry. [5] [7] However, in context to this thesis, since the Butler Matrix has this great ability to provide varying phase shifts to the elements of an antenna array, it can essentially be used for providing directional modulation, which has been further discussed and proved in the latter part of chapter 3. Table 2: Progressive Phase Shifts with each Excited Input Port of a 4x4 Butler Matrix Excited Input Port Progressive Phase Shift 1 -45° 2 +135° 3 -135° 4 +45° A NxN Butler Matrix consists of ! 2 !"#!! 90°/3dB Hybrid Couplers, ! 2 (!"#!! − 1) Phase Shifters & a few 0dB Crossovers. [5] Hence, as shown in Figure 1 below, the 4x4 Butler Matrix consists of four Hybrid Couplers, two -45° Phase Shifters and two Crossovers. These components are essential as it allows it to excite the elements of an antenna array with the progressive phase shifts. Moreover, Figure 1 shows the process by which the 4x4 Butler Matrix can achieve 4 outputs out of phase with each other for every excited input port. Assuming that the first input port of the Butler Matrix is excited with a signal of amplitude 1 and phase 0°, then it provides four output signals, which are out of phase with each other by -45° and have an attenuated amplitude. To further understand how this is achieved, the individual components of a Butler Matrix have been described in detail. Figure 1: 4x4 Butler Matrix Block Diagram
  • 13. 6 a. Hybrid Coupler Figure 2: 90 Degree Hybrid Coupler Structure The 90° Hybrid Coupler, implemented in microstrip of length λ/4 and constructed using two striplines with characteristic impedance,!!!=50Ω & two striplines with !!/ 2=35.4Ω, has four ports as shown Figure 2 with Port 1 or 4 being for the input. It is generally used due to its ability to generate two equi-power output signals (with 3dB attenuation) at Port 2 & Port 3 (coupled) with 90° phase difference between them. Port 4 or 1 is isolated (no power) depending on which Port is excited. [5] b. Crossover Figure 3: 0dB Crossover Structure The Crossover, implemented in microstrip of length λ/4 and constructed using striplines with characteristic impedance,!!!=50Ω, has four ports as shown in Figure 3, It is used to transfer the signal from Port 1 or 4 to Port 3 or 2 respectively without any change in the power level or the phase of the signal. [5] c. Phase Shifter The Phase Shifter, implemented in microstrip of length, ! =! !∗! !! where ! is the value of phase shift required. [5] The design and simulation of the 4x4 Butler Matrix and its components using CST has been further discussed in chapter 3.
  • 14. 7 ii. Antenna Array This thesis is concerned with the concept of only linear or 1-D antenna arrays. These arrays consist of N antenna elements, spaced at a distance d as shown in Figure 4. [9] Figure 4: 4 Element Linear Antenna Array Antenna arrays are used as they provide a higher directivity, gain and reduced sidelobe levels as compared to a single element. These characteristics have been shown and discussed in chapter 3. The main lobe can be steered depending on the phase shifts provided to the array, thus forming a phased array, which in turn forms an essential concept in directional modulation, where, these phase shifts are varied as well but at every symbol transmission to obtain a direction dependent M-ary constellation. The overall farfield of the array is the summation of each element’s field and assuming all elements are identical and isotropic, it can be also calculated by multiplying the field of a single element with the Array Factor, a property of the array, which depends on its geometry. [9] The Array Factor of a N element linear antenna array is given by [9], !" ! = !!!![ !!! !"#$%&!!!]! !!! (1), where, !: Elevation Angle !!: Amplitude Excitation N: Number of Elements k: Propagation Constant = 2π/λ d: Spacing between Elements !!: Phase Shift With respect to this thesis, the number of elements of the antenna array has been set to, N=4 as a 4x4 Butler Matrix is being used to excite it. Also, the spacing between elements has been set to λ/2 as it sufficiently provides a narrow main beam and reduced sidelobe levels.
  • 15. 8 The Array factor can be re-written as, !" ! = !!!![ !!! !"#$%!!!]! !!! (2) The Array Factor provides a method to visualize the change in the variation of radiation pattern as a function of transmission angle by providing different combinations of amplitude excitations and phase shifts to the elements of the array. These simulations have been further discussed in chapter 3. Furthermore, in order to synthesize the complex radiation pattern of a transmitted signal as a complex digital symbol with magnitude and phase, which in turn can be observed as a complex constellation point on the constellation diagram (or the real- imaginary coordinate system), assuming a line-of-sight (LOS) communications exists between the transmitter and m receivers in m directions, this digital symbol, x(t), is obtained in m directions at a specific time t, using the following equation [2], !!! ! ⋮ !!! ! = !!! , 1 ⋯ !!! , ! ⋮ ⋱ ⋮ !!! , 1 ⋯ !!! , ! ∗! !! ! ⋮ !! ! (3), where, !!! ! : Symbol in direction m !!! , !: Field of element n in direction m !! ! : Signal excitation of element n, given by, !! ! = !!!!!! (4), where, [2] !!: Amplitude excitation !!: Phase shift iii. Direction Dependent Antenna Modulation Direction Dependent Antenna Modulation is a M-Level modulation, which is direction dependent as the modulation has been implemented at the antenna level, not the baseband. The best way to introduce the concept of a directional modulation transmitter system is by comparing it with a conventional modulation transmitter system. In a conventional transmitter system as shown in Figure 5, data modulation takes place at the baseband level, thus, a modulated signal is first converted into RF and then transmitted in all directions with a fixed radiation pattern. This results in the same data or constellation being transmitted in all directions with a lower power levels in unwanted directions, which can still be detected by a sensitive receiver. [1] – [3]
  • 16. 9 Figure 5: Conventional Transmitter Block Diagram This conventional transmission scheme can be better understood from Figure 6, where a QPSK constellation is transmitted with a fixed radiation pattern, which in turn provides with the same constellation in all directions but with reduced power levels. Figure 6: Conventional Transmission Scheme
  • 17. 10 On the other hand, in a directional modulation transmitter system as shown in Figure 7, modulation is imparted at the antenna level by providing varying phase shifts to the elements of an array at each symbol transmission. This results in the modulation being dependent on the transmission angle as the signal is transmitted with a time varying radiation field at each symbol transmission. Thus, data can be transmitted in the correct direction with a low error rate, and can be corrupted in any undesired direction in both power level and shape with a high error rate. This makes it a very difficult job for sensitive receivers in unwanted directions to detect the signal and sometimes even impossible. [2] [3] The directional modulation scheme shown in Figure 8 provides a better understanding to the same. Figure 7: Directional Modulation Transmitter Block Diagram Figure 8: Directional Modulation Transmission Scheme
  • 18. 11 A high error rate in unwanted directions can be achieved by obtaining a constellation point on the constellation, which moves a considerable distance in directions away from the desired receiver direction. In doing so, with the constellation changing in both shape and power levels, when subject to Additive White Gaussian Noise (AWGN), a received signal has a high probability to be detected as an error. [3] Comparing Figure 9 and Figure 10, it can be inferred that both conventional and DM transmitter systems provide a low error rate in the desired directions, however, in the undesired direction, the error rate provided by the conventional transmitter is lower than the error rate provided by the directional transmitter due to its change in shape, which in turn is due to the fact that the constellation is direction dependent. [2] [3] Figure 9: Conventional QPSK in Desired Receiver Direction (left) & in Eavesdropper Direction (Right) with AWGN Figure10: Directional Modulation QPSK in Desired Receiver Direction (left) & Eavesdropper Direction (right) with AWGN
  • 19. 12 Figure 11 shows the ideal error rate curve as a function of transmission angle. With directional modulation, this narrow error rate curve can be achieved, with a low error rate in the undesired direction and a high error rate elsewhere. [2] [3] Figure 11: Ideal Directional Modulation Error Rate Curve as a Function of Transmission Angle To determine the probability of a received constellation point is an error, an algorithm based on minimum distance decoding can be implemented. [3] Here, firstly, the Euclidean distance is calculated between any received constellation point and the points on the transmitted constellation. Then, this received constellation point is decoded as a constellation point to which it is closest to and compared with the constellation point that was originally transmitted. Finally, if these two points don't correlate then it can be inferred that the receiver has detected a signal with error. [8] To simulate the error rate as shown in Figure 11, using minimum distance decoding, the following equation for the symbol error rate [8] could be taken into account as well. !! = !!"#$!!( !!"# !!! ) (5), where, !!"#$ is the largest number of nearest neighbours, !!"# is the minimum Euclidean distance in the constellation, Q (x) is the complimentary Gaussian function and !! is the noise power spectral density.
  • 20. 13 CHAPTER 3 V. CST Design & Simulations Computer Simulation Technology (CST) was used to design a 4x4 Butler Matrix (in copper microstrip). Thereafter, Waveguide ports were implemented to the design to carry out its S-Parameter and Power Flow simulations. Moreover, a Four Element Linear Dipole Antenna Array was designed using copper wire. Discrete ports were then implemented to the design to simulate the array for its Farfield and S-Parameters. i. 4X4 Butler Matrix The Butler Matrix, as described in chapter 2 was designed using state-of-the-art CAD software, Computer Simulation Technology. The 4X4 Butler Matrix was implemented in copper (annealed) microstrip on a FR4 substrate operating at 2.45 GHz. Initially, the individual components that form a Butler Matrix i.e. the 90°/3dB Hybrid Coupler, the 0dB Crossover and the -45° Phase Shifter were individually designed and simulated. Finally, these components were cascaded together to design and simulate the 4x4 Butler Matrix. a. 90°/3dB Hybrid Coupler Design The 90° Hybrid Coupler was constructed with two !! (50Ω) and two !!/ 2 (35.4Ω) transmission lines of length λ/4 shunt together as shown in Figure 12. [5] Figure 12: 90 Degree/3dB Hybrid Coupler CST Design with Multipin Waveguide Ports The width, W, of the two transmission lines was calculated using the following equations [5], !/ℎ = ! ! {! − 1 − log 2! − 1 + !!!! !!! log ! − 1 + 0.39 − !.!" !! } (6) ! = !"!! !! !! (7), where, h=1.6mm is the thickness of the FR4 substrate and !! = 4.3 is the dielectric constant of the FR4 substrate.
  • 21. 14 The length, L of the transmission lines was then calculated using the equation [5], ! = ! (4 ∗ ! ∗ !!"##) (8), where, c is the speed of light, f=2.45GHz is the operating frequency and !!"## is the effective dielectric constant. The derivation of the above equation for length, L, and the equation to calculate !!"## has been described in Appendix B. Using these equations, the values obtained for the above parameters are shown in Table 3. Table 3: Microstrip Parameter Dimensions Parameter Dimension Width, W, of 50Ω Stripline 4.1mm Width, W, of 35.4Ω Stripline 6.52mm !!"## (50Ω) 3.34 !!"## (35.4Ω) 3.48 Length, L of 50Ω Stripline 16.75mm Length, L of 50Ω Stripline 16.41mm Simulation The S-Parameters and the Power Flow of the Hybrid Coupler were simulated to observe desired results and proper functioning. The S-Parameter magnitude simulation in Figure 13 shows a high return loss of - 28.16dB and the two output ports have an insertion loss close to -3dB as desired. Figure 62: Hybrid Coupler S-Parameter Magnitude Simulation
  • 22. 15 The S-Parameter phase simulation in Figure 14 shows the difference in phase between its output ports is 53.77°-(-33.85) = 87.62°, which is very close to the desired phase difference of 90°. Figure 14: Hybrid Coupler S-Parameter Phase Simulation Figure 15: Hybrid Coupler Power Flow Simulation Finally, the Power Flow simulation in Figure 15 shows that attenuated power has been equally distributed between its output ports.
  • 23. 16 b. 0 dB Crossover Design Figure 16: 0dB Crossover CST Design with Waveguide Ports The 0dB Crossover was constructed only with 50Ω striplines using the same set of equations for length and width as for the Hybrid Coupler. Simulation The S-Parameter magnitude simulation in Figure 17 shows that the output port has a very low insertion loss of -2.43dB, which is in turn very close to the ideal value of 0dB. Figure 17: Crossover S-Parameter Magnitude Simulation
  • 24. 17 Figure 18: Crossover Power Flow Simulation Again, the Power Flow simulation in Figure 18 shows that most of the power has been transferred diagonally from Port 1 to Port 3 with very little attenuation. c. 45° Phase Shifter Design Figure 19: -45 Degree Phase Shifter CST Design The Phase Shifter was constructed using a single 50Ω transmission line of length, L, using the following equation [5], ! = ! (8 ∗ ! ∗ !!"##) (9) The derivation of the above equation is described in Appendix B.
  • 25. 18 Simulation The S-Parameter phase simulation in Figure 20 shows that a phase of -40.43° has been achieved, which is very close to the ideal phase requirement of -45°. Figure 20: Phase Shifter S-Parameter Phase Simulation d. 4x4 Butler Matrix Design Finally, the above components were then cascaded together to complete the design of the 4x4 Butler Matrix as shown in Figure 21. Figure 21: 4x4 Butler Matrix CST Design with Multipin Waveguide Ports
  • 26. 19 Simulation The S-Parameter magnitude and phase simulations for the 4x4 Butler Matrix have been shown in Figure 22 and 23 respectively, for when input port 3 is excited. The simulations for other input port excitations are provided in Appendix B. Figure 22: Butler Matrix S-Parameter Magnitude Simulation for Input Port 3 Excitation Figure 23: Butler Matrix S-Parameter Phase Simulation for Input Port 3 Excitation The output ports tend to show a low insertion loss and the input port shows a high return loss, however, the simulated results are not perfect and vary for every input and output port. The results for the S-Parameter magnitude simulations have been provided in Table 4, with undesired results highlighted. Similarly, the phase difference between the output ports shows a considerable error compared with the theoretical values [7] as can be seen in Table 6. Again, the S-Parameter phase simulation results have been provided in Table 5.
  • 27. 20 Table 4: Return Loss & Insertion Loss for Each Excited Input Port of a 4x4 Butler Matrix Excited Input Port Return Loss (dB) Insertion Loss o/p Port 1 (dB) Insertion Loss o/p Port 2 (dB) Insertion Loss o/p Port 3 (dB) Insertion Loss o/p Port 4 (dB) 1 -11.22 -16.80 -25.86 -2.67 -6.97 2 -25.76 -3.35 -6.92 -14.71 -8.01 3 -26.32 -8.02 -14.85 -6.94 -3.31 4 -11.13 -6.94 -2.67 -26.01 -17.29 Table 5: Output Port Phases for each Excited Input Port of a 4x4 Butler Matrix Excited Input Port Output Port 1 Phase (°) Output Port 2 Phase (°) Output Port 3 Phase (°) Output Port 4 Phase (°) 1 -100.44 -162.85 126.40 79.94 2 -112.48 124.42 3.19 165.19 3 164.32 5.25 124.83 -112.31 4 79.92 126.90 -155.58 -99.69 Table 6: Phase Difference b/w Consecutive Output Ports for each Excited Input Port of a 4x4 Butler Matrix. Error in the Progressive Phase Shifts compared with the Theoretical Target Excited Input Port Port 2- 1(°) Port 3- 2(°) Port 4- 3(°) Achieved Target (°) (Average) Theoretical Target (°) Error (°) 1 -62.41 -70.75 -46.46 -59.87 -45 14.87 2 236.9 238.77 162 212.56 +135 77.56 3 -159.07 -240.42 -237.14 -212.21 - 135 77.21 4 46.98 77.52 55.89 60.13 +45 15.13 In order to reduce the error in magnitude and phase of the Butler Matrix, a couple of recommendations for future implementation have been provided in chapter 5. However, as this design is not being implemented experimentally, what is more important is that from these results it can be inferred that for every excited input port a NxN Butler Matrix provides N outputs out of phase with each other.
  • 28. 21 Figure 24: Butler Matrix Power Flow Simulation for All Input Ports Excitation The Power Flow simulation in Figure 24 shows the power flow in a Butler Matrix when all input ports are excited. ii. Four Element Linear Antenna Array Initially, a λ/2 dipole antenna was designed using CST. The design and S-Parameter simulation is provided in Appendix B. Then four of these antennas were put together at a distance of λ/2 as specified earlier. This linear dipole antenna array was then simulated to observe its Farfield. Design Figure 25: Four Element Linear Dipole Antenna Array CST Design The 4 Element Linear Dipole Antenna shown in Figure 25 was designed by combining four Half-Wave Dipole Antennas. The dipole antenna operating at 2.45GHz was
  • 29. 22 designed using copper wires and the following equations [9] were used to calculate the parameters of the antenna. Length of antenna (half-wavelength), L= λ/2 = c/(2*f) (10), where c is the speed of light and f is the operating frequency. Radius of antenna, R= λ/1000 (11). Feeding gap of antenna, g= λ/400 (12). Using these equations, the antenna was designed with the parameters shown in Table 7. Table 7: Dipole Antenna Array Parameters Parameter Dimension (mm) Length 58.2 Radius 0.1225 Feeding Gap 0.29 These antennas were then used to form the linear array and were placed at distance, d= λ/2 from each other. Discrete ports were implemented to this array design, which was simulated to observe its S-Parameters and Farfield. Simulation A comparison has been carried out between a single antenna element and an antenna array using the Farfield simulations of the Dipole Antenna and the Linear Dipole Antenna Array. The Farfield of the single dipole antenna in Figure 26 shows a lower directivity and gain (2.18dB) as compared with the Farfield of the dipole antenna array in Figure 27, which shows a higher directivity and gain (9.4dB). Thus, the simulations prove that a higher directivity, gain and reduced sidelobe levels are obtained with antenna array. Figure 26: Dipole Antenna Farfield Simulation
  • 30. 23 Figure 27: Linear Dipole Antenna Array Farfield (left) & 2-D Polar Plot (right) Simulation without Phase Shifts Figure 28 shows the Farfield of an antenna array, which has been subject to progressive phase shifts unlike the Farfield in Figure 27. From the Farfield simulations it can be inferred that a variation in the radiation pattern is achieved by providing these phase shifts to the elements of an array, which can be observed more clearly from the Polar plots of the array’s farfields. Figure 28: Linear Dipole Antenna Array Farfield (left) & 2-D Polar Plot (right) Simulation with Progressive Phase Shifts V. MATLAB Simulations To visualise the effect of different sets of amplitude excitations and phase shifts on the radiation pattern of a 4-element linear antenna array, the Array Factor was simulated. Furthermore, digital symbols were simulated for different combination of amplitudes and phase shifts obtained from different input port combinations of a 4x4 Butler Matrix and represented as constellation points on the complex I-Q diagram to achieve M-ary modulation constellations, which are dependent on the transmission angle and thus, improve data communications security.
  • 31. 24 i. Array Factor The array factor of a 4-element linear array with each element spaced at a distance of λ/2 was simulated using MATLAB. Simulations were carried out for different combinations of amplitude excitations and phase shifts to observe the change brought in by these different combinations to the radiation pattern. These can be visualised for the three different cases shown below in Figures 29, 30 and 31. Case 1: Amplitude Excitations: 1, 1, 1, 1; Phase Shifts: 0, 0, 0, 0 Figure 29: Array Factor Simulation with Constant Amplitude Excitations and Phase Shifts Case 2: Amplitude Excitations: 0.5, 1, 1, 0.5; Phase Shifts: 0, 0, 0, 0 Figure 30: Array Factor Simulation with Varying Amplitude Excitations and Constant Phase Shifts
  • 32. 25 Case 3: Amplitude Excitations: 1, 1, 1, 1; Phase Shifts: 0, -45, -90, -135 Figure 31: Array Factor Simulation with Constant Amplitude Excitations and Progressive Phase Shifts ii. M-ary Constellations Before simulating the M-ary constellations, it was important to prove the validity of the model implemented using MATLAB to simulate complex symbols as constellation points on the complex constellation diagram. To prove this, for a set of amplitude excitations and phase shifts, the magnitude of the normalised constellation simulated was compared with the magnitude of the normalised array factor at boresight. Figure 32 shows the same, where the magnitude of the normalised array factor at boresight is equal to 0.6533, which in turn is equal to the magnitude of the simulated normalised constellation point, which is (−0.25)! + (−0.6036)! = 0.6533. Figure 32: Array Factor Simulation (left) & Constellation Point at Boresight Simulation (right) to prove Model Validity
  • 33. 26 Using different port combinations of a 4x4 Butler Matrix, which in turn provide a different set of amplitude excitations and phase shifts to the elements of an antenna array, M-ary constellations were simulated to prove that M-Level modulation as a function of transmission angle can be achieved using a Butler Matrix Directional Modulation Transmitter System, which is shown in Figure 33. Here, keeping the amplitude and phase of the signal generated from the Voltage Crystal Oscillator constant, at each symbol transmission, the signal is modulated at the antenna level using a certain combination of input ports, which provide a set of amplitude excitations and phase shifts to the elements of the antenna array. Figure 33: Directional Modulation Transmitter System using a 4x4 Butler Matrix Table 8 shows that for a constant input signal from the VCO, with amplitude 1 and phase 0°, for a combination of excited input ports of a 4x4 Butler Matrix, a set of amplitudes and phase shifts are obtained at the four output ports. Table 8: Theoretical Output Phases & Amplitude Excitations for each or combination of Excited Input Ports of a 4x4 Butler Matrix Excited i/p Port(s) o/p Port 1 Phase (°) o/p Port 2 Phase (°) o/p Port 3 Phase (°) o/p Port 4 Phase (°) Progressive Phase Shift (°) o/p Amplitude Excitation 1 -45 -90 -135 -180 -45 0.5 2 -135 0 +135 -90 +135 0.5 3 -90 +135 0 -135 -135 0.5 4 -180 -135 -90 -45 +45 0.5 1 & 2 -180 -90 0 +90 +90 1 1 & 3 -135 +45 -135 +45 -180 1 1 & 4 +135 +135 +135 +135 0 1 2 & 3 +135 +135 +135 +135 0 1 2 & 4 +45 -135 +45 -135 +180 1 3 & 4 +90 0 -90 -180 -90 1 1, 2 & 3 +90 +45 0 -45 -45 1.5 1, 2 & 4 0 +135 -90 +45 +135 1.5 1, 3 & 4 +45 -90 +135 0 -135 1.5 2, 3 & 4 -45 0 +45 +90 +45 1.5 1, 2, 3 & 4 -90 -90 -90 -90 0 2
  • 34. 27 Now, using all of these port combinations, i.e. modulating one signal using one port combination and then changing the input port combination at every symbol transmission, a 14-ary constellation was simulated at -60° from Boresight shown in Figure 34. If the transmitter system is modified in such a way that the input signal phase and amplitude can be changed at every symbol transmission than ideally an ∞- ary constellation can be achieved and this has been discussed briefly in chapter 4. Figure 34: 14-ary Constellation Simulation at -60 Degrees from Boresight (Desired Receiver Direction) Figure 35 shows the 14-ary constellation at -30° from Boresight. The constellation shows how the each constellation point from the desired receiver direction in Figure 34 has moved across the constellation, which has resulted in the change in shape of the constellation. Moreover, only 7 constellation points have been received at this undesired direction. This is an exciting result as these two 14-ary constellations at different directions have proved that the M-ary constellations achieved from a 4x4 Butler Matrix are direction dependent, i.e. M-Level Modulation has been achieved using a 4x4 Butler Matrix and more importantly, the loss of constellation points at the undesired direction makes it impossible for the eavesdropper to detect a signal. Figure 35: 14-ary Constellation Simulation at -30 Degrees from Boresight (Eavesdropper Direction)
  • 35. 28 Communication channels add Additive White Gaussian Noise (AWGN) to the transmitted signal and thus the received constellation is actually received with noise. The 14-ary constellation shown before has been subject to AWGN in Figure 36 with the Signal to Noise Ratio (SNR) set to 10. As can be seen from this figure, this addition of noise to the constellation has a negative impact on the error rate at the desired direction, as there is a high probability that the receiver may detect a received signal as another transmitted signal, which would result in an error. Figure 36: 14-ary Constellation Simulation in Desired Direction with AWGN & SNR=10 One way to improve the error rate at the desired direction would be to increase the value of SNR to 20 as shown in Figure 37, however, the simulated constellation anyways has few constellation points very close to each other, which would still result in an error with improved SNR. Figure 37: 14-ary Constellation Simulation in Desired Direction with AWGN & SNR=20
  • 36. 29 If this 14-ary scheme is not considered ideal for experimental work, alternative 8-ary and 4-ary constellations, which are used widely in industry, have been simulated using the best eight and four input port combinations of the 4x4 Butler Matrix respectively shown in Table 9 and 10 respectively. Table 9: Best 8 Input Port Combinations of a 4x4 Butler Matrix Excited i/p Port(s) o/p Port 1 Phase (°) o/p Port 2 Phase (°) o/p Port 3 Phase (°) o/p Port 4 Phase (°) Progressive Phase Shift (°) o/p Amplitude Excitation 1 & 3 -135 +45 -135 +45 -180 1 2 & 4 +45 -135 +45 -135 +180 1 3 & 4 +90 0 -90 -180 -90 1 1, 2 & 3 +90 +45 0 -45 -45 1.5 1, 2 & 4 0 +135 -90 +45 +135 1.5 1, 3 & 4 +45 -90 +135 0 -135 1.5 2, 3 & 4 -45 0 +45 +90 +45 1.5 1, 2, 3 & 4 -90 -90 -90 -90 0 2 Table 10: Best 4 Input Port Combinations of a 4x4 Butler Matrix Excited i/p Port(s) o/p Port 1 Phase (°) o/p Port 2 Phase (°) o/p Port 3 Phase (°) o/p Port 4 Phase (°) Progressive Phase Shift (°) o/p Amplitude Excitation 1 & 3 -135 +45 -135 +45 -180 1 2 & 4 +45 -135 +45 -135 +180 1 1, 2 & 4 0 +135 -90 +45 +135 1.5 1, 3 & 4 +45 -90 +135 0 -135 1.5
  • 37. 30 The desired 4-ary constellation shown in Figure 38 was achieved at a direction that is - 70° from boresight. The constellation points are further apart from each other as desired to provide low error rate at this direction. Figure 38: 4-ary Constellation Simulation at -70 Degrees from Boresight (Desired Receiver Direction) Figure 39 shows the 4-ary constellation at -40° from boresight, which is an undesired direction. Here, again, the constellation shows that the constellation points have moved (from the desired direction shown in Figure 38 previously) in such a way that the constellation has changed in both power level and shape. This would make detection by an eavesdropper a much harder prospect. Moreover, three points have moved much closer to each other, which would in turn provide with a higher error rate. Figure 39: 4-ary Constellation Simulation at -40 Degrees from Boresight (Eavesdropper Direction) showing change in Shape of Constellation
  • 38. 31 To further prove the direction dependency of this constellation, a single constellation point was simulated from a direction that is -90° from boresight to the boresight direction in increments of 10° as shown in Figure 40. The figure shows that the constellation point moves a considerable distance from the desired direction, which in turn scrambles the constellation, thus making it very difficult for an eavesdropper to detect the signal. Figure 40: Constellation Point Simulation from -90 Degrees from Boresight to Boresight As discussed before, the 4-ary constellation has been subject to AWGN as shown in Figure 41. With the constellation points being further apart from each other, the probability of a received signal being detected as another transmitted signal is negligible and thus this constellation provides a low error rate in the desired receiver direction. Figure 41: 4-ary Constellation Simulation at Desired Direction with AWGN & SNR=10
  • 39. 32 Since, the constellation at -40° from boresight had three points close to each other, when subjected to AWGN as shown in Figure 42, the error rate at this undesired direction would be very high. This is exactly what is desired and thus the 4-ary constellation achieved using a 4x4 Butler Matrix can easily be implemented experimentally to enhance wireless data communications security. Figure 42: 4-ary Constellation Simulation at Eavesdropper Direction with AWGN & SNR=10 To prove the fact that a directional modulation transmitter system provides enhanced security as compared to a conventional transmitter, the phases of the constellation points in Figure 38 (4-ary directional modulation constellation at desired receiver direction) were calculated as shown in Table 11 and used to modulate the signal at baseband, remembering the fact that the radiation pattern is now kept constant at every symbol transmission. This provided with a 4-ary conventional constellation as shown in Figure 43 in the desired Boresight direction. It can be inferred from this figure that the constellation obtained at the desired receiver direction for the conventional transmitter has a higher power level compared to that of a directional modulation transmitter in Figure 38, with all the constellation points further apart from each other. Table 11: Phase of 4-ary Constellation Points (from Desired Receiver Direction at -70 Degrees from Boresight) Constellation Point Phase (°) -0.1285 + j1.18 96.2 0.8574 + j0.4698 28.7 0.08056 – j0.7395 276.2 -0.8574 – j0.4698 208.7
  • 40. 33 Figure 43: 4-ary Conventional Constellation Simulation at Boresight (Desired Receiver Direction) However, Figure 44, which shows the conventional constellation at an undesired direction at 20°, it can be seen that only the power level and phase of constellation has changed but the shape of the constellation has remained the same. Thus a sensitive receiver in an undesired direction would be easily able to detect the signal. Figure 44: 4-ary Conventional Constellation Simulation at 20 Degrees from Boresight (Eavesdropper Direction) showing Change in only Power Level & Phase of Constellation
  • 41. 34 Again, subjecting the constellation to AWGN, in the desired direction as shown in Figure 45, a low error rate would be obtained. However, at an undesired direction, as shown in Figure 46, the constellation has not changed sufficiently enough to have a high error rate. This result is in total contrast to that of directional modulation, where a narrow error rate can be obtained with a high error rate in all undesired directions, as explained before in chapter 2. Figure 45: 4-ary Conventional Constellation Simulation at Desired Direction with AWGN & SNR=10 Figure 46: 4-ary Conventional Constellation Simulation at Eavesdropper Direction with AWGN & SNR=10
  • 42. 35 Finally, the 8-ary constellation was simulated as shown in Figure 47. The desired constellation was achieved at -70° from boresight, where the constellation points were furthest away from each other. Figure 47: 8-ary Constellation Simulation at -70 Degrees from Boresight (Desired Receiver Direction) Again, as shown in Figure 48 below, at an undesired direction, the constellation points have moved in a way that the entire constellation has scrambled due to change in both power level and shape. This would make signal detection a very hard prospect for the eavesdropper. Figure 48: 8-ary Constellation Simulation at -40 Degrees from Boresight (Eavesdropper Direction)
  • 43. 36 Finally, subjecting the constellation to AWGN, it is observed in Figures 49 and 50 that the error rate in the desired direction would considerably be lower to that in the undesired direction due to the movement of constellation points across the constellation such that they scramble the constellation and move very close to each other. Figure 49: 8-ary Constellation Simulation at Desired Direction with AWGN & SNR=15 Figure 50: 8-ary Constellation Simulation at Eavesdropper Direction with AWGN & SNR=15
  • 44. 37 CHAPTER 4 VII. Discussion A 4x4 Butler Matrix has been easily implemented in copper microstrip on a FR4 substrate using state-of-the-art CAD software CST, thus being an efficient and cheap alternative to n-bit phase shifters for use in a directional modulation transmitter systems. Although the simulated S-Parameters obtained were not ideal, they did provide sufficient knowledge about the performance of a 4x4 Butler Matrix. Such imperfections in microwave designs can be easily corrected or tweaked for use of this design in future experiments. Also, the 4 Element Linear Dipole Antenna was designed using copper wires (again a cheap, reliable and efficient component of the system) and simulated to observe its farfield. Firstly, its farfield, as compared to that of a single antenna element, showed a higher directivity, gain and reduced levels of sidelobes. More importantly, the farfield of this array showed a variation with change in phase shifts to its elements. Thus, all these properties of the antenna array make it an ideal and essential component for use in directional modulation. Moving on to the theoretical Array Factor simulations of an antenna array, it has been clearly shown that by providing different amplitude excitations and phase shifts to the antenna array, a time varying radiation pattern, which is dependent on the transmission angle is obtained. Thus, this proves that by changing the phase shifts of the elements at every signal synthesis or symbol transmission, an M-ary constellation of direction dependent symbols can be achieved. The final work carried out in this thesis proves that directional modulation can be and has been achieved using a 4x4 Butler Matrix, i.e. the M-ary constellations obtained using the different amplitude excitations and phase shifts from different port combinations of a Butler Matrix are direction dependent and the constellation points move sufficiently across the constellation as a function of transmission angle. This direction dependency of the constellation essentially provides with a certain constellation in the desired receiver direction with a low error rate, but provides a scrambled constellation in other undesired directions with a high error rate, again due to change in the shape of the constellation. It has been assumed that the input signal amplitude and phase to the power divider is kept constant at every symbol transmission. This provides with a maximum of a 14-ary constellation (best constellation at -60° from boresight), achieved using all the possible port combinations of a 4x4 Butler Matrix. This 14-ary constellation has been further proved to be direction dependent, changing in both power level and shape with transmission angle, thus providing a high error rate in the undesired directions when subject to AWGN. However, since the 14-ary constellation does seem to provide error at the desired receiver direction as well, the best 8 input port combinations of the Butler Matrix were used to provide with an 8-ary constellation at -70° from boresight. Similarly, the best 4 input port combinations were used to provide with a 4-ary constellation, which was then compared with a conventional 4-ary constellation, which in turn showed that a directional modulation transmitter provides enhanced wireless data security compared to a conventional transmitter. This direction dependency of the M-ary constellations was obtained, which proves that the 4x4 Butler Matrix is capable
  • 45. 38 of providing directional modulation to enhance wireless date communications security at the physical level. VIII. Conclusion Conclusively, a unique transmitter system, which provides M-level modulation as a function of transmission angle, i.e. Direction Dependent Antenna Modulation for physical layer security has been proposed in this thesis. The CST design and simulations of the most important components of this system, i.e. the 4x4 Butler Matrix and the 4 Element Linear Dipole Antenna Array have been carried out. The effect of amplitude excitations and phase shifts to the elements of a 4-element antenna array has been discussed with the theoretical concept of Array Factor. Finally, using different input port combinations of a 4x4 Butler Matrix at each symbol transmission, different M-ary constellations were simulated, which were then proved to be direction dependent i.e. changing in both power level and shape with the transmission angle, providing a high error rate in undesired directions and a low error rate in desired receiver direction. IX. Future Recommendations i. Firstly, the design of the 0dB Crossover of the 4x4 Butler Matrix implemented in this thesis should be replaced with the suggested one as shown in Figure 51. This design has a wider central stripline, which should decrease the error in the phase differences of the output ports. Also, further tweaking of the microwave design should be carried out to get near to perfect S-Parameter simulations. This is important if this design needs be implemented to carry out an experiment for directional modulation. Figure 51: Recommended Horizontal Crossover Design with Wider Central Stripline ii. Secondly, for the suggested input port combinations of the 4x4 Butler Matrix, which provided with direction dependent 14-ary, 8-ary and 4-ary constellations, an experiment with the directional modulation transmitter system design mentioned in this thesis should be carried out to prove directional modulation using a 4x4 Butler Matrix. iii. Thirdly, the error rate, as a function of transmission angle, as discussed in chapter 2, should be simulated using MATLAB for the suggested M-ary constellations when subject to AWGN. The idea behind this has been thoroughly discussed in this thesis and the direction dependence of the M-ary constellations intuitively shows that a low
  • 46. 39 error rate can be achieved at the desired receiver location and a high error rate in the undesired directions. iii. Finally, the directional modulation transmitter system design should be modified (as shown below) such that, the phase of the VCO should be varied at each symbol transmission. In an ideal case, this would provide an infinite M-ary constellation in a single transmission period, thus, an optimised or genetic algorithm [2] needs to implemented, which would chose the best input port combinations as well as the best sets of amplitudes and phase of the input signal in order to propose the best M-ary constellations that provide a high error rate in all unwanted directions and a low error rate in the desired receiver direction. Figure 52: Modified Directional Modulation Transmitter System using a 4x4 Butler Matrix with a Control Unit for VCO Signal
  • 47. 40 CHAPTER 5 X. Bibliography [1] A. Babakhani, D. B. Rutledge, and A. Hajimiri “Transmitter Architectures Based on Near-Field Direct Antenna Modulation,” IEEE JOURNAL OF SOLID-STATE CIRCUITS, vol. 43, no. 12, pp. 2674-2692, 2008 [2] M. P. Daly, and J. T. Bernhard, “Directional Modulation Technique for Phased Arrays,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol. 57, no. 9, pp. 2633-2640, September 2009. [3] H. Shi, A. Tennant: ‘Direction Dependent Antenna Modulation Using a Two Element Array’, Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP), Rome, Italy, pp. 812-815, 2011. [4] Y. Ding, Y. Zhang, and V. Fusco, “Fourier Rotman Lens Enabled Directional Modulation Transmitter,” International Journal of Antennas and Propagation, vol. 2015, Article ID 285986, pp. 1-13, 2015. [5] W. Bhowmik and S. Srivastava, “Optimum Design of a 4x4 Planar Butler Matrix Array for WLAN Application,” JOURNAL OF TELECOMMUNICATIONS, vol. 2, ISSUE 1, pp. 68-74, April 2010. [6] M. UENO, “A Systematic Design Formulation for Butler Matrix Applied FFT Algorithm,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol. AP- 29, no. 3, pp. 496-501, 1981. [7] S. Z. Ibrahim, M. K. A. Rahim: ‘Switched Beam Antenna using Omnidirectional Antenna Array’, In 2007 ASIA-PACIFIC CONFERENCE ON APPLIED ELECTROMAGNETICS PROCEEDINGS. Melaka, MALAYSIA, December 4-6, 2007, IEEE, pp. 1-4. [8] A. Goldsmith, “Wireless Communications”, 1st edition. New York, NY: Cambridge University Press. 2005. [9] C. A. Balanis, “Antenna Theory: Analysis and Design”, 3rd edition. New Jersey: John Wiley & Sons, INC. 2005. [10] Prof. Tzong-Lin Wu. Microwave Filter Design. [ONLINE] Available at: http://ntuemc.tw/upload/file/2011021716275842131.pdf. [Accessed 28 April 15].
  • 48. i XI. Appendices Appendix A: MATLAB Code Array Factor Code clc; N=4; %Number Of Elements j=sqrt(-1); An=ones(1,N); Ph=zeros(1,N); A=zeros(1,N); %Amplitude Excitations An(1,2)=1; An(1,3)=1; An(1,4)=1; An(1,5)=1; %Phase Shifts Ph(1,2)=0; Ph(1,3)=-45; Ph(1,4)=-90; Ph(1,5)=-135; for n=2:N+1 A(1,n)=An(1,n)*exp(j*(Ph(1,n)*pi/180)); End %Array Factor Simulation (as a function of Elevation Angle) AF=zeros(181,N); i=0; for theta=-90:90 i=i+1; for n=2:N+1 af(i,n)=A(1,n)*(exp(-j*(n-1)*pi*sin((theta)*pi/180))); [Equation (2)] af(i,n)=af(i,n) + af(i,n-1); end AF(i,n)=abs(af(i,n)); End %Plot of Normalised Array Factor with Elevation Angle figure; theta=-90:90; plot(theta,AF/N); xlabel('Elevation Angle'); ylabel('Normalised Array Factor'); title('Array Factor vs Elevation Angle'); grid on; hold on;
  • 49. ii M-ary Constellation Code clc; N=4; %Number Of Elements j=sqrt(-1); bits = 1000; %Number of Bits b=(randn(1,bits)>0.5); % Generating 0,1 with Equal Probability An=ones(1,N); Pn=zeros(1,N); A=zeros(1,N); for n=1:N A(1,n)=An(1,n)*exp(j*Pn(1,n)*pi/180); end s=zeros(N,length(b)/4); %4 Bits Transmitted as 1 Symbol for k=1:length(b)/4 a=b(4*k); c=b(4*k-1); d=b(4*k-2); e=b(4*k-3); %14-ary Constellation using 4x4 Butler Matrix Input Port Combinations %Varying Element Excitation using formula, sn=An*exp(j*Pn) at each symbol transmission [Equation (4)] %Port1 if (a==0)&&(c==0)&&(d==0)&&(e==0) s(1,k)=0.5*exp(j*((-45)*pi/180)); s(2,k)=0.5*exp(j*((-90)*pi/180)); s(3,k)=0.5*exp(j*((-135)*pi/180)); s(4,k)=0.5*exp(j*((-180)*pi/180)); end %Port2 if (a==0)&&(c==0)&&(d==0)&&(e==1) s(1,k)=0.5*exp(j*((-135)*pi/180)); s(2,k)=0.5*exp(j*((0)*pi/180)); s(3,k)=0.5*exp(j*((135)*pi/180)); s(4,k)=0.5*exp(j*((270)*pi/180)); end %Port3 if (a==0)&&(c==0)&&(d==1)&&(e==0) s(1,k)=0.5*exp(j*((-90)*pi/180)); s(2,k)=0.5*exp(j*((-225)*pi/180)); s(3,k)=0.5*exp(j*((0)*pi/180)); s(4,k)=0.5*exp(j*((-135)*pi/180)); end
  • 50. iii %Port4 if (a==0)&&(c==0)&&(d==1)&&(e==1) s(1,k)=0.5*exp(j*((-180)*pi/180)); s(2,k)=0.5*exp(j*((-135)*pi/180)); s(3,k)=0.5*exp(j*((-90)*pi/180)); s(4,k)=0.5*exp(j*((-45)*pi/180)); end %Port1&2 if (a==0)&&(c==1)&&(d==0)&&(e==0) s(1,k)=1*exp(j*((-180)*pi/180)); s(2,k)=1*exp(j*((-90)*pi/180)); s(3,k)=1*exp(j*((0)*pi/180)); s(4,k)=1*exp(j*((90)*pi/180)); end %Port1&3 if (a==0)&&(c==1)&&(d==0)&&(e==1) s(1,k)=1*exp(j*((-135)*pi/180)); s(2,k)=1*exp(j*((-315)*pi/180)); s(3,k)=1*exp(j*((-135)*pi/180)); s(4,k)=1*exp(j*((+45)*pi/180)); end %Port1&4 if (a==0)&&(c==1)&&(d==1)&&(e==0) s(1,k)=1*exp(j*((135)*pi/180)); s(2,k)=1*exp(j*((135)*pi/180)); s(3,k)=1*exp(j*((135)*pi/180)); s(4,k)=1*exp(j*((135)*pi/180)); end %Port2&3 if (a==0)&&(c==1)&&(d==1)&&(e==1) s(1,k)=1*exp(j*((-225)*pi/180)); s(2,k)=1*exp(j*((-225)*pi/180)); s(3,k)=1*exp(j*((-225)*pi/180)); s(4,k)=1*exp(j*((-225)*pi/180)); end %Port2&4 if (a==1)&&(c==0)&&(d==0)&&(e==0) s(1,k)=1*exp(j*((-315)*pi/180)); s(2,k)=1*exp(j*((-135)*pi/180)); s(3,k)=1*exp(j*((45)*pi/180)); s(4,k)=1*exp(j*((-135)*pi/180)); end %Port3&4 if (a==1)&&(c==0)&&(d==0)&&(e==1) s(1,k)=1*exp(j*((-270)*pi/180)); s(2,k)=1*exp(j*((0)*pi/180)); s(3,k)=1*exp(j*((-90)*pi/180)); s(4,k)=1*exp(j*((-180)*pi/180)); end
  • 51. iv %Port1,2&3 if (a==1)&&(c==0)&&(d==1)&&(e==0) s(1,k)=1.5*exp(j*((-270)*pi/180)); s(2,k)=1.5*exp(j*((-315)*pi/180)); s(3,k)=1.5*exp(j*((0)*pi/180)); s(4,k)=1.5*exp(j*((-45)*pi/180)); end %Port1,2&4 if (a==1)&&(c==0)&&(d==1)&&(e==1) s(1,k)=1.5*exp(j*((0)*pi/180)); s(2,k)=1.5*exp(j*((135)*pi/180)); s(3,k)=1.5*exp(j*((270)*pi/180)); s(4,k)=1.5*exp(j*((315)*pi/180)); end %Port1,3&4 if (a==1)&&(c==1)&&(d==0)&&(e==0) s(1,k)=1.5*exp(j*((45)*pi/180)); s(2,k)=1.5*exp(j*((-90)*pi/180)); s(3,k)=1.5*exp(j*((135)*pi/180)); s(4,k)=1.5*exp(j*((90)*pi/180)); end %Port2,3&4 if (a==1)&&(c==1)&&(d==0)&&(e==1) s(1,k)=1.5*exp(j*((-45)*pi/180)); s(2,k)=1.5*exp(j*((0)*pi/180)); s(3,k)=1.5*exp(j*((45)*pi/180)); s(4,k)=1.5*exp(j*((90)*pi/180)); end %Port1,2,3&4 if (a==1)&&(c==1)&&(d==1)&&(e==0) s(1,k)=2*exp(j*((-90)*pi/180)); s(2,k)=2*exp(j*((-90)*pi/180)); s(3,k)=2*exp(j*((-90)*pi/180)); s(4,k)=2*exp(j*((-90)*pi/180)); end end af=zeros(181,N); i=0; for theta=-90:90 i=i+1; for n=1:N af(i,n)=af(i,n)+ A(1,n)*exp(-j*(n-1)*pi*sin((theta)*pi/180)); end end
  • 52. v i=0; AFn=zeros(181,N); SNR=10; %Signal To Noise Ratio for theta=-90:90 i=i+1; AFn(i,:)=af(i,:)/N; x=AFn*s; %Received Symbols at Each Value of Theta [Equation (3)] y=awgn(x,SNR, 'measured'); %Adding AWGN end q=31; %Value of Theta %Scatter Plot figure; % M-ary Constellation at Direction q X=real(x(q,:)); Y=imag(x(q,:)); scatter(X,Y,'k','filled'); hold on; X=real(y(q,:)); Y=imag(y(q,:)); scatter(X,Y,'y','filled'); hold on; axis([-1 1 -1 1]); grid on; xlabel('Real'); ylabel('Imaginary'); legend('Original Constellation', 'Noisy Data Points'); title('M-ary Constellation');
  • 53. vi Appendix B: Miscellaneous Microstrip Equations and their Derivations i. The effective dielectric constant, !!"##, was calculated using the equation [10], !!"##! !!!! ! + !!!! ! (1 + 12 ! ! )!!.! , where, !! is the dielectric constant of the FR4 substrate, h is the thickness of the FR4 substrate and W is the width of the microstrip. ii. Length, L, of microstrip for Hybrid Coupler and Crossover was calculated using the following equation [5], Length, ! = !!/4, where, !! = !/ !!"## & λ = c/f, hence, ! = ! (4 ∗ ! ∗ !!"##) iii. Length, L, of microstrip for 45 Degree Phase Shifter was calculated using the following equations [5], Φ = 2π !! ∗ ! !! = !/ !!"## , λ = c/f, Φ = ! ! hence, ! = ! (8 ∗ ! ∗ !!"##)
  • 54. vii Butler Matrix S-Parameter Magnitude & Phase Simulations Figure 53: Butler Matrix S-Parameter Amplitude Simulation for Input Port 1 Excitation Figure 54: Butler Matrix S-Parameter Magnitude Simulation for Input Port 2 Excitation
  • 55. viii Figure 55: Butler Matrix S-Parameter Magnitude Simulation for Input Port 4 Excitation Figure 56: Butler Matrix S-Parameter Phase Simulation for Input Port 1 Excitation
  • 56. ix Figure 57: Butler Matrix S-Parameter Phase Simulation for Input Port 2 Excitation Figure 58: Butler Matrix S-Parameter Phase Simulation for Input Port 4 Excitation
  • 57. x Linear Antenna Array S-Parameter Simulation & Dipole Antenna Design Figure 59: Dipole Antenna Array S-Parameter Simulation Figure 60: Dipole Antenna CST Design Figure 61: Dipole Antenna S-Parameter Simulation
  • 58. EEE"360" Interim"Report" 1" THE UNIVERSITY OF SHEFFIELD Department of Electronic and Electrical Engineering BEng Final Year Individual Design Project Student Bhavishya Sehgal Registration Number & Course 110232799 BEng (Hons) Electronic & Communications with a Year in Industry Project Title Direction Dependent Antenna Modulation using a Butler Matrix and a Four Element Array Supervisor Dr. Alan Tennant Second Marker Dr. Xiaoli Chu
  • 59. EEE"360" Interim"Report" 2" Direction Dependent Antenna Modulation using a Butler Matrix and a Four Element Array Introduction This design project aims to achieve enhanced data security due to the advent in wireless data communications technology over the last few years. One of the suggested methods to achieve this high level of security is the concept of Directional Modulation, for which, a few techniques and ideas have been researched into and provided with. Similarly, this project aims to provide with a different approach to directional modulation using a unique system, as shown in Figure 1 below, of a 4x4 Butler Matrix and a four-element linear antenna array. Figure 1: Transmitter system to achieve Directional Dependent Antenna Modulation In conventional transmitter systems, data is only modulated at the baseband level and is transmitted by an antenna system that has a fixed radiation pattern. Although, the system provides a variation in signal power in different directions, sensitive receivers located in undesired directions can still demodulate this signal as the signal has the same characteristics in every direction. On the other hand, with directional modulation, modulation is implemented at the antenna level as well. In the context of this project, directional modulation would be achieved by using a 4x4 Butler Matrix, which provides the linear antenna array with four progressive phase shifts for each of the four input signals. This linear phased array would then provide with a variable radiation pattern for each of the excited inputs, thus, scrambling the signal characteristics in the undesired directions and retaining them in the desired boresight direction.
  • 60. EEE"360" Interim"Report" 3" This difference in signal modulation characteristics in desired and undesired directions for a directionally modulated antenna array can be shown below in Figure 2, using Constellation or I-Q diagrams. Figure 2: Constellation diagram visualising the effect of directional modulation Aims & Specification The aim of this project is to achieve m-level modulation as a function of the transmission angle, i.e. direction dependent antenna modulation using the unique system discussed and presented in the previous section of this report. MATLAB Simulations 1) To simulate the Array Factor, as a function of the transmission angle, of the four element linear array. This is required to observe the change in the Array Factor, as a function of the transmission angle, with the change in progressive phase shifts and amplitudes of the output signals from the Butler Matrix. 2) To simulate the modulated signals as symbols on the Constellation diagram, using modulation techniques such as M-PSK or QAM. This is required to observe the movement of symbols on the constellation diagram with change in the transmission angle and thus, prove the direction dependency of the system. To further prove the system’s direction dependency and enhanced security with the concept of Bit Error Rate (BER), i.e. to observe a higher BER in undesired directions and a lower BER in the desired boresight direction. System Design & Simulations - Design & Simulation Software: Computer Simulation Technology (CST) - System Operating/Resonant Frequency: 2.45GHz - Materials: - Copper (annealed): for Microstrip (thickness = 0.1mm) and Dipole Antenna Array - FR4 (lossy): for Substrate (thickness = 1.6mm) - Teflon (PTFE) (lossy): for Connector
  • 61. EEE"360" Interim"Report" 4" 1) To design and simulate individual components of a Butler Matrix, i.e. the Hybrid Coupler, the Crossover and the Phase Shifter. Then, combine these components for the final design of a 4x4 Butler Matrix and carry out the required S-parameter simulations. The Butler Matrix would provide the necessary progressive phase shifts and beam forming. 2) To design and simulate a half wave dipole antenna. Then, combine four of these dipoles to form a four element antenna array and carry out its farfield simulations. 3) To design a Power Divider and carry out the required S-parameter simulations. The Power Divider would switch the input signal phase to the Butler Matrix. Finally, combine all the individual designs for the design of the transmitter system as shown in Figure 1 previously and carry out the required simulations. Finally, input the data from those simulations into the MATLAB programs and carry out the comparisons between the experimental and the CST design simulations to confirm that the system actually provides directional modulation and enhanced wireless data security. Progress 1) Completed the literature review of many topics relevant to this project including directional modulation, Butler Matrix, microstrip technology, half wave dipole, array factor, phased arrays, antenna radiation theory, M-Ary signalling etc. 2) Mastered the use of MATLAB for the simulations required in this project and of Computer Simulation Technology (CST) software required for the design and simulation of the transmitter system. 3) Wrote a MATLAB program to simulate the Array Factor of a four element linear array. A change in the array factor is observed, as a function of the transmission angle, when the elements are provided with progressive phase shifts, as shown below in Figures 3 and 4. 0 20 40 60 80 100 120 140 160 180 0 0.5 1 1.5 2 2.5 3 3.5 4 Figure 3: Array Factor (Theta) - No Progressive Phase Shifts
  • 62. EEE"360" Interim"Report" 5" 0 20 40 60 80 100 120 140 160 180 0 0.5 1 1.5 2 2.5 Figure 4: Array Factor (Theta) - Progressive Phase Shifts: 0,90,0,90 0 20 40 60 80 100 120 140 160 180 0 0.5 1 1.5 2 2.5 3 3.5 4 Figure 5: Array Factor (Theta) - for all four excited inputs of Butler Matrix - Different Phase Shifts & Amplitude Excitations 4) Undertook the design and simulation of the Half Wave Dipole antenna as shown below in Figures 6, 7 & 8. Four of these dipoles will be combined in the future to produce a design of the four element linear array. Figure 6: CST design of a Half Wave Dipole Antenna with a Discrete Port
  • 63. EEE"360" Interim"Report" 6" Figure 7: Return Loss S-Parameter showing the antenna operation at 2.45GHz Figure 8: Farfield Simulation of Antenna with Directivity = 2.176 dBi 5) Undertook the design and simulation of the components of a Butler Matrix. These components will be combined in the future to produce a final design of a 4x4 Butler Matrix. i) 90 Degree Hybrid Coupler A Hybrid coupler is used to generate two signals at its two outputs, which are ideally 90 degrees out of phase with each other and this is shown, with the difference in phases between the two ports at 2.45GHz to be approximately (54 – (-32)) = 86 Degrees, in Figures 10 and 11 on the next page. Also, the power applied to its input port is equally distributed between its two output ports, which can be shown in Figure 12 on page 8.
  • 64. EEE"360" Interim"Report" 7" Figure 9: CST Design of a 90 Degree Hybrid Coupler Figure 10: Port 2 Phase at 2.45GHz = 54 Degrees Figure 11: Port 3 Phase at 2.45GHz = -32 Degrees
  • 65. EEE"360" Interim"Report" 8" Figure 12: Power from Input Port 1(1) equally distributed between two Output Ports 2(1) & 2(2) (Two Multipin Ports shown here) ii) -45 Degrees Phase Shifter This was implemented using a microstrip line as shown below in Figure 13. Figure 13: CST design of a -45 Degree Phase Shifter iii) 0dB Crossover The Crossover provides an approximately -2dB gain at Port 3 (ideal 0dB), which is as shown in Figure 15 on the next page.
  • 66. EEE"360" Interim"Report" 9" Figure 14: CST design of a Crossover Figure 15: -2dB gain at Port 3 Figure 16: Power flow from Port 1 to Port 3
  • 67. EEE"360" Interim"Report" 10" Revised Gantt Chart A | Literature Review B | Research C | Array Factor Simulation Using MATLAB D | Learning Computer Simulation Technology (CST) E | Design & Simulation Of Butler Matrix Components & Dipole Antenna F | Complete Design & Simulation Of Transmitter System G | Constellation Diagram & Bit Error Rate Simulation Using MATLAB H | Improve Design & Carry Out Further Simulations I | Evaluate Theoretical & CST Simulations Component 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A B C D E F G H I