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Modeling Propagation Characteristics for Arm Motion in Wireless Body Area Networks

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Abstract and Figures

To monitor health information using wireless sensors on body is a promising new application. In health care technology Wireless Body Area Networks (WBANs) are expected to be a breakthrough technology. Human body acts as a transmission channel in wearable wireless devices, so electromagnetic propagation modeling is well thought-out for transmission channel in Wireless Body Area Sensor Network (WBASN). In this research, I have presented the wave propagation in WBASN which is modeled as point source (Antenna), close to the arm of the human body. In this thesis, I have deduced the wave propagation model in WBASNs; transmission sensor is close to the arm of the human body. To model the arm motion of human body, we used Dyadic Green's Function (DGF) and Mathieu Functions (MF). DGF is specifically used to propose a channel model for arm motion of human body model. Using terms of vector wave function and scattering superposition this function can be expanded. MF is developed for Angular Mathieu Functions (AMF), Radial Mathieu Functions (RMF), sine and cosine-sphere terms. This thesis, describes the analytic derivation of electric field distribution derived by both DGF and MF, in spherical pattern and the simulation results of those derivations.
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i
Modeling Propagation Characteristics for Arm
Motion in Wireless Body Area Networks
By
Miss Aamrah Ikram
Registration Number: CIIT/FA11-REE-065/ISB
MS Thesis
In
Electrical Engineering
COMSATS Institute of Information Technology
Islamabad Pakistan
ii
Modeling Propagation Characteristics for Arm-
Motion in Wireless Body Area Networks
A Thesis presented to
COMSATS Institute of Information Technology
In partial fulfillment
of the requirement for the degree of
MS (Electrical Engineering)
By
Miss Aamrah Ikram
CIIT/FA11-REE-065/ISB
Fall, 2012
iii
Modeling Propagation Characteristics for Arm-
Motion in Wireless Body Area Networks
A Graduate Thesis submitted to Department of Electrical Engineering as
partial fulfillment of the requirement for the award of M. S. Degree
(Electrical Engineering).
Name
Registration Number
Aamrah Ikram
CIIT/FA11-REE-065/ISB
Supervisor:
Dr. Mahmood Ashraf Khan,
Director,
Center for Advanced Studies in Telecommunications (CAST),
COMSATS Institute of Information Technology (CIIT),
Islamabad, Pakistan
December, 2012
Co-supervisor:
Dr. Nadeem Javaid,
Assistant Professor,
Center for Advanced Studies in Telecommunications (CAST),
COMSATS Institute of Information Technology (CIIT),
Islamabad, Pakistan
December, 2012
iv
Final Approval
This thesis entitled
Modeling Propagation Characteristics for Arm-
Motion in Wireless Body Area Networks
By
Miss Aamrah Ikram
CIIT/FA11-REE-065/ISB
has been approved
for the COMSATS Institute of Information Technology, Islamabad
External Examiner: __________________________________
(To be decided)
Supervisor: ________________________
Dr. Mahmood Ashraf Khan/Director,
Center for Advanced Studies in Telecommunications (CAST),
CIIT, Islamabad, Pakistan.
Co-Supervisor: ________________________
Dr. Nadeem Javaid /Assistant professor,
Center for Advanced Studies in Telecommunications (CAST),
CIIT, Islamabad, Pakistan.
Head of Department:________________________
Dr. Raja Ali Riaz / Associate professor,
Department of Electrical Engineering,
CIIT, Islamabad, Pakistan.
v
Declaration
I Miss Aamrah Ikram CIIT/FA11-REE-065/ISB herebyxdeclare that I
havexproduced the workxpresented in this thesis, duringxthe
scheduledxperiod of study. I also declare that I havexnot taken anyxmaterial
from anyxsource exceptxreferred toxwherever due that amountxof
plagiarism isxwithin acceptablexrange. If a violationxof Higher Education
Commission rulesxon research hasxoccurred in thisxthesis, I shall be
liablexto punishablexaction under the plagiarismxrules of the Higher
Education Commission, Pakistan.
Date: ________________
________________
Miss Aamrah Ikram
CIIT/FA11-REE-065/ISB
vi
Certificate
It is certified that Miss Aamrah Ikram, CIIT/FA11-REE-065/ISB has carried
out all the work related to this thesis under my supervision at the
Department of Electrical Engineering, COMSATS Institute of Information
Technology, Islamabad and the work fulfills the requirements for the
award of MS degree.
Date: _________________
Supervisor: ________________________
Dr. Mahmood Ashraf Khan/Director,
Center for Advanced Studies in Telecommunications (CAST),
CIIT, Islamabad.
Co-Supervisor:____________________
Dr. Nadeem Javaid /Assistant professor,
Center for Advanced Studies in Telecommunications (CAST),
CIIT, Islamabad
____________________________
Head of Department:
Dr. Raja Ali Riaz/Associate Professor,
Department of Electrical Engineering,
CIIT, Islamabad.
vii
DEDICATION
Dedicated to my parents.
viii
ACKNOWLEDGMENT
I am heartily grateful to my supervisor, Dr. Mahmood Ashraf Khan, and co-
supervisor Dr. Nadeem Javaid whose patient encouragement, guidance
and insightful criticism from the beginning to the final level enabled me
have a deep understanding of the thesis.
Lastly, I offer my profound regard and blessing to everyone who supported
me in any respect during the completion of my thesis especially my friends
in every way offered much assistance before, during and at completion
stage of this thesis work.
Miss Aamrah Ikram
CIIT/FA11-REE-065/ISB
ix
List of Abbreviations
WBANs
Wireless Body Area Networks
WBASNs
Wireless Body Area Sensor Networks
DGF
Dyadic Green’s Function
MF
Mathieu Functions
AMF
Angular Mathieu Functions
RMF
Radial Mathieu Functions
PDA
Personal Digital Assistant
BAN
Body Area Networks
UWB
Ultra-Wide Band
EM
Electromagnetic
IBC
Impedance Boundary Conditions
FT
Fourier Transform
x
List of Publications
[1] Ain.Q, Ikram. A, Javaid. N, Qasim. U, Khan. Z. A, “Modeling Propagation Characteristics
for Arm- Motion in Wireless Body Area Sensor Networks”, published in 7th International
Conference on Broadband and Wireless Computing, Communication and Applications
(BWCCA-2012), Victoria, Canada, 2012.
[2] Ikram. A, Javaid.N “Modeling Wave Propagations for Bio-sensors with Arm-Motion",
submitted in 4th IEEE International Conference on Ambient Systems, Networks and
Technologies (ANT-13) June 25-28, 2013, Halifax, Nova Scotia, Canada.
xv
Abstract
To monitor health information using wireless sensors on body is a promising new application. In
health care technology Wireless Body Area Networks (WBANs) are expected to be a
breakthrough technology. Human body acts as a transmission channel in wearable wireless
devices, so electromagnetic propagation modeling is well thought-out for transmission channel in
Wireless Body Area Sensor Network (WBASN). In this research, I have presented the wave
propagation in WBASN which is modeled as point source (Antenna), close to the arm of the
human body. In this thesis, I have deduced the wave propagation model in WBASNs;
transmission sensor is close to the arm of the human body. To model the arm motion of human
body, we used Dyadic Green's Function (DGF) and Mathieu Functions (MF). DGF is specifically
used to propose a channel model for arm motion of human body model. Using terms of vector
wave function and scattering superposition this function can be expanded. MF is developed for
Angular Mathieu Functions (AMF), Radial Mathieu Functions (RMF), sine and cosine-sphere
terms. This thesis, describes the analytic derivation of electric field distribution derived by both
DGF and MF, in spherical pattern and the simulation results of those derivations.
Table of Contents
1 Introduction 1
2 Related Work 4
3 Motivation 5
4 Functions for Boundary Value Problems 7
4.1 Dyadic Green’s Functions: . . . . . . . . . . . . . . . . . . . . . . . 7
4.2 MathieuFunctions ........................... 8
4.3 HelmholtzEquation........................... 9
4.4 Inhomogeneous Helmholtz Equation: . . . . . . . . . . . . . . . . . 9
4.5 HankelFunctions:............................ 9
4.6 Wronskian Relationship: . . . . . . . . . . . . . . . . . . . . . . . . 10
4.7 FourierTransform............................ 10
4.8 Spherical Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5 Mathematical Modeling for Arm Motion using DGF. 13
5.0.1 Electric Field Propagation Characteristics . . . . . . . . . . 14
5.0.2 Spherical Wave Vector Eigen Function . . . . . . . . . . . . 14
5.0.3 Scattering Superposition . . . . . . . . . . . . . . . . . . . . 16
5.0.4 Superposition of Direct Wave . . . . . . . . . . . . . . . . . 18
5.0.5 Superposition of Scattered Wave . . . . . . . . . . . . . . . . 18
5.1 Transmitter and Receiver Located Outside the Body . . . . . . . . 21
6 Propagation Model Geometry for Arm-Motion using MF 22
6.1 Conversion of three-D problems to two-D problems . . . . . . . . . 22
6.1.1 Vector of Scattered Wave . . . . . . . . . . . . . . . . . . . . 24
6.1.2 Vector of Incident Wave . . . . . . . . . . . . . . . . . . . . 25
6.1.3 Resultant Vector Field . . . . . . . . . . . . . . . . . . . . . 25
6.2 Impedance Boundary Conditions for Human Body . . . . . . . . . . 27
6.3 Field Distribution (On-Body Sensor) . . . . . . . . . . . . . . . . . 28
i
6.4 Pathloss................................. 30
7 Simulations and Discussions 32
7.1 Simulations using DGF . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.2 Simulations using MF . . . . . . . . . . . . . . . . . . . . . . . . . 35
8 Conclusion 40
References 40
ii
List of Figures
5.1 Human body model showing arm motion in 3D. . . . . . . . . . . . 13
5.2 Scattering Superposition . . . . . . . . . . . . . . . . . . . . . . . . 17
6.1 2-D model of wave propagation for WBANs . . . . . . . . . . . . . 23
7.1 Magnitude of scattered field component Eϕversus angle ϕ,with dif-
ferent values of dand the angle is θ=π
6............... 33
7.2 Magnitude of scattered field component Eϕversus angle ϕ,with dif-
ferent values of dand the angle is θ=π
3............... 34
7.3 Magnitude of scattered field component Eϕversus angle ϕ,with dif-
ferent values of dand the angle is θ=π............... 35
7.4 Magnitude of electric field Erat different values of d, and θ=π
2. . . 36
7.5 Magnitude of electric field Erat different values of d, and θ=π
4. . . 37
7.6 Magnitude of electric field Erat different values of d, and θ=π
6. . . 37
7.7 Magnitude of electric field Erat different values of d, and θ=π
10 . . 38
7.8 Magnitude of electric field Erat different values of d, and θ=π
3. . . 38
7.9 Magnitude of electric field Erat different values of d, and θ=π. . . 39
iii
List of Tables
4.1 Functions and their uses in thesis. . . . . . . . . . . . . . . . . . . . 12
6.1 Human body Impedance parameters at different frequencies . . . . 28
iv
Chapter 1
Introduction
Hospitals throughout the world are facing a unique problem, as the aged popu-
lation is increased, health-care population is decreased. Telecommunication com-
munity is not doing much work in the field of medicine however, there is a need of
remote patient monitoring technology. To fulfill this task, it is required to build
communication network between an external interface and portable sensor devices
worn on and implemented within the body of the user which can be done by Body
Area Networks.
BAN is not only useful for remote patient monitoring, but can also establishes
within the hospitals; like in operation theaters and intensive care units. It would
enhance patient comfort as well as provide ease to doctors and nurses to perform
their work efficiently. BAN is used for connecting body to wireless devices and
finds applications in various areas such as entertainment, defense forces and sports.
Wireless Body Area Networks (WBANs) is providing promising applications in
bio-medical sensor systems. The large range and prospective of these applications
makes it an exhilarating new research track. There is a requirement of home
health care monitoring for elder or aged population. Particularly, advancement is
required in physiological sensors, wireless communications and channel modeling.
These sensors measure the parameters, which are under observation and sends the
data to the nearest Personal Digital Assistant (PDA). The sensor and PDA both
are worn directly on the body. Automatic emergency calls are built, when their is
rapid change in brain, heart, diabetes and high blood pressure etc for diagnosis.
Importantly, range of sensors and its’s effect on field with the movement of human
1
body should be under consider.
The basic step in building any wireless device is to study the transmission chan-
nel and to model it accurately. Channel modeling is a technique that has been
initiated by a group of researchers throughout the world [1]. They have studied
path loss and performed measurement campaigns for wireless node on the body
[2-8]. Some researchers have taken into account, the implanted devices which are
the area of BAN called as intra-body communication [9].
Many researchers paid attention on developing the propagation model around
cylinder. They have developed models by taking the human body as lossy cylin-
der. For the short range low data rate communication in BAN, measurement
groups have considered UWB (Ultra-Wide Band) as the appropriate air interface.
The models developed by measurement campaigns are only path loss models and
do not provide any description of propagation channel.
For this we need simple and generic body area propagation model to develop
low power radio systems for inspection of human body. To model the transmis-
sion channel correctly is the main step to build up the wireless devices. Channel
modeling also assists to understand the wave propagation in and around human
body. It is important to study the propagation mechanism of radio waves on
and inside the body in order to develop an accurate BAN channel model. This
study will show the underlying propagation characteristics. It would help in the
development of BAN transceivers which are much suited to the body environment.
In this thesis, wave propagation model for Upper half of human body (spherical
symmetry) is developed by using two ways; DGF and MF. These propagation
models can tackle as electromagnetic boundary-value problem and solved by es-
tablished methods but with complicated process. The course of action of these
two functions are:
1. DGF:
For a given position of the transmitter on or inside the body it is required to find
out the electromagnetic field on or inside the body for a BAN channel model. This
is quite a critical problem that requires a large amount of computational power.
Therefore, it is necessary to derive an analytical expression which will perform this
objective. In short this determines which propagation mechanism takes place, that
2
is reflection, diffraction and transmission [10]. An appropriate method of doing
this task is by using Dyadic Green’s function. The solution of canonical problems,
such as cylinder, multi layer and sphere have been solved in electromagnetic (EM)
theory, using Dyadic Green’s Functions [11-13].
2. MF:
Mathieu functions allow an accurate and time saving computation. The expan-
sion coefficients are derived and can be easily implemented in computer code.
Compared to the calculation with series of Bessel function products. The derived
solution of 2-D problem is expanded in term of eigenfunctions in the spherical
coordinates by MF, using separation of variables. Solving boundary conditions on
sphere’s surface, expansion coefficients can be calculated. Mainly, focus is on the
field outside the body as surface impedance of human body is easy to be tested.
Also human body is not an ideal for the radio frequency transmission. This will
be very helpful for the Channel modeling of WBANs.
3
Chapter 2
Related Work
Wen Xun Zhang [10], find out the field distribution in cylindrical coordinates.
He formulated the path gain of electromagnetic field around the human body at
15-MHz and 2.40-GHz frequencies.
Attaphongse Taparugssanagorn, Carlos Pomalaza-Rez, Ari Isola, Raffaello Tesi,
Matti Hmlinen [11], they worked on Wideband (UWB) for the channel modeling
of WBANs. Contribution is, they toke measurements in the frequency.
Arthur Astrin, Takahiro Aoyagi [14], worked on WBAN for the devices which are
implanted inside the body. They compared the path loss of BAN devices by taking
into account obstacles near the human body an different postures of human body
in daily life.
L. An, M. J. Bentum [15], have investigated propagation around the human body
and proposed the channel modeling for various scenarios. That channel model-
ing is done in the way to understand wave propagation in and around human body.
Asthag Gupta, Thushara D [16], they developed analytical channel model for hu-
man body in cylindrical form. They have used DGF for the channel modeling for
BAN communication.
4
Chapter 3
Motivation
Recently, WBASNs shows potential due to increasing application in medical health
care. New applications in WBANs are facilitating the patient to being monitored
and stay connected to its health care system. Characterization of the electro-
magnetic wave propagation is an important step for the development of WBANs.
Although, complexity of human tissue structure and geometry makes it difficult
to derive wave propagation model.
In WBASNs, each sensor in the body sends it’s data to antenna, both sensors
and antenna are worn directly on the body. Examples include sensors which can
measure brain activity, blood pressure, body movement and automatic emergency
calls. We require straightforward and basic body area propagation models to de-
velop efficient and low power radio systems near the human body. To achieve bet-
ter performance and reliability, wave propagation needs to be modeled correctly.
Few studies have focused on analytic model of propagation around a cylinder (as
human body resembles a cylinder) using different functions.
The disadvantage is that, the earlier studies have not concentrated on wave prop-
agation, and only focused on propagating around a circular cylinder based on
analytic model [17-19]. Most of the researchers have focused on the analytical
wave propagation model for cylinder using different differential functions. All of
them, discussed and developed the wave propagation model for cylindrical distri-
bution as geometry of human body resembles to cylinder.
BAN channel model requires extensive study for manipulation of the body on the
radio propagation as antennas are placed on or inside the human body. As I have
described before that a simple and standard wave propagation model is needed.
The propagation characteristics of cylindrical shaped human body have been de-
5
rived using Dyadic Green’s functions [20]. The model includes the cases of trans-
mitter and receiver presents either inside or outside of the body and also provides
simulation plots of Electric field with different values of angle (θ).
All the above proposals describe the propagation characteristics of cylindrically
shaped human model [21]. I have developed a simple but generic approach to body
area propagation derived from Dyadic Green’s Function (DGF) and MF. These
approaches are for arm motion of human body. When the human arm is moved in
r, θ, ϕ direction, propagation characteristics of spherical shaped have been derived
using DGF and MF.
6
Chapter 4
Functions for Boundary Value
Problems
4.1 Dyadic Green’s Functions:
Green’s function is a kind of function which solves inhomogeneous differential
equations having specific initial conditions or boundary-value problem. Dyadic
Green’s function is basically depends on the spherical vector eigen functions. These
eigen functions are Lnhk(χ), Mnhk (χ) and Nnhk (χ).
Lnhk(χ) = nhk (χ)] (4.1)
Mnhk(χ) = ∇ × nhk (χ)] (4.2)
Nnhk(χ) = 1
k∇×∇nhk(χ)] (4.3)
where kis the wave number of medium, nis an integer, his a real number and x
is a point in space.
7
4.2 Mathieu Functions
Mathieu Functions are kind of special functions use to solve the problems in applied
mathematics.
It can solve the problems related to:
1. Elliptical cylinder coordinates.
2. Electrical dipoles.
3. Wave motion in periodic medium.
4. Spherical Coordinates.
The main equation for Mathieu differential equation is given as:
d2y
dx2+ [a2qcos(2x)]y= 0 (4.4)
ais the constant.
Mathieu function is further divided into two parts:
1. Angular Mathieu function.
It is denoted by Sn(x) and have even and odd components Meand Mo.
2. Radial Mathieu function.
It is denoted by Rn(x) and have even and odd components Ceand So.
Even and odd Mathieu functions:
1. Even Mathieu Function
Me=
l=0
Be
l(h, m)cosnθ (4.5)
mand nare both even or both odd.
2. Odd Mathieu function
Mo=
l=0
Bo
l(h, m)cosnθ (4.6)
In above equations (Be
l) and (Bo
l) are the expansion coefficients for even and odd
functions respectively.
8
4.3 Helmholtz Equation
This equation is used solve the inhomogeneous and homogeneous partial differen-
tial equations.
1. Homogeneous Helmholtz equation:
(2+k2)U(y, t) = 0 (4.7)
2= laplacian operator, k= Wave Number and U(y, t)= Vector function.
4.4 Inhomogeneous Helmholtz Equation:
(2+k2)U(y, t) = δ(4.8)
i. 2-D Inhomogeneous Helmholtz equation:
(2+k2)U(y, t) = δ(xx0)δ(yy0)δ(zz0) (4.9)
ii. 3-D Inhomogeneous Helmholtz equation:
(2+k2)U(y, t) = ejkzz0δ(xx0)δ(yy0) (4.10)
4.5 Hankel Functions:
Hankel functions are solution of bessel’s equations which are linearly Independent.
Mathematical representation of Hankel Function is:
Hl=Jl(Z) + ıYl(z) (4.11)
Jl(z)=First kind of bessel function and Yl(z)=Second kind of bessel function .
9
Orders of 2nd kind of spherical Hankel Function:
Zero order of Hankel Function of 2nd kind:
h(2)
o=ıeız
z(4.12)
First order of Hankel Function of 2nd kind:
h(2)
1=eız(zı)
z2(4.13)
Second order of Hankel Function of 2nd kind:
h(2)
1=ıeız(z23ıZ 3)
z3(4.14)
Third order of Hankel Function of 2nd kind:
h(2)
1=eız(z336ıZ215z+ 15ı)
z4(4.15)
4.6 Wronskian Relationship:
Wroskian is determinant, used to study differential equations and to show the set
of solution is linearly independent. let xand yare two functions, wronskian of
these two functions are given as:
W(x, y) = x´y´xy
or
W(f1, f2, f3) =
f1(x)f2(x)f3(x)
´
f1(x)´
f2(x)´
f2(x)
f′′
1(x)f′′
2(x)f′′
2(x)
(4.16)
4.7 Fourier Transform
The Fourier transform is a standardization of the complex Fourier series in the
limit as n→ ∞ . It replace the discreet Blto continuous F(z)dz, in this way sum
is changed to integral form.
10
Generalized equation is :
F(z) =
−∞
F(k)e2πıkz dz (4.17)
and Inverse Fourier Transform is given as:
F(k) =
−∞
F(z)e2πıkz dk (4.18)
4.8 Spherical Coordinates
It is a three coordinate system having three-dimensional space. A single point is
defined by three different numbers:
1. The radial angle(also called radius and radial coordinate) denoted by r,
2. The polar angle represented by θ,
3. The azimuthal angle as ϕ.
Mathematically they are defined as:
x=rsin θcos ϕ(4.19)
y=rsin θsin ϕ(4.20)
z=rcos θ(4.21)
11
centering
Functions Used to Solve Equations
Dyadic Green’s Functions Solves inhomoge-
neous boundary value
problems with the help of vector eigen functions. G(x, x0) = δ(x, x0)
Mathieu Functions Gives near and far electric field magnitude. d2y
dx2+ [a2qcos(2x)]y= 0
Helmholts Equation To find out magnetic potential vector in 3-D
model.
(2+k2)U(x, t) = 0
Hankle Function Combining the scattered and Incident waves. H(1)
n=Jn(Z) + ıYn(z)
Wronskian relationship Simplifies the equation for even and odd Mathieu
Functions.
W(x, y) = x´y´xy
Fourier Transform Converts three dimension problem to two dimen-
sion
F(z) =
−∞ F(k)e2πıkz dz
Inverse Fourier Transform Converts two dimension problem to two dimension
problem
F(k) =
−∞ F(z)e2πıkz dk
Spherical Coordinates Use for the representation of polar coordinates to
spherical coordinates
x=rsin θcos ϕ,y=rsin θsin ϕ,z=rcos θ
Table 4.1: Functions and their uses in thesis.
12
Chapter 5
Mathematical Modeling for Arm
Motion using DGF.
In this thesis, spherical symmetry is used to represent in and around the arm of
the human body. A point on body is a sensor, denoted by x which represents
(r,Θ,ϕ) coordinates in the spherical coordinate system and x0is the location of
transmitting antenna. (r,Θ,ϕ) are unit vectors along radial, angle of elevation
from z-axis and azimuthal angle from x-axis as shown in figure 3.1.
Figure 5.1: Human body model showing arm motion in 3D.
13
5.0.1 Electric Field Propagation Characteristics
Let E(x) be electric field at point x due to current source J(x0). The general
formula for Electric field can be written as:
E(x) = iωµp  V
G(x, xo)J(x, x0)dv (5.1)
where V is volume of source,J(X0) is the current source, G(x, x0) is the Dyadic
Green’s function ωis the radian frequency of transmission and µ
pis magnetic
permeability of the medium. A Dyadic Green’s function is a type of function used
to solve inhomogeneous differential equations subject to specific initial conditions
or boundary condition.
5.0.2 Spherical Wave Vector Eigen Function
As we are considering arm motion of human body, therefore, spherical symmetry
is used by taking shoulder as center. For this, spherical eigen functions are used
to write the Dyadic Green’s function.
Dyadic Green’s function is basically depends on the spherical vector eigen func-
tions [14]. These eigen functions are Lnhk (χ), Mnhk(χ) and Nnhk (χ), where kis
the wave number of medium, nis an integer, his a real number and x is a point
in space. These all are the solutions to the Helmholtz equation having three com-
ponents in r, Θ and ϕ. These vector eigen functions are given by [22]:
Lnhk(χ) = nhk (χ)] (5.2)
Mnhk(χ) = ∇ × nhk (χ)] (5.3)
Nnhk(χ) = 1
k∇×∇nhk(χ)] (5.4)
14
In above eigen functions, Laplacian operator in the spherical coordinate system is
. It’s mathematical expression is given as:
=
∂r +
r∂θ +
rsin θ∂ϕ (5.5)
where x represents the point in space having components r,Θ and ϕ. Solution of
Helmoltz equation is Ψnhk(x) which is the scalar eigen function [22].
nhk(χ)] = Zn(ηr)Ph
n(cos θ)cos
sin (5.6)
where Znis a general spherical function of order n. For sphere we use Hankle
function of first and second order which are defined as:
[Zn(ηr)] = (1)n(ηr)( d
drη2r)n(sin(ηr)
ηr )n(5.7)
ηis the propagation constant in direction of ϕ,whereas k2=η2+h2. The laplace
operator is applied and find the eigen values Lnhk,Mnhk and Nnhk by using eigen
function. The vector eigen function in (3.2), (3.3) and (3.4) becomes:
Lnhk(χ) = Zn(ηr)
∂r Ph
n(cos θ)cos
sin +zn(ηr)
r
∂θ Ph
n(cos θ)cos
sin +hZn(ηr)
rsin θPh
n(cos θ)sin
cos
(5.8)
Mnhk(χ) = hZn(ηr)
sin θPh
n(cos θ)sin
cosZn(ηr)
∂θ Ph
n(cos θ)cos
sin
(5.9)
Nnhk(χ) = nZn(ηr)
kr Ph
n(cos θ)cos
sin +1
kr
∂rZn(ηr)
∂r Ph
n(cos θ)cos
sin h
sin θPh
n(cos θ)sin
cos
(5.10)
15
These three vector eigen function are perpendicular among themselves as well as
with respect to each other [11]. In the form of matrices, vector Eigen functions
can be written in this form,
Lnhk(χ) =
∂Zn)(ηr)
∂r Ph
n(cos θ)cos
sin
Zn(ηr)
rPh
n(cos θ)cos
sin
hZn(ηr)
sin θPh
n(cos θ)sin
cos
(5.11)
Mnhk(χ) =
0
hZn(ηr)
rPh
n(cos θ)cos
sin
Zn(ηr)∂P h
n(cos θ)sin
cos
∂θ
(5.12)
Nnhk(χ) =
hZn(ηr)
kr Ph
n(cos θ)cos
sin
n(ηr)
kr∂r
Ph
n(cos θ)cos
sin
∂θ
h
sin θPh
n(cos θ)sin
cos
(5.13)
5.0.3 Scattering Superposition
In scattering problems, it is desirable to determine an unknown scattered field that
is due to a known incident field. Using the principle of scattering superposition we
can write Dyadic Green’s equation as superposition of direct wave and scattering
wave. In Figure 3.2, concept of scattering superposition is shown in which there is
a sensor located inside the arm of body considered as sphere. The sensor transmits
the wave to antenna which is divided in two parts as Direct wave and Scattered
wave. The Direct wave is considered as wave directly transmits from sensor to
transmitter and scattered wave is composed of reflection and transmission waves.
Therefore, general equation of scattering superposition is illustrated as:
G(x, x0) = Gd(x, x0) + Gs(x, x0) (5.14)
16
Figure 5.2: Scattering Superposition
17
Dyadic Green’s equation is divided in to two parts as direct wave [Gd(x, x0)] and
scattered wave [Gs(x, x0)]. The direct wave corresponds to direct from source to
measuring point and scattered is the reflection and transmission waves due to
presence of dielectric interface.
5.0.4 Superposition of Direct Wave
The direct component of DGF is given as [11]:
Gd(x, x0) = rr
k2(δ(xx0) + ȷ
8π
−∞
dh
n=−∞
1
n2x×
M(1)
nhk(X)M
nhk(X0) + N(1)
nhk(X)N
nhk(X0)
Mnhk(X)M(1)
nhk (X0) + Nnhk(X)N(1)
nhk (X0)
(5.15)
In the above equation of DGF, r > r0is for first case and r < r0is second case.The
denotes the conjugation and is for the Dyadic product. Here we introduces
superscript (1) for outgoings wave and other for standing waves. If the vector
eigen function has the superscript (1) then, H(1)
nis chosen for Znand Jnshould
be used otherwise.
5.0.5 Superposition of Scattered Wave
Here we discuss four different scenarios for the scattering components of DGF
along with boundary conditions Gs(x, x0).
(i). Both receiver and transmitter are inside the body.
(ii). The receiver is located outside and transmitter is located inside the body.
(iii). The receiver is located inside and transmitter is outside the body.
(iv). Both transmitter and receiver are located outside the body.
Receiver and transmitter are in the order: 1 denotes the medium inside human
body and 2 is for free space medium.
1) Transmitter and Receiver located inside the body. In this case, Receiver
and Transmitter both located inside the body so we can write Dyadic Green’s
equation as,
18
G(11)
s(x, x0) = ȷ
8π
−∞
dh
−∞
1
η2x
×[Mnhk1Nnhk1]R12×
Nnhk1(X0)T
Mnhk1(X0)T
(5.16)
where R12 contains reflection coefficients. R12 is calculated in literature using
boundary conditions, its matrix is given by [16]:
R12 = [Jn(η1d)Hn(η2d)Hn(η2d)Jn(η1d)]1
×[Hn(η2d)Hn(η1d)Hn(η1d)Jn(η2d)]1(5.17)
In the above equation of reflection coefficient ’d’ represents radius of spherical
body model, η2
1=k2
1h2, η2
2=k2
2h2, k2
1=ω2µ1ϵ1, k2
2=ω2µ2ϵ2. The 2x2
matrices for jn(ηd) and Hn(ηd) are expressed as:
Bn(ηpd) = 1
η2
pd×ȷωϵpηpdBn(ηpd)nhBn(ηp
nhBn(ηpȷωµpηpdBn(ηpd)(5.18)
Bnis either H(1orJn)
n,B(.) is the derivative of Bw.r.t the whole argument, and
p=1,2
2) Transmitter located inside and Receiver located outside the body
In this case DGF can be written as :
G(21)
s(x, x0) = ȷ
−∞
dh
n=−∞
1
η2
×[Nnhk.Mnhk ]T12 N
nhk1(x0)T
M
nhk1(x0)T(5.19)
In the above equation T12 is a transmission coefficient Matrix and given as:
19
T12 = 2ω
πη2
1d[Jn(η1d)Hn(η2d)Hn(η2d)Jn(η1d)]1
×ε10
0ε(5.20)
3) Both Transmitter and Receiver located outside the body
Gs(x, x0) = ȷ
−∞
dh
n=−∞
1
n2
×[MnhkNnhk ]R21
Nnhk(X0)TMnhk(X0)T
(5.21)
Similarly as R12,R21 is the reflection coefficient matrix and it is given as:
R21 = [Jn(η1d)Hn(η2d)Hn(η2d)Jn(η1d)]1
×[Jn(η2d)Jn(η1d)Jn(η1d)Jn(η2d)] (5.22)
4) Transmitter located outside and Receiver is inside the body In this
case we can write DGF as:
Gs(x, x0) = ȷ
−∞
dh
n=−∞
1
n2
×[MnhkNnhk ]T21
N
nhk1(x0)T
M
nhk1(x0)T
(5.23)
where T12 is the transmission coefficient matrix, given as:
T21 = 2ω
Πηd [Jn(η1d)Hn(η2d)Hn(η2d)Jn(η2
2d)]1
×ε20
0µ2(5.24)
20
5.1 Transmitter and Receiver Located Outside
the Body
In this section I present the equation which is required for simulation. With the
help of simulation it will be easy to study the propagation characteristics of arm
motion making spherical pattern.
Gs(x, x0) = ȷ
−∞
dh
n=−∞
1
n2Gnh(x, x0)dh
(5.25)
Gnh(x, x0) is stated as:
Gnh(x, x0) = Nnhk (X)1Mnhk (X)1×R21
Nnhk(X0)TMnhk (X0)T(5.26)
21
Chapter 6
Propagation Model Geometry for
Arm-Motion using MF
The geometry of the WBAN channel model for arm motion is spherical [23]. To
understand the geometry of model, cartesian coordinates (x, y, z) are translated
to spherical polar coordinates (r, θ, ϕ) using the following general equations:
x=rsin θcos ϕ(6.1)
y=rsin θsin ϕ(6.2)
z=rcos θ(6.3)
where as θϵ[0, π], ϕϵ[0,2π] and [0.) and ris sphere’s radius. ϕis describing the
different angles at which arm is moving. Let point source is located at (r0, θ0, ϕ0)
and r=r1is defining the interface between the body and free space.
6.1 Conversion of three-D problems to two-D
problems
First, it is needed to covert the three-D problem to two-D problem. Resultant
field will be the combination of first and fourth kind of MF. We know MF involves
complex computations, to avoid this complexity problem is transformed to two-D.
22
Figure 6.1 is showing the 2-D transform of spherical polar coordinates. Sensor is
place on (r1,θ1,ϕ1) coordinates, whereas (r,θ,ϕ) are representing the coordinates
at origin.
Figure 6.1: 2-D model of wave propagation for WBANs
Transformation of sphere into two-D presents circular geometry. Magnetic po-
tential vectors have to be calculated before measuring magnetic field. Magnetic
potential vector
His the solution to inhomogeneous Helmholtz equation [22]. It’s
general formula is stated as:
(2+k2)
H(x, y, z) = δ(xx0)δ(yyo)δ(zz0).(6.4)
Mathematically three-D geometry can be converted to two-D by using fourier
transform with respect to z, on both sides of equation (4) [24]. Therefore, equa-
tion 4.4 becomes:
(2
t+k2)
H(x, y, z) = ˆreikzroδ(xx0)δ(yyo) (6.5)
23
This equation is combination of two parts; inhomogeneous Helmholtz equation
and homogeneous Helmholtz equation.
where, 2
t=2
∂x2+2
∂y2and kt2=k2k2
r. By expanding both scattered wave
and incident wave using MF ( i. e eigen functions for spherical coordinates). Us-
ing IBC (Impedance boundary conditions) [25], expansion coefficient of scattered
wave can be measured on the surface of sphere.
6.1.1 Vector of Scattered Wave
Here, we are only considering the homogeneous equation for scattered wave. Po-
tential scattered wave
Hsc in spherical coordinates can be written as:
2
d2(cosh2rcos2θ)(2
∂r2+2
∂θ2) + k2
r
Hsc(r, θ, kr) = 0 (6.6)
In above equations (Be
n) and (Bo
n) are the expansion coefficients for even and odd
functions respectively. General solution of this equation is the combination of
RMF and AMF, the notations are same as in [26]:
Hsc(r, θ, kr) = ˆz
n=0
Rn(r)Sn(θ)eikrr0(6.7)
where Rn(r) is RMF and Sn(θ) is AMF. Potential vector of scattered wave outside
the sphere (rr1) can be expressed using 4th kind of MF. Fourth kind of MF is
used to express the far field and combination of even and odd MF as:
Hsc(r, θ, kr) = ˆz
n=0 BenM(4)
en(r, q0)cen(θ, q0)
+BonM(4)
sn(r, q0)sen(θ, q0)eikrr0
(6.8)
where, q0= (kr0
d
2)2is parameter of MF, krois representing wave number. Ben and
Bon are expansion coefficient of even and odd MF respectively.
Similarly, AMF are cenand sen,nis an integer describing the order. Notation
ceand secomes from sine-sphere and cosine-sphere. These functions are peri-
odic from πto 2π.
24
6.1.2 Vector of Incident Wave
The potential vector of the incident wave can be derived from equation (4.5) using
the 2nd kind of the Hankel function of 0(th)order [24]. It’s mathematical formula
is stated as:
Hinc(k0, r, kr) = ˆreikrr0
4ih(2)
0(kuOr) (6.9)
In this equation h(2)
0is the 2nd kind of Hankel Function with 0(th)order. The
source point (x0, y0) and the field point (x, y) are separated with the distance r
and mathematically formulated as:
r=(xx0)2+ (yy0)2(6.10)
If field points close to the body are (r1rr0), by applying addition theorem
of Hankel Function on MF [27], equation (4.9) becomes:
Hinc(r, θ, kr) = ˆreikrr0
2i×
n=0
Mc(4)
n(r0, q0)Mc(1)
n(r.q0)
×cen(θ0, q0)cen(θ, q0) +
n=1
Ms(4)
n(r0, q0)Ms(1)
n(r, q0)
×sen(θ0, q0)sen(θ, q0)
(6.11)
For the field points far away from the surface of body, we use boundary conditions
(r0r≤ ∞).
Hinc(r, θ, kr) = ˆreikrr0
2i×
n=0
Mc(1)
n(r0, q0)Mc(4)
n(r.q0)
×cen(θ0, q0)cen(θ, q0) +
n=1
Ms(1)
n(r0, q0)Ms(4)
n(r, q0)
×sen(θ0, q0)sen(θ, q0)
(6.12)
6.1.3 Resultant Vector Field
Summation of potential vectors of incident and scattered waves gave resultant
potential vectors.
25
In the form of MF, this vector can be expressed by the following equation:
H= ˆr˜
Hr(6.13)
ˆr˜
Hr= ˜reikrr0
4i
+
n=0
Mn(r, θ) (6.14)
For the field close to the body r1rr0, generalize term for Mn(r, θ) becomes:
Mn(r, θ) = BenM(4)
cn (r, q0)cen(θ, q0)
+BenM(4)
sn (r, q0)senθ, q0
+2M(4)
cn (r0, q0)×M(1)
cn (r, q0)cen(θ0, q0)cen(θ, q0)
+M(4)
sn (u0, q0)M(1)
sn (r, q0)×sen(θ0, q0)sen(θ, q0)
(6.15)
For the field far away from the body r1r≤ ∞, can be written as:
Mn(r, θ) = BenM(4)
cn (r, q0)cen(θ, q0)
+BenM(4)
sn (r, q0)senθ, q0
+2M(1)
cn (r0, q0)×M(4)
cn (r, q0)cen(θ0, q0)cen(θ, q0)
+M(1)
sn (u0, q0)M(4)
sn (r, q0)×sen(θ0, q0)sen(θ, q0)
(6.16)
In spectral domain the total radiated field has ˆrcomponent, mathematically it
can be written as:
˜
Er=k2
r
ıωϵ eıkrr0
H
˜
Er=k2
r
4ωϵ eıkrr0
+
n=o
Mn(r, θ)
(6.17)
As spectral domain has only ˆrcomponent, Using equation of magnetic potential
26
vector transversal component can be deduced; which are as follow:
˜
hr=µ
4πr eıkrr0cos θ˜
hr
∂θ (6.18)
˜
hθ=µ
4πr eıkrr0sin θ˜
hr
∂r (6.19)
6.2 Impedance Boundary Conditions for Human
Body
Human body impedance is defined as:
Z=µb
εb
(6.20)
The generalized form of Impedance Boundary Condition is:
ˆ
l×(ˆ
lט
E) = Z(ˆ
lט
h) (6.21)
Spectral domain can be defined by total magnetic field defined by ˜
Eand ˜
hand
given as:
ˆ
l×(ˆ
lט
E)|(r=r1)=ˆr˜
Er|(r=r1)(6.22)
Z(ˆ
lט
h)|(r=r1)= ˆrZ ˜
hθ|(r=r1)(6.23)
so equation (21) becomes:
ˆr˜
Er|(r=r1)= ˆrZ ˜
hθ|(r=r1)(6.24)
Substituting values of ˜
Erand ˜
hθin equation (4.24), we get the following equation:
k2
r
ıωε ˜
Hr|(r=r1)=2Zeıkrr0
4πr sin θ˜
Hr
∂r |(r=r1)(6.25)
potential vector ˜
Hr|(r=r1)can be expressed as (4.14) and expanded up to finite
term using (15).
27
Frequency (Hz) Electric Permittivity Conductivity (S.m1) Wavelength (m)
1MHz 1 0 299.79
915MHz 36.6642 0.6231 0.32764
2GHz 33.089 1.1708 0.0226
2.40MHz 35.1940 1.1367 0.0226
Table 6.1: Human body Impedance parameters at different frequencies
suppose
B(θ) = ıωε02Z
k2
rπr sin θ(6.26)
Even and odd terms are expressed as:
Ben =2M(4)
cn (r0, q0)cen(θ0, q0) (6.27)
and
Bon =2M(4)
sn (r0, q0)sen(θ0, q0) (6.28)
These are the basic formulas for even and odd expansion coefficients and expanded
terms are defined as:
Ben =k2
r(4πr) sin θM(1)
cn (r1, q0) + ık0˘
Z´
M1
cn(r1, q0)
k2
r(4πr) sin θM(4)
cn (r1, q0) + ık0˘
Z´
M4
cn(r4, q0)(6.29)
and
Bon =k2
r(4πr) sin θM(1)
sn (r1, q0) + ık0˘
Z´
M1
sn(r1, q0)
k2
r(4πr) sin θM(4)
sn (r1, q0) + ık0˘
Z´
M4
sn
˘(r4, q0)(6.30)
In above equations ˘
Zis the normalized surface impedance it’s formula is ˘
Z=Z
Z0.
Whereas Z0is the wave impedance in the air.
Different parameters, which effects the human body impedance at different fre-
quencies are given in table 6.1.
6.3 Field Distribution (On-Body Sensor)
The field distribution around the sphere can be solved in the spatial domain using
inverse fourier transform [28].
Er=1
2π
−∞
˜
Ereıkrrdkr(6.31)
28
For WBANs applications, on-body sensors are near the body surface of human.
Therefore, radial components of sensor and receiver (field point) considered same
as the body surface i.e, (r0rr1).
Mn(r, θ) = Me
n(r1, θ) + Mo
n(r1, θ) (6.32)
Me
n(r1, θ) and Mo
n(r1, θ) are defined as:
Me
n(r1, θ) = M(4)
cn (r1, q0)cen(θ0, q0)
×[Ben + 2M(1)
cn (r1, q0)cen(θ0, q0)] (6.33)
and
Mo
n(r1, θ) = M(4)
sn (r1, q0)sen(θ0, q0)
×[Bon + 2M(1)
sn (r1, q0)sen(θ0, q0)] (6.34)
Substituting the values of (Ben) and (Bon) in equation (4.33) and (4.34), we get
the following equations:
Me
n(r, θ) = M(4)
sn (r1, q0)cen(θ, q0)
×k2
r(4πr) sin θM(1)
cn (r1, q0) + ık0˘
ZM(1)
cn
k2
r(4πr) sin θM(4)
cn (r1, q0) + ık0˘
ZM(4)
cn
+2M(1)
cn (r1, q0)cen(θ0, q0)
(6.35)
By applying Wronskian relationship on equation (4.35) [29], we get the simplified
equation for even and odd MF:
Me
n(r, θ) = K0(4πr)M(4)
cn (r1, q0)cen(θ, q0)cen(θ0, q0)
k2
r(4πr) sin θM(4)
cn (r1, q0) + ık0˘
ZM(4)
cn
(6.36)
Similarly,
Mo
n(r, θ) = K0(4πr)M(4)
sn (r1, q0)sen(θ, q0)sen(θ0, q0)
k2
r(4πr) sin θM(4)
sn (r1, q0) + ık0˘
ZM(4)
sn
(6.37)
The final equation for electric field distribution by substituting equation (4.36),
(4.37) and (4.32)in equation (4.31):
29
Er(r, θ, ϕ) = 2×Zs
ωϵ
0
eıkrr
n=0
cen(θ, q0)cen(θ0, q0)
kr24πsinθ +ıkrM(4)
cn ˇ
Z
M4
cn(r1,q0)
+
0
eıkrr
n=0
sen(θ, q0)sen(θ0, q0)
kr24πsinθ +ıkrM(4)
sn ˇ
Z
M4
sn(r1,q0)dkr
(6.38)
6.4 Path loss
WBANs are greatly influenced by the amount of path loss that occurs due to
different impairments. Devices for WBANs are generally placed inside or on the
body surface, so, losses between these devices would affect the communication and
can degrade the performance monitoring in. In the following sections, we study in
detail about the WBANs communication and path loss that occurs in it and how
it affects the performance.
Reduction in intensity of electromagnetic wave introduces path loss. Path loss
is mainly caused by free space impairments of propagating signal like refraction,
attenuation, absorption and reflection etc. It also depends on the distance be-
tween transmitter and receiver antennas, the height and location of the antennas,
propagation medium such as moist or dry air etc, and environment around the
antennas like rural and urban etc. Path loss for WBANs is different from tradi-
tional wireless communication because it depends on both distance and frequency.
Frequency is catered because body tissues are greatly affected by the frequency
on which sensor device is working.
Path loss in WBANs is very important parameter. WBANs work effectively when
the path loss between the transmitter and receiver is less. Path loss in WBAN
occurs due to many factors such as reflection, diffraction and refraction etc, from
the body parts. So, data may face distortion due to path loss which causes dif-
ficulty for medical team located at far distance to correctly retrieve data. Path
loss will decrease the efficiency of monitoring different vital signs in human body
at patient’s level as well as at medical team’s level. The main focus of this section
is to minimize the path loss that occurs at different stages in WBANs. Path loss
depends on the frequency of the transmitter and distance of the receiver. This
increases the efficiency of monitoring in BAN which is our main goal. Path loss
dependence on distance as well as frequency is given in following equations:
P L =P L0+ 10nlog10
d
d0
+σs(6.39)
30
Whereas Lis the path loss, dis the distance between transmitting antenna and
receiving antenna, d0is the notation for reference distance, nis representing the
path loss exponent and σsis standard deviation. The above equation of path loss
can also expressed as:
P L = 20log10 (4πdf
c) (6.40)
31
Chapter 7
Simulations and Discussions
7.1 Simulations using DGF
As I have defined earlier, arm motion at different angles are presenting spherical
pattern. Therefore, I simulate the radio propagation environment having radius
d= 15cm, magmatic permeability for human body (assume that permeability of
human body is approximately equal to air) µ2= 1.256 ×106, similarly electric
permittivity ε2= 2.563 ×1010. The dielectric constant is mean value of all tis-
sues of human body.
I consider the surrounding homogeneous medium to be air with magmatic perme-
ability µ1= 1.256×106 and electric permittivity ε1= 8.8542×1012. Frequency
up to GHz is used for BAN communication, which is for ISM band. The Transmis-
sion frequency for simulation is 1GHz. We assumed that the transmitter is acting
as point source at x0= (16cm, π
2,0). The radial distance of receiver is r0= 18cm
from the central spherical axis of shoulder. For the simulation, we assumed that
receiver move along the azimuthal angle for varying values of ϕ0and different
heights from the center of shoulder.
For simulation, we consider equation (3.26) in which Gnh(x, x0) is used in matrix
form of eigen functions. This equation has an integration which is not possible
so, approximated to summation. Thus, I approximate equation (3.26) in to this
form:
32
Gs(x, x0) = ȷ
L
l=L
Q
n=Q
1
n2Gnh(x, x0)dh
(7.1)
where L and Q are the truncation limits and ∆Hare the step size of integration.
N and ∆Hare so small that could be ignored and has no effect on calculations. I
only presents electric propagation of multipath reflection and transmission waves
of scattering DGF.This is more significant to represent the attribute of arm mo-
tion as compared to the direct DGF.Figure 2, 3 and 4 shows the scattering DGF
(simulation) of electric field with the change in θ.
Figure 7.1: Magnitude of scattered field component Eϕversus angle ϕ,with different
values of dand the angle is θ=π
6
Using equation (8.1), there are three components in r,θand ϕdirection. Every
Component of electric field is plotted as a function of azimuthal angle ϕ. The val-
ues of ϕis (0 to 2π), whereas at z coordinate different values of receiver has been
plotted. The electric field is plotted, which is vector addition of three components.
These all parameters are shown in the simulation graph.
33
By taking the value of θ=π
6, figure 8.2 shows that magnitude of electric field
(Eϕ) is decreasing as the distance of receiving antenna is increasing from the sen-
sor (transmitting antenna). The plot shows electric field component at different
values of ϕ, varying from 0 to 2π. In this case, Eϕis decreasing from (4080 to
4065)dB by replacing the receiving antenna from 0 cm to 10 cm.
Figure 7.2: Magnitude of scattered field component Eϕversus angle ϕ,with different
values of dand the angle is θ=π
3
In Figure 8.3, having value of θ=π
3, magnitude of electric field (Eϕ) again de-
creases as the antenna moves away from sensor. For the values of ϕfrom 0 to
2π,Eϕhas different values from (4060 from 4068)dB. By changing position of
receiving antenna from 0 cm to 10 cm.
The values of distance and ϕare same, as described in the above graphs by only
replacing the parameter θ=π. Similarly in figure 4 values of Eϕchange from (4082
to 4074)dB by moving the position of receiver away from transmitting antenna,
which in return decreases the electric field intensity.
34
Figure 7.3: Magnitude of scattered field component Eϕversus angle ϕ,with different
values of dand the angle is θ=π
7.2 Simulations using MF
For simulation I take electric permittivity of air, ε0=107
4πc2where cis speed of
light and relative permittivity εr= 36.6647. The conductivity of human body is
approximated to σ= 0.6321 at frequency of 915MHz.
By taking the value of θ=π/6 for d= 20cm, which is the radius of propagation
environment. We set the transmission frequency at 915Mhz and radial distance
from the central spherical axis is r= 0.15cm. We also assumed that with the
movement of arm, ϕ0varies at different angles.
Using equation 4.38, we have three components r, θ, ϕ direction, each component
of electric field is plotted as a function of azimuthal angle ϕ. At z-coordinates
values of receiver is plotted at different distances by changing the values of ϕfrom
0toπ. Electric field is plotted as a function of all three components, all these pa-
rameters are shown in the simulation graphs.
I have done simulation in six scenarios by varying θat different angles. Taking
θ=π
2, figure 5.4 shows that magnitude of electric field is decreasing as receiving
35
antenna is moving away from the source. The simulation graph is also presenting
the change in electric field by varying ϕfrom 0 to π. from simulation, we can also
understand change in magnitude with motion of arm at differen angles of Φ in
radians.
0
5
10
1
1.2
1.4
1.6
1.8
2x 104
0
5
10
15
20
phi(radians)
magnnitude(dB)
phi vs magnitude vs distance
distance(cm)
Figure 7.4: Magnitude of electric field Erat different values of d, and θ=π
2.
In second scenario we repositioned theta at θ=π
4and observed that magnitude of
electric field is diminishing as replacing the receiving antenna away from source.
We can also study the field distribution at different angular positions of ϕ, as
shown in figure 8.5.
In third scenario we have replaced θ=π
6and monitor that magnitude of electric
field intensity is lowing down as receiving antenna is moving far from the sensor,
which is implanted on the center of shoulder.The field distribution at different
azimuthal positions, are depicted in 8.6.
We take θ=π
10 and study that magnitude of electric field is exponentially decreas-
ing by increasing distance of the receiver away from the source. In spherical field
distribution, how magnitude of electric field is distributed by changing the angle
ϕfrom 0 t0 πb8.7.
36
0
5
10
0
2
4
6
8
10
x 104
0
5
10
15
20
phi(radians)
magnnitude(dB)
phi vs magnitude vs distance
distance(cm)
Figure 7.5: Magnitude of electric field Erat different values of d, and θ=π
4.
0
5
10
0
2
4
6
8
10
x 104
0
5
10
15
20
phi(radians)
phi vs magnitude vs distance
magnnitude(dB)
distance(cm)
Figure 7.6: Magnitude of electric field Erat different values of d, and θ=π
6.
By putting θ=π
3, again we have observed the same pattern of decreasing magni-
tude of field, when receiver is going away from the transmitter. As shown in 3-D
plot of 8.8.
In last Scenario values of distance and ϕare same, as mentioned in above graphs.
37
0
5
10
1
2
3
4
5
6
7
8
x 104
0
5
10
15
20
phi(radians)
phi vs magnitude vs distance
magnnitude(dB)
distance(cm)
Figure 7.7: Magnitude of electric field Erat different values of d, and θ=π
10 .
0
5
10
0
2
4
6
8
10
x 104
0
5
10
15
20
phi(radians)
phi vs magnitude vs distance
magnnitude(dB)
distance(cm)
Figure 7.8: Magnitude of electric field Erat different values of d, and θ=π
3.
By replacing the value of θ=π, in return we can see in figure 8.9 as distance
of receiver is increasing from the transmitting antenna intensity of electric field is
decreasing.
By studying and comparing all above six 3-D plots we I have prove that magni-
38
0
5
10
1
2
3
4
5
6
7
x 104
0
5
10
15
20
phi(radians)
phi vs magnitude vs distance
magnnitude(dB)
distance(cm)
Figure 7.9: Magnitude of electric field Erat different values of d, and θ=π.
tude of electric field and distance of receiving antenna has inversely proportional
relationship.
39
Chapter 8
Conclusion
I have proposed a standard approach to derive an analytical channel modeling
and propagation characteristics of arm motion as spherical model. To predict the
electric field around body, I have formulated two procedures based on DGF and
MF.
First, I derive Eigen functions of spherical model then calculated the scattering
superposition to come across reflection and transmission waves of antenna. The
model includes four cases where transmitter or receiver is located inside or outside
of the body. This model is presented to understand complex problem of wave
propagation in and around arm of human body. Simulation shows that Electric
field decreases when receiver moves away from the shoulder with change of angle
θ.
Secondly, I develop mathematical formulation in terms of MF. This function in-
volve complicated terms of AMF, RMF, cosine and sine-sphere. Using this func-
tion I derive only one case, when transmitter and receiver both are located outside
human body. Simulation results show, how magnitude of electric field varies with
the change of arm motion. Similarly, graphical results describe if distance between
receiver and sensor increases, electric intensity decreases.
40
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