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5 Figures# Modeling Propagation Characteristics for Arm-Motion in Wireless Body Area Sensor Networks

Abstract

To monitor health information using wireless sensors on body is a promising
new application. 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
paper we have presented the wave propagation in WBASN which is modeled as point
source (Antenna), close to the arm of the human body. Four possible cases are
presented, where transmitter and receiver are inside or outside of the body.
Dyadic Green's function is specifically used to propose a channel model for arm
motion of human body model. This function is expanded in terms of vector wave
function and scattering superposition principle. This paper describes the
analytical derivation of the spherical electric field distribution model and
the simulation of those derivations.

Figures - uploaded by Nadeem Javaid

Author content

arXiv:1208.2332v1 [cs.SY] 11 Aug 2012

1

Modeling Propagation Characteristics for

Arm-Motion in Wireless Body Area Sensor

Networks

Q. Ain, A. Ikram, N. Javaid, U. Qasim

‡

, Z. A. Khan

§

‡

University of Alberta, Alberta, Canada

Department of Electrical Engineering, COMSATS

Institute of Information Technology, Islamabad, Pakistan.

§

Faculty of Engineering, Dalhousie University, Halifax, Canada.

Abstract—To monitor health information using wireless sensors

on body is a promising new application. Human body acts as a

transmission channel in wearable wireless devices, so electromag-

netic propagation modeling is well thought-out for transmission

channel in Wireless Body Area Sensor Network (WBASN). In

this paper we have presented the wave propagation in WBASN

which is modeled as point source (Antenna), close to the arm

of the human body. Four possible cases are presented, where

transmitter and receiver are inside or outside of the body. Dyadic

Green’s function is speciﬁcally used to propose a channel model

for arm motion of human body model. This function is expanded

in terms of vector wave function and scattering superposition

principle. This paper describes the analytical derivation of the

spherical electric ﬁeld distribution model and the simulation of

those derivations.

Index Terms—Wireless Body Area Networks, Dyadic Green’s

Function

I. INTRODUCTION

Hospitals throughout the world are facing a unique problem,

as the aged population is increased, health-care population is

decreased. Telecommunication community 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 BASNs.

BASNs 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.

The basic step in building any wireless device is to study

the transmission channel 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]. For the short range low

data rate communication in BAN, measurement groups have

considered Ultra-Wide Band (UWB) 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.

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.

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 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 Electro Magnetic (EM) theory,

using Dyadic Green’s Functions [11-13].

II. MOTIVATION

Recently, WBASNs shows potential due to increasing ap-

plication in medical health care. 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

simple and generic body area propagation models to develop

efﬁcient and low power radio systems near the human body. To

achieve better 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. These

functions involve Mathieu function, Dyadic Green’s function,

Maxwell’s equations, Finite Difference Time Domain (FDTD)

and Uniform Theory of Diffraction (UTD). Some of these

approaches have already proven effective for evaluating body

area communication system proposals.

2

Finite Difference Time Domain had successfully measured

the communication scenarios. Complete Ultra-Wide band

models have been developed using measurements and simula-

tions, however they do not consider the physical propagation

mechanism. So, the researchers have to rely on ad-hoc model-

ing approaches which can result in less accurate propagation

trends and inappropriate modeling choices [14, 15].

Uniform Theory of Diffraction depends on a ray tracing

mechanism allowing propagation channel to be explained in

terms of ray diffraction around the body . It typically based

on high-frequency approximations which is not valid for low

frequencies, also not useful when antenna is very close to the

body [16].

A generic approach is proposed to understand the body area

propagation by considering the body as a lossy cylinder and

antenna as a point source by using Maxwell’s equation. A

solution for a line source near lossy cylinder is derived using

addition theorem of Hankel functions then the line source

is converted into the point source by taking inverse Fourier

transform. The model accurately predicts the path loss model

and can be extended to all frequencies and polarities but this

is limited in scope and not always physically motivated [17].

Mathieu functions are also used for body area propagation

model. The human body is treated as a lossy dielectric elliptic

cylinder with inﬁnite length and a small antenna is treated as

three-dimensional (3-D) polarized point source. First the three-

dimensional problem of cylinder is resolved into 2-D problem

by using Fourier transform and then this can be expanded in

terms of Eigen functions in cylindrical coordinates. By using

Mathieu function exact expression of electric ﬁeld distribution

near the human body is deduced [18].

The propagation characteristics of cylindrical shaped human

body have been derived using Dyadic Green’s functions.

The model includes the cases of transmitter 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 [19].

We have developed a simple but generic approach to

body area propagation derived from Dyadic Green’s Function

(DGF). This approach is 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. First, we use spherical vector Eigen functions for ﬁnding

the scattering superposition. Four cases are considered for

either transmitter or receiver is located inside or outside the

body. Finally, simulated results of electric ﬁeld distribution

with different values of angle have shown.

III. MATHEMATICAL MODELING FOR ARM MOTION

USING DYADIC GREEN’S FUNCTION

In this paper, 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 x

0

is 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 1.

Fig. 1. Human body model showing arm motion in 3D.

A. Electric Field Propagation Characteristics

Let E(x) be electric ﬁeld at point x due to current source

J(x

0

). The general formula for Electric ﬁeld can be written

as:

E(x) = iωµ

p

Z Z Z

V

G(x, x

o

)J(x, x

0

)dv (1)

V is volume of source, J(X

0

) is the current source,

G(x, x

0

) is the Dyadic Green’s function

′

ω

′

is the radian

frequency of transmission and

′

µ

′

p

is magmatic 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.

B. Spherical Wave Vector Eigen Function

As we are considering arm motion of human body, so

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 spher-

ical vector eigen functions [14]. These eigen functions are

L

nhk

(χ), M

nhk

(χ) and N

nhk

(χ), where k is the wave number

of medium, n is an integer, h is a real number and x is a point

in space. These all are the solutions to the Helmholtz equation

having three components in r, Θ and φ. These vector eigen

functions are given by [19]:

L

nhk

(χ) = ∇[Ψ

nhk

(χ)] (2)

M

nhk

(χ) = ∇ × [Ψ

nhk

(χ)] (3)

N

nhk

(χ) =

1

k

∇ × ∇[Ψ

nhk

(χ)] (4)

3

In above eigen functions, Laplacian operator in the spherical

coordinate system is ∇. It’s mathematical expression is given

as:

∇ =

∂

∂r

+

∂

r∂θ

+

∂

r sin θ∂φ

(5)

x represents the point in space having components r, Θ

and φ. Solution of Helmoltz equation is Ψ

nhk

(x) which is the

scalar eigen function [19].

[Ψ

nhk

(χ)] = Z

n

(ηr)P

h

n

(cos θ)

cos

sin

hφ (6)

Z

n

is a general spherical function of order n. For sphere

we use Hankle function of ﬁrst and second order which are

deﬁned as:

[Z

n

(ηr)] = (−1)

n

(ηr)(

d

drη

2

r

)

n

(

sin(ηr )

ηr

)

n

(7)

η is the propagation constant in direction of φ, whereas

k

2

= η

2

+ h

2

. The laplace operator is applied and ﬁnd the

eigen values L

nhk

, M

nhk

and N

nhk

by using eigen function.

The vector eigen function in (2), (3) and (4) becomes:

L

nhk

(χ) =

∂Z

n

(ηr)

∂r

P

h

n

(cos θ)

cos

sin

hφ +

z

n

(ηr)

r

∂

∂θ

P

h

n

(cos θ)

cos

sin

hφ +

hZ

n

(ηr)

r sin θ

P

h

n

(cos θ)

sin

cos

hφ

(8)

M

nhk

(χ) = ∓

hZ

n

(ηr)

sin θ

P

h

n

(cos θ)

sin

cos

hφ − Z

n

(ηr)

∂

∂θ

P

h

n

(cos θ)

cos

sin

hφ

(9)

N

nhk

(χ) =

nZ

n

(ηr)

kr

P

h

n

(cos θ)

cos

sin

hφ +

1

kr

∂rZ

n

(ηr)

∂r

P

h

n

(cos θ)

cos

sin

hφ ∓

h

sin θ

P

h

n

(cos θ)

sin

cos

hφ

(10)

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,

L

nhk

(χ) =

∂Z

n

)(ηr)

∂r

P

h

n

(cos θ)

cos

sin

hφ

Z

n

(ηr)

r

P

h

n

(cos θ)

cos

sin

hφ

hZ

n

(ηr)

sin θ

P

h

n

(cos θ)

sin

cos

hφ

(11)

M

nhk

(χ) =

0

∓

hZ

n

(ηr)

r

P

h

n

(cos θ)

cos

sin

hφ

−Z

n

(ηr)

∂P

h

n

(cos θ)

sin

cos

hφ

∂θ

(12)

N

nhk

(χ) =

hZ

n

(ηr)

kr

P

h

n

(cos θ)

cos

sin

hφ

∂

n

(ηr)

kr∂r

P

h

n

(cos θ)

cos

sin

hφ

∂θ

∓

h

sin θ

P

h

n

(cos θ)

sin

cos

hφ

(13)

C. 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 2, concept of scattering superposi-

tion 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, x

0

) = G

d

(x, x

0

) + G

s

(x, x

0

) (14)

Dyadic Green’s equation is divided in to two parts as direct

wave [G

d

(x, x

0

)] and scattered wave [G

s

(x, x

0

)]. 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.

D. Superposition of Direct Wave

The direct component of DGF is given as [11]:

G

d

(x, x

0

) =

rr

k

2

(δ(x − x

0

) +

8π

Z

∞

−∞

dh

∞

X

n=−∞

1

n

2

x×

(

M

(1)

nhk

(X)

N

M

∗

nhk

(X

0

) + N

(1)

nhk

(X)

N

N

∗

nhk

(X

0

)

M

nhk

(X)

N

M

(1∗)

nhk

(X

0

) + N

nhk

(X)

N

N

(1∗)

nhk

(X

0

)

(15)

In the above equation of DGF, r > r

0

is for ﬁrst case and

r < r

0

is second case.The ∗ denotes the conjugation and

N

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)

n

is chosen for

Z

n

and J

n

should be used otherwise.

E. Superposition of Scattered Wave

Here we discuss four different scenarios for the scatter-

ing components of DGF along with boundary conditions

G

s

(x, x

0

). (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.

F. Transmitter and Receiver Located Inside Body

In this case, Receiver and Transmitter both located inside

the body so we can write Dyadic Green’s equation as,

4

Fig. 2. Scattering Superposition

G

(11)

s

(x, x

0

) =

8π

Z

∞

−∞

dh

∞

X

−∞

1

η

2

x

×[M

nhk1

N

nhk1

]R

1

2 ×

(

N

nhk1

(X

0

)

T

M

nhk1

(X

0

)

T

(16)

R

12

contains reﬂection coefﬁcients. R

12

is calculated in

literature using boundary conditions, its matrix is given by

[16]:

R

12

= [J

n

(η

1

d)H

n

(η

2

d) − H

n

(η

2

d)J

n

(η

1

d)]

−

1

×[H

n

(η

2

d)H

n

(η

1

d) − H

n

(η

1

d)J

n

(η

2

d)]

−

1

(17)

In the above equation of reﬂection coefﬁcient ’d’ represents

radius of spherical body model, η

2

1

= k

2

1

− h

2

, η

2

2

= k

2

2

−

h

2

, k

2

1

= ω

2

µ

1

ǫ

1

, k

2

2

= ω

2

µ

2

ǫ

2

. The 2x2 matrices for j

n

(ηd)

and H

n

(ηd) are expressed as:

B

n

(η

p

d) =

1

η

2

p

d

×

ωǫ

p

η

p

dB

n

(η

p

d) −nhB

n

(η

p

−nhB

n

(η

p

−ωµ

p

η

p

dB

n

(η

p

d)

(18)

B

n

is either H

(1orJ

n

)

n

, B(.) is the derivative of B w.r.t the

whole argument, and p=1,2

G. Transmitter Located Inside and Receiver Located Outside

Body

In this case DGF can be written as :

G

(21)

s

(x, x

0

) =

8Π

Z

∞

−∞

dh

∞

X

n=−∞

1

η

2

×[N

nhk

.M

nhk

]T

12

N

∗

nhk1

(x

0

)

T

M

∗

nhk1

(x

0

)

T

(19)

In the above equation T

12

is a transmission coefﬁcient

Matrix and given as:

T 12 =

2ω

πη

2

1

d

[J

n

(η

1

d)H

n

(η

2

d) − H

n

(η

2

d)J

n

(η

1

d)]

−

1

×

ε

1

0

0 ε

(20)

H. Both Transmitter and Receiver Located Outside Body

G

s

(x, x

0

) =

8Π

Z

∞

−∞

dh

∞

X

n=−∞

1

n

2

×[M

nhk

N

nhk

]R

2

1

n

N

n

hk(X

0

)

T

M

n

hk(X

0

)

T

(21)

Similarly as R

12

, R

21

is the reﬂection coefﬁcient matrix

and it is given as:

R21 = [J

n

(η

1

d)H

n

(η

2

d) − H

n

(η

2

d)J

n

(η

1

d)]

−

1

×[J

n

(η

2

d)J

n

(η

1

d) − J

n

(η

1

d)J

n

(η

2

d)]

(22)

I. Transmitter Located Outside and Receiver Inside Body

In this case, we can write DGF as:

G

s

(x, x

0

) =

8Π

Z

∞

−∞

dh

∞

X

n=−∞

1

n

2

×[M

nhk

N

nhk

]T

21

N

∗

nhk1

(x

0

)

T

M

∗

nhk1

(x

0

)

T

(23)

5

T

12

is the transmission coefﬁcient matrix, given as:

T 21 =

2ω

Πηd

[J

n

(η

1

d)H

n

(η

2

d) − H

n

(η

2

d)J

n

(η

2

2

d)]

−

1

×

ε

2

0

0 −µ

2

(24)

IV. TRANSMITTER AND RECEIVER LOCATED OUTSIDE OF

THE BODY

In this section we presents 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.

G

s

(x, x

0

) =

8Π

Z

∞

−∞

dh

∞

X

n=−∞

1

n

2

G

nh

(x, x

0

)dh

(25)

G

nh

(x, x

0

) is stated as:

G

nh

(x, x

0

) =

N

nhk

(X)

1

M

nhk

(X)

1

× R21

N

nhk

(X

0

)

T

M

nhk

(X

0

)

T

(26)

V. SIMULATIONS

As we have deﬁned earlier, arm motion at different angles

are presenting spherical pattern. Therefore, we simulate the

radio propagation environment having radius d = 1 5cm, meg-

natic permeability for human body (assume that permeability

of human body is approximately equal to air) µ

2

= 1.256 ×

10

−

6, similarly electric permittivity ε

2

= 2.5 63 × 10

−

10.

The dielectric constant is mean value of all tissues of human

body. We take the surrounding homogeneous medium to be

air with megnatic permeability µ

1

= 1.256 × 1 0

−

6 and

electric permittivity ε

1

= 8.8542 × 10

−

12. Frequency up

to GHz is used for BAN communication, which is for ISM

band. The Transmission frequency for simulation is 1GHz.

We assumed that the transmitter is acting as point source

at x

0

= (16cm,

π

2

, 0). The radial distance of receiver is

r

0

= 18cm from the central spherical axis of shoulder. For the

simulation, we assumed that receiver move along the azimuthal

angle for varying values of φ

0

and different heights from the

center of shoulder.

For simulation, we consider equation (25) in which

G

nh

(x, x

0

) is used in matrix form of eigen functions. This

equation has an integration which is not possible so we

approximate it to summation. Thus, we approximate equation

(25) in to this form:

G

s

(x, x

0

) =

8Π

L

X

l=−L

Q

X

n=−Q

1

n

2

G

nh

(x, x

0

)dh

(27)

L and Q are the truncation limits and ∆H are the step

size of integration. N and ∆H are so small that could be

ignored and has no effect on calculations. We only presents

electric propagation of multi-path reﬂection and transmission

waves of scattering DGF.This is more signiﬁcant to represent

the attribute of arm motion as compared to the direct DGF.

Figure 2,3 and 4 show the scattering DGF (simulation) of

electric ﬁeld with the change in θ.

Fig. 3. Magnitude of scattered ﬁeld component E

φ

versus angle φ,with

different values of d and the angle is θ =

π

6

Using equation (27), we have three components in r,θ and

φ direction. Every Component of electric ﬁeld is plotted as a

function of azimuthal angle φ. The values of φ is (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.

By taking the value of θ =

π

6

, ﬁgure 2 shows that magnitude

of electric ﬁeld (E

φ

) is decreasing as the distance of receiving

antenna is increasing from the sensor (transmitting antenna).

The plot shows electric ﬁeld component at different values of

φ, varying from 0 to 2π. In this case, E

φ

is decreasing from

(4080 to 4 065)dB by replacing the receiving antenna from 0

cm to 10 cm.

In Figure 3 , when we take value of θ =

π

3

, magnitude of

electric ﬁeld (E

φ

) again decreases as the antenna moves away

from sensor. For the values of φ from 0 to 2π, E

φ

has different

values from (4060 from 4068)dB. By changing position of

receiving antenna from 0 cm to 10 cm.

The values of distance and φ are same, as described in the

above graphs by only replacing the parameter θ = π. Similarly

in ﬁgure 4 values of E

φ

change from (4082 to 4074)dB

by moving the position of receiver away from transmitting

antenna, which in return decreases the electric ﬁeld intensity.

6

Fig. 4. Magnitude of scattered ﬁeld component E

φ

versus angle φ,with

different values of d and the angle is θ =

π

3

Fig. 5. Magnitude of scattered ﬁeld component E

φ

versus angle φ,with

different values of d and the angle is θ = π

VI. CONCLUSION

We have proposed a generic approach to derive an ana-

lytical channel modeling and propagation characteristics of

arm motion as spherical model. To predict the electric ﬁeld

around body, we have formulated a two step procedure based

on Dyadic Green’s function. First, we 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.

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