ULAB JOURNAL OF SCIENCE AND ENGINEERING

Editorial: Introducing ULAB JSE Ultra Wideband Compact Double Inverted-F Antenna for WLAN/WiMAX/RFID Applications Debabrata Kumar Karmokar, Khaled Mahbub Morshed, Md. Selim Hossain, Md. Aminur Rahman, Md.Nurunnabi Mollah Analysis of Odd Order Distortion in Mach-Zehnder Modulator for CATV System M. Shahidul Islam, M. S. Islam, Mohammad Shorif Uddin The Performance Measurement of WCDMA Channel using HSDPA Md. Sipon Miah, M. Mahbubur Rahman, Tapan Kumar Joadder, Bikash Chandra Singh A Simple Approach to Recognize a Person Using Hand Geometry R. H. M. Alaol Kabir, Md. Atikur Rahman, Mohammad Ahsanul haque, Mohammad Osiur Rahman, M. H. M. Imrul Kabir Human Emotion Recognition Using PCA, ICA and NMF Paresh Chandra Barman, Chandra Shekhar Dhir, Soo-Young Lee

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ULAB JOURNAL OF SCIENCE AND ENGINEERING A RESEARCH PUBLICATION OF ULAB

November 2010 Vol. 1 ISSN: 2079-4398

CONTENTS

( Contents Continued on Back Cover )

Department of Computer Science & EngineeringUNIVERSITY OF LIBERAL ARTSBANGLADESH

-

Design of a Microcontroller-Based Duobinary Encoder Circuit R. R. Mahmud, M. A. G. Khan, S. M. A. Razzak Development of a Knowledge-Based Diagnosis and Management System for Diabetes Mellitus through Web-Based Technique Mohammad Shorif Uddin and Morium Akter

Bangladesh H. M. Jahirul Haque and Manjurul Haque Khan

Md. Sazadul Hasan and Md. Rashedul Islam A Fi imensional Heat E M. H. Kabir, A. Afroz, M. M. Hossain, M. O. Gani A Note for Contributors List of Reviewers

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ULAB JOURNAL OF SCIENCE AND ENGINEERING Vol. 1, November 2010

House 56, Rd 4/A @ Satmasjid Road Dhanmondi, Dhaka-1209, BangladeshPhone: 966-1255, 966-1301, 0171-309-1936. Web: www.ulab.edu.bd

ULAB JOURNAL OF SCIENCE AND ENGINEERING VOL. 1, NO. 1, NOVEMBER 2010 (ISSN: 2079-4398) 1

Editorial

Introducing ULAB JSE

ARM welcome to the first issue of the University of Liberal Arts Bangladesh Journal of Science and Engineering (ULAB JSE). According to UGC statistics there are 29 public, 54 private and 2 international universities are now in Bangladesh. Almost all universities have science subject. Besides, there are many postgraduate colleges under

Bangladesh National University. International conferences ICCIT (Internalational Conference on Computer and Infor-mational Technology), ICECE (International Conference on Electrical and Computer Engineering) and ICECC (Interna-tional Conference on Electronics, Computer and Communication) are being organized regularly. Approximately 500 papers are being submitted in each conference. The motivation for this new scholarly research journal is the rapidly growing need for publishing quality articles in the diverse field of science and engineering. Its editorial board strives to publish original research contributions with technical novelty in a timely manner. The main focus of this journal includes all traditional areas of both theoretical and practical applications of physics, ma-thematics, environmental science, electronics, computer science, information and communication engineering. Besides, the journal will gladly accept papers on emerging technologies and new areas related to the above fields. We are de-lighted to report the important statistical chronology of thus journal until publication of its first issue.

14 March 2010: Decision for publishing this joural and formation of editorial board 22 April 2010: ISSN number received 28 April 2010: Hosting journal website 18 May 2010: Call for papers circulated in both electronic and print versions 31 July 2010: 29 papers received within deadline for submission for its first issue 30 September 2010: Editorial decision has been notified to corresponding authors 15 October 2010: Received camera-ready manuscripts 30 November 2010: Print version of the journal published.

Among 28 papers submitted for the first issue, 10 papers have been accepted for publication (acceptance rate: 35.71%). You are most welcome to read the first issue of the ULAB Jouranl of Science and Engineering. To fulfil the mission for publishing a high-quality journal, we are really dependent upon you readers to submit excellent contributions, original research works as well as reviews. Its editorial board is working hard to offer a rapid high-quality reviewing process.

We would like to thank authors, reviewers and readers for your contributions, support, and dedications to the journal.

We strongly believe that together, we will bring the journal to a higher level in quality, impact, and reputation.

Mohammad Shorif Uddin Editor-in-Chief

Sazzad Hossain

Associate Editor

A.H.M. Asadul Huq

Associate Editor

W

© 2010 ULAB JSE


Wideband Compact Double Inverted-F Antenna for WLAN/WiMAX/RFID Applications Debabrata Kumar Karmokar, Khaled Mahbub Morshed, Md. Selim Hossain, Md. Aminur Rahman,

Md. Nurunnabi Mollah

Abstract—This paper presents a wideband compact double Inverted-F antenna (DIFA) for WLAN/WiMAX/RFID applications by

means of numerical simulation. The antenna has compact size of 9×18 mm2 and provides a wide bandwidth of 2.5 GHz

(5000MHz~7500MHz) which cover the 5.2 GHz WLAN, 5.5 GHz WiMAX and 5.8 GHz WLAN/RFID application bands. Moreover

it has very high peak gain of 7.14, 7.11 and 6.50 dBi with less than 0.5, 0.7 and 0.6 dBi gain variation within the 10 dB return

loss bandwidth at 5.2, 5.5 and 5.8 GHz band respectively. Also the VSWR of DIFA varies from 1.09877 to 1.61467 within the

antenna bandwidth.

Keywords— Inverted-F antenna (IFA), Double IFA (DIFA), Radio frequency identification (RFID), Worldwide interoperability for

microwave access (WiMAX), Wireless local area networks (WLAN).

1 INTRODUCTION

ODERN wireless communication systems are ris-ing rapidly and the function of these devices is in-creasing as well as the size decreasing. The size of

the antenna often has a great influence on the whole size of wireless systems so for meet up the demand of multi-function small wireless devices, the antenna has to be compact, light and easy to be embedded with the system. Antenna designer’s encountered difficulty in designing antennas that could maintain high performance; even the antenna size is smaller. In order to satisfy these demands, IFA has been widely used in mobile devices due to its low profile, ease of fabrication and superior electrical perfor-mance. At present the demand of WLANs are increasing numerously worldwide, because they provide high speed connectivity and easy access to networks without wiring. Also in recent times the applications of WiMAX, which can provide a long operating range with a high data rate for mobile broadband wireless access, faultless internet access for wireless users becomes more popular [1-4]. On the other hand the RFID system has recently using effi-ciently for tracking and identifying objects in the various supply chains from security and control point of view [6-7]. The fast growing WLAN protocals operating bands are IEEE 802.11 b/a/g at 2.4 GHz (frequency ranges 2400–2484 MHz), 5.2 GHz (frequency ranges 5150–5350 MHz) and 5.8 GHz (frequency ranges 5725–5825 MHz).

The operating bands of WiMAX are 2.5 (frequency ranges 2500 –2690), 3.5 (frequency ranges 3400–3600) and 5-GHz (frequency ranges 5250–5850 MHz) bands [1–5]. The fre-quency band used for the RFID system is 125 kHz; 13.56, 869 and 914 MHz; 2.45 and 5.8 GHz band [6-7]. There is a trend all over the world for the advance of compact, low-profile, multi-function antenna with the ability to support various commercial protocols [8]. For this reason compact antenna with suitable gain, low gain variation and satis-factory bandwidth for WLAN/WiMAX/RFID applica-tions are extremely enviable.

A novel composite monopole antenna for 2.4/5.2/5.8 GHz WLAN and 2.5/3.5/5 GHz WiMAX operation in a laptop computer [1], a CPW-fed triangle-shaped mono-pole antenna for 2.4/5 GHz WLAN and 3.4 GHz WiMAX applications [2], a capacitively fed hybrid monopole/slot chip antenna for 2.5/3.5/5.5 GHz WiMAX operation in the mobile phone [3], a printed antenna with a quasi-self-complementary structure for 5.2/5.8 GHz WLAN opera-tion [4], a novel dual-broadband T-shaped monopole an-tenna with dual shorted L-shaped strip-sleeves for 2.4/5.8 GHz WLAN operation [5], a simple coplanar waveguide (CPW)-fed patch antenna and a novel CPW-fed F-shaped planar monopole antenna obtained by embedding folded slots in a rectangular patch on a single-layer substrate for 5.8 GHz RFID application [6–7], a compact monopole an-tenna for dual industrial, scientific and medical (ISM) band (2.4 and 5.8 GHz) operation [8], a novel wideband metal-plate antenna suitable for application as an internal laptop antenna for 2.4/5.2/5.8 GHz WLAN or 2.83–5.85 GHz WMAN operation [9], a printed antenna which is working in 2.4 GHz bluetooth, 3.5 and 5.8 GHz WiMAX, 2.4–2.5 and 5.0–5.8 GHz Wi-Fi, 2.4–2.84 GHz, 5.15–5.35 and 5.72–5.83 GHz WLAN operation [10], a broadband low-profile printed T-shaped monopole antenna for 5 GHz WLAN application [11] and a compact PIFA for

M

© 2010 ULAB JSE

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D. K. Karmokar, K. M. Morshed and Md. S. Hossain are with the Faculty of Electrical & Electronic Engineering, Khulna University of Engineering & Technology (KUET), Khulna-9203, Bangladesh. E-mail: [email protected].

Md. A.Rahman is with the Department of Electrical & Electronic Engi-neering, IBAIS University, Dhaka, Bangladesh.

M. N. Mollah is with the Department of Engineering & Technology, East-ern University, Dhaka, Bangladesh

Manuscript received on 21 July 2010 and accepted for publication on 26 August 2010.

D. K. KARMOKAR ET AL.: WIDEBAND COMPACT DOUBLE INVERTED-F ANTENNA FOR WLAN/WIMAX/RFID APPLICATIONS 3

Bluetooth, satellite-digital multimedia broadcasting (S-DMB), wireless broadband (WiBro), WiMAX and WLAN applications [12] have been proposed. To provide the in-creasing demand and cover up the widespread applica-tions of WLAN, WiMAX or RFID an antenna with com-pact size, wider bandwidth, high gain and less gain varia-tion within the antenna bandwidth is desired. To meet up most of mentioned requirements, IFA is one of the good candidates within the micro-strip printed antennas be-cause of its compact size and good input impedance than other printed antennas.

2 ANTENNA DESIGN

In designing the compact wideband antenna for WLAN, WiMAX and RFID operation, we examine the possibility of increasing antenna bandwidth with simplifying its structure. Using method of moments (MoM’s) in Numeri-cal Electromagnetic Code (NEC) [13], we conducted pa-rameter studies to ascertain the effect of different loading on the antenna performance to find out the optimal de-sign. In our analysis we assume the copper conductor and the antenna was intended to be matched to 50 Ω system impedance.

For the analysis of the accuracy optimum segmenta-tion of each geometrical parameter are used in NEC. Fig-ure 1 represents the basic geometry of the IFA. Here one leg of IFA directly connected to the feeding and another leg spaced s from the ground plane. For the simulation we consider printed circuit board (PCB) with permittivity of εr = 2.2 and substrate thickness of 1.58 mm.

The antenna is assumed to feed by 50 Ω coaxial con-

nector, with its central conductor connected to the feeding point and its outer conductor connected to the ground plane just across the feeding point. In the analysis the

(a)

(b)

(c)

Figure 1: Structure of Inverted-F Antenna (IFA) (a) 3-D front, (b) 3-D top and (c) 2-D view.

(c)

Figure 2: Structure of Double Inverted-F Antenna (DIFA) (a) 3-D front, (b) 3-D top and (c) 2-D view.

(a)

(b)

Feed

w

l t

h h1

s

Feed

w

l t

h h1

h1

s

d

4 ULAB JOURNAL OF SCIENCE AND ENGINEERING

dimensions of the ground plane considered as 60 × 60 mm2. Figure 2 represents the modified IFA where load equal to the IFA is applied to the horizontal strip by shorting the end terminals is titled as double IFA (DIFA).

For IFA of Figure 1, the resonant frequency related to w given as [14]

(1) Where c is the speed of light. The effective length of

the current is l+t+h1+w. Under this case the resonant con-dition can be expressed as

(2)

The other resonant frequency that is a part of linear combination with the case 0<w< (1+t) and is expressed as

(3) The resonant frequency (fr) is a linear combination of

resonant frequency associated with the limiting case. For the antenna geometry of Figure 1, fr can be written from equation (1) and (2) as [15]

f r=r. f 1 +(1-r )f 2 (4) Where r=w/(l+t). With the help of resonant frequency

theory of IFA and impedance matching concept, we con-sider the dimension of the IFA as l=14 mm, t=6 mm, h1=4 mm, h=4 mm, s=0 mm, w=3 mm. Figure 3 (a) and (b) shows the effects of l and s on the antenna performance. From the simulated results, antenna has desired bandwidth at l=13 mm and s=1 mm. When l=14 or 15 mm, the values of return loss much better than l=13 mm but at that condi-tion antenna does not cover the whole 5 GHz operating band (frequency ranges 5150 – 5850 MHz) because our aim to design an antenna for 5 GHz operation so that it can cover the whole operating band. A higher value of l shifts the antenna resonance to the higher frequencies. When s=0 mm the value of return loss stay above the 10 dB level throughout the 5 GHz band and when s=2 mm the antenna has very poor S11 characteristics. Figure 4 (a) and (b) shows the effects of t and w on the antenna per-formance. From the simulation, the optimum dimensions of IFA are l=13 mm, t=5 mm, h=4 mm, h1=3 mm, w=4 mm and s=1 mm.

4 5 6 7 8-25

-20

-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

l=11 mm

l=12 mm

l=13 mm

l=14 mm

l=15 mm

(a)

4 5 6 7 8-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

s=0 mm

s=1 mm

s=2 mm

(b)

Figure 3: Effects of (a) length l and (b) spacing s on the return loss as a function of frequency on the antenna structure of Figure 1.

4 5 6 7 8-25

-20

-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

t=4 mm

t=5 mm

t=6 mm

t=7 mm

(a)

4 5 6 7 8-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

w=2 mm

w=3 mm

w=4 mm

(b)

Figure 4: Effects of (a) tap distance t and (b) width w on the return loss of the antenna of Figure 1 as a function of frequency.

)(4 11

htl

cf

4

01

whtl

)(4 12

whtl

cf


When load is applied to the horizontal strip of IFA then the modified structure is shown in Figure 2 which titled as double IFA (DIFA). In this double IFA the struc-ture of load is the same as source IFA. But the change made in separation d for the better performance. Figure 5 presents the characteristics of S11 as a function of fre-quency with different spacing s and separation d. From the obtained data, antenna provides better performance when d is set to 2 mm and s is to 1 mm. Variation of l and its effects on S11 for DIFA is shown in Figure 6. It is clear from the characteristics of S11, when l=12 mm the antenna provide good characteristics than l=13 mm but the band-width does not cover the whole 5 GHz band. For different values of t and w for the antenna of Figure 2, S11 are shown in Figure 7 (a) and (b) respectively. From the ob-served data proposed antenna cover the 5 GHz band, when t=5 mm and w=4 mm. When strip width is at w=3 mm, then the nature of S11 for the variation of l and t are

shown in Figure 8 (a) and (b). Moreover, at w=2 mm the characteristics of S11 are shown in Figure 9 (a) and (b) with the change in l and t. From Figure 8 and 9, when l=14 mm the DIFA has much better return loss characteris-tics than l=13or 15 mm. Also, the antenna has good S11 characteristics at l=15 mm when w=2 mm with respect to

l=13or 14 mm. But the problem is that, when w=2 or 3 mm, DIFA does not cover the whole 5 GHz band and reso-nance shifted to the frequency greater than 6 GHz.

Under these values of w (=2, 3 mm) with different val-ues of t, antenna resonance shifts are not desired for the mentioned application. From Figure 5 to 9, in overall analysis, DIFA fully cover the 5 GHz WLAN operating band, when l=13 mm and w=4 mm. The optimized dimen-sions of the proposed DIFA are listed in Table 1.

4 5 6 7 8-60

-50

-40

-30

-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

d=0 mm

d=2 mm

d=4 mm

(a)

4 5 6 7 8-60

-50

-40

-30

-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

s=0 mm

s=1 mm

s=2 mm

(b)

Figure 5: Return loss as a function of frequency with the different (a) separation d and (b) spacing s of the antenna of Figure 2.

4 5 6 7 8-60

-50

-40

-30

-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

t=4 mm

t=5 mm

t=6 mm

t=7 mm

(a)

4 5 6 7 8-60

-50

-40

-30

-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

l=11 mm

l=12 mm

l=13 mm

l=14 mm

l=15 mm

Figure 6: Effects of length l on the S11 as a function of frequency while t, h, h1 and w remains unchanged of the antenna of Figure 2.

TABLE 1 OPTIMIZED DIMENSIONS OF THE PROPOSED ANTENNA

Antenna Name

Antenna Parameters

Value (mm)

Dimension (mm2)

DIFA

l 13

9×18

t 5 h 4

h1 3 d 2

w 4 s 1


3 NUMERICAL SIMULATION RESULTS

The proposed antenna is constructed and numerically analyzed using MoM’s. The numerical results of the an-tenna are shown below. The proposed antenna have the return loss appreciable than the commonly required 10 dB level. If we apply a suitable structured load equal to the IFA on the horizontal branch of IFA and shorted the ends of the both IFA as shown in Figure 2, the impedance bandwidth improves extensively. The numerical simula-tion analysis of the proposed DIFA to realize the opera-tion for WLAN/WiMAX/RFID is presented below.

Figure 10 (a) shows the voltage standing wave ratio (VSWR) variation and Figure 10 (b) shows the return loss variation of DIFA with frequency. The DIFA provides a large impedance bandwidth of 2500 MHz (5000–7500 MHz) which fully covers the 5.2, 5.5 and 5.8 GHz bands and the peak value of return loss is -50.51082 dB. The value of VSWR of DIFA varies from 1.09877 to 1.61467 within the 5 GHz operating band that indicates the varia-tion of VSWR is very low and it is near to 1 as shown in Figure 10 (a).

4 5 6 7 8-60

-50

-40

-30

-20

-10

0S

11 (

dB

)

Frequency (GHz)

w=2 mm

w=3 mm

w=4 mm

(b)

Figure 7: Return loss as a function of (a) tap distance t and (b) width w for the antenna of Figure 2.

4 5 6 7 8-30

-25

-20

-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

l=11 mm

l=12 mm

l=13 mm

l=14 mm

l=15 mm

(a)

4 5 6 7 8-30

-25

-20

-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

t=3 mm

t=4 mm

t=5 mm

t=6 mm

t=7 mm

(b)

Figure 9: Return loss as a function of (a) length l and (b) tap dis-tance t for the antenna structure of Figure 2, when w=2 mm.

4 5 6 7 8-50

-40

-30

-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

l=11 mm

l=12 mm

l=13 mm

l=14 mm

l=15 mm

(a)

4 5 6 7 8-40

-30

-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

t=4 mm

t=5 mm

t=6 mm

t=7 mm

(b)



Figure 11 (a) shows the gain variation of DIFA. The peak

gains of DIFA is 7.14, 7.11 and 6.50 dBi with less than 0.5, 0.7 and 0.6 dBi gain variation within the 10 dB return loss band-width at 5.2, 5.5 and 5.8 GHz band respectively, which indi-cates that the antenna has stable gain within the operating bandwidth which is desired for the wireless applications. Fig-ure 11 (b) represents the antenna input impedance variation and Figure 12 represents the antenna phase shift causes due the impedance mismatch as a function of frequency. From the obtained results, the input impedance of DIFA is near about 50 Ω which is desired for the impedance matching with the feeding system. Also, from the simulation study, within the return loss bandwidth, DIFA has phase shift closer to 00 all over the antenna bandwidth except at the start of 5.2 GHz band, where phase shift closer to 300. A comparison between the reference antennas and proposed DIFA in gain, band-width and size are listed in Table 2. In overall considerations, DIFA is much better than all other antennas. Figure 13 to 15 shows the normalized radiation patterns of DIFA at 5.2, 5.5 and 5.8 GHz bands respectively. The antenna’s normalized total radiation in H and E-plane is almost omnidirectional which is desired for the WLAN/WiMAX/RFID applications. For the better analysis of the antenna, for three resonant fre-

quencies antenna’s normalized radiation patterns are shown as: total gain in H-plane, total gain in E-plane, horizontal gain in E-plane and vertical gain in H-plane.

4 5 6 7 8

0

2

4

6

8

An

ten

na G

ain

(d

Bi)

Frequency (GHz)

(a)

4 5 6 7 80

20

40

60

80

100

Inp

ut

imp

ed

an

ce (

Oh

m)

Frequency (GHz)

(b)

Figure 11: (a) Total gain and (b) Impedance variation of DIFA with frequency.

4 5 6 7 8-90

-60

-30

0

30

60

90

Ph

ase

(d

eg

ree)

Frequency (GHz)

Figure 12: Phase variation of DIFA with frequency.

4 5 6 7 80

1

2

3

4

5

6

7

8V

SW

R

Frequency (GHz)

(a)

4 5 6 7 8-60

-50

-40

-30

-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

(b)

Figure 10: (a) VSWR and (b) Return loss variation of DIFA with frequency.


-20

-10

0

10

0

30

6090

120

150

180

210

240270

300

330

-20

-10

0

10

-40

-20

0

030

60

90

120

150180

210

240

270

300

330

-40

-20

0

(a) (b)

-40

-20

0

0

30

6090

120

150

180

210

240270

300

330

-40

-20

0

-40

-20

0

030

60

90

120

150180

210

240

270

300

330

-40

-20

0

(c) (d)

Figure 13: Radiation pattern (normalized) (a) Total gain in E-plane (b) total gain in H-plane (c) horizontal gain in E-plane and (d) vertical gain in H-plane of DIFA at 5.2 GHz.

-20

-10

0

10

0

30

6090

120

150

180

210

240270

300

330

-20

-10

0

10

-40

-20

0

030

60

90

120

150180

210

240

270

300

330

-40

-20

0

(a) (b)

-40

-20

0

0

30

6090

120

150

180

210

240270

300

330

-40

-20

0

-40

-30

-20

-10

0

100

30

60

90

120

150180

210

240

270

300

330

-40

-30

-20

-10

0

10

(c) (d)


TABLE 2 GAIN, BANDWIDTH AND SIZE COMPARISON BETWEEN THE PROPOSED AND REFERENCE ANTENNAS

Antenna Peak Gain (dBi) Bandwidth

at 5 GHz

Band

Dimension

(mm2) 5.2 GHz

WLAN

5.5 GHz

WiMAX

5.8 GHz

WLAN/RFI

D

DIFA (Proposed) 7.14 7.11 6.50 2.5 GHz 9×18

Composite monopole antenna [1] 4.6 ~ 5.3 841 MHz 8×19.5

CPW-fed triangle-shaped monopole antenna [2] 3.59 - 3.05 3.1 GHz 25×34

Capacitively fed hybrid monopole/slot chip an-

tenna [3]

2.7-3.8 945 MHz 5.2×16

Printed antenna with a quasi-self-complementary

structure [4]

3.3-4.0 - 3.2 ~ 3.8 1.462 GHz 6×21

T-shaped monopole antenna with dual Shorted

L-shaped strip-sleeves [5]

- 1.0 554 MHz 40×68

Simple coplanar waveguide (CPW)-fed patch

antenna [6]

- - 2.9 ~ 4.7 490 MHz 15×10

Coplanar waveguide (CPW)-fed F-shaped planar

monopole antenna [7]

- - 3.4 ~ 4.3 640 MHz 16.8×13

Compact monopole antenna [8] - - 2.105 330 MHz 4×30

Metal-plate antenna [9] 4.6 ~ 5.2 3.9 GHz 8.5×36

Printed antenna [10] 1.6 & 3.05

(H & E

Plane)

3.07 & 4.67

(H & E

Plane)

1.49 & 3.21

(H & E

Plane)

850 MHz 7.6×20

Low-profile printed T-shaped monopole antenna

[11]

3.5 - 3.5 1.155 GHz 3×11

Compact PIFA [12] 4.95 at 6.3 GHz 2.53 GHz 8.2×24.3


4 CONCLUSION

An optimized wideband double IFA for WLAN/WiMAX/RFID applications is proposed using numerical simulations. Effects of antenna geometry pa-rameters are also presented here. The proposed antenna occupies a small area of 9×18 mm2 with bandwidths of 2.5 GHz (5000MHz~7500MHz). Moreover the gain of the antenna is incredibly high and the gain variation of the antenna within the return loss bandwidth are very low at the required band means the antenna provides stable gain for the desired applications. From the analysis on the an-tenna’s gain, radiation pattern, return loss and input im-pedance is suitable for the specified applications then the antennas proposed earlier. Due to the compactness of the antenna, it is promising to be embedded within the dif-ferent portable devices employing WLAN/WiMAX/RFID applications.

REFERENCES

[1] K. -L. Wong and L. -C. Chou, “Internal Composite Monopole Antenna for WLAN/WiMAX Operation in A Laptop Computer,” Microwave and Optical Technology Letters, Vol. 48, No. 5, pp. 868-871, 2006.

[2] Y. Song, Y. -C. Jiao, G. Zhao and F. -S. Zhang, “Multiband CPW-Fed Triangle-Shaped Monopole Antenna for Wireless Applications,” Progress in Electromagnetics Research, PIER 70, pp. 329–336, 2007.

[3] P. -Y. Lai and K. -L. Wong, “Capacitively Fed Hybrid Monopole/Slot Chip Antenna for 2.5/3.5/5.5 GHz WiMAX Operation in the Mobile Phone,” Microwave and Optical Technology Letters, Vol. 50, No. 10, pp. 2689-2694, 2008.

[4] K. -L. Wong, T. -Y. Wu, S. -W. Su and J. -W. Lai, “Broadband Printed Quasi-Self-Complementary Antenna for 5.2/5.8 GHz WLAN Opera-tion,” Microwave and Optical Technology Letters, Vol. 39, No. 6, pp. 495-496, 2003.

[5] J. -W. Wu, Y. -D. Wang, H. -M. Hsiao and J. -H. Lu “T-Shaped Mono-pole Antenna with Shorted L-Shaped Strip-Sleeves for WLAN 2.4/5.8-

GHz Operation,” Microwave and Optical Technology Letters, Vol. 46, No. 1, pp. 65-69, 2005.

[6] W. -C. Liu, “A Coplanar Waveguide-Fed Folded-Slot Monopole An-tenna for 5.8 GHz Radio Frequency Identification Application,” Micro-wave and Optical Technology Letters, Vol. 49, No. 1, pp. 71-74, 2007.

[7] W. -C. Liu and C. -M. Wu, “CPW-Fed Shorted F-Shaped Monopole Antenna for 5.8-GHz RFID Application,” Microwave and Optical Tech-nology Letters, Vol. 48, No. 3, pp.573-575, 2006.

[8] J. Jung, H. Lee and Y. Lim, “Compact Monopole Antenna for Dual ISM-

Bands (2.4 and 5.8 GHz) Operation,” Microwave and Optical Technology

Letters, Vol. 51, No. 9, pp. 2227-2229, 2009. [9] K. L. Wong and L. C. Chou, “Internal wideband metal-plate

monopole antenna for laptop application,” Microwave and Optical Technology Letters, Vol. 46, No. 4, pp. 384–387, 2005.

[10] S. -Y. Sun, S. -Y. Huang and J. -S. Sun, “A Printed Multiband Antenna for Cellphone Applications,” Microwave and Optical Technology Letters, Vol. 51, No. 3, pp. 742-744, 2009.

[11] S. -W. Su, K. -L. Wong and H. -T. Chen, “Broadband Low-Profile Printed T-Shaped Monopole Antenna for 5-GHz WLAN Operation,” Microwave and Optical Technology Letters, Vol. 42, No. 3, pp. 243-245, 2004.

[12] Y. -S. Shin and S. -O. Park “A novel compact PIFA for Wireless Communication applications,” IEEE Region 10 Conference 2007, pp. 1-3, 2007. [13] G. J. Burke, and A. J. Poggio, “Numerical Electromagnetic Code-2,” Ver. 5.7.5, Arie Voors, 1981.

[14] M. –C. T. Huynh, “A Numerical and Experimental Investigation of Planar Inverted-F Antennas for Wireless Communication Applica-tions,” M.Sc. Thesis, Virginia Polytechnic Institute and State University, October 2000.

[15] K. Hirisawa and M. Haneishi, “Analysis, Design, and Measurement of small and Low-Profile Antennas,” Artech House, Boston, 1992.

Debabrata Kumar Karmokar was born in Satkhira, Bangladesh. He received the B. Sc. in electrical & electronic engineering (EEE) from Khulna University of Engineering & Technology (KUET), Khulna-9203, Bangla-desh, in 2007. He is currently working as a Lecturer in the same department of this uni-versity. He has authored or coauthored over 10 referred journal and conference papers. His main interests include analysis and de-sign of microstrip antennas, antennas for

biomedical and RFID applications, antenna miniaturization, high gain microstrip antennas for satellite communications, power system, nano-particles and nano medicine. Mr. Karmokar is a member of Consultancy Research and Testing Services (CRTS), Dept. of EEE, KUET and a Member of Institute of Engineers Bangladesh (IEB).

Khaled Mahbub Morshed received Bache-lor of Science in electronics & communica-tion engineering (ECE) with honors from Khulna University of Engineering & Technol-ogy, Khulna – 9203, Bangladesh, in 2007. He is currently working as a Lecturer in the same department of this university. He au-thored and co-authored more than 18 publi-cations in refereed journals and conference proceedings in national and international level. His current research interests include

analysis and design of microstrip/patch antennas, antennas for bio-medical and RFID applications, antenna miniaturization, high gain microstrip antennas for satellite communications, eletromagnetics. Mr. Morshed is a Member of Institute of Engineers Bangladesh (IEB), Life Member of Bangladesh Electronic Society (BES).

-20

-10

0

10

0

30

6090

120

150

180

210

240270

300

330

-20

-10

0

10

-40

-20

0

030

60

90

120

150180

210

240

270

300

330

-40

-20

0

(a) (b)

-40

-20

0

0

30

6090

120

150

180

210

240270

300

330

-40

-20

0

-40

-20

0

030

60

90

120

150180

210

240

270

300

330

-40

-20

0

(c) (d)



Md. Selim Hossain was born in Kushtia, Bangladesh. He received the Bachelor of Science in electrical and electronic engineer-ing (EEE) from Khulna University of Engineer-ing & Technology (KUET), Khulna-9203, Bangladesh, in 2008. He completed the SPACE (Saga University Programs for Academic Exchange) program from Saga University, Japan in 2007. He is currently working as a Lecturer in the same department of EEE, KUET. His research interests include

analysis and design of Microstrip filter for microwave communication, measurement system, microstrip antennas, antennas for biomedical and RFID applications, antenna miniaturization. Mr. Hossain is a member of Consultancy Research and Testing Services (CRTS), KUET and an Assiociate Member of Institute of Engineers Bangla-desh (IEB).

Muhammad Aminur Rahman obtained his B.Sc. degree in electrical & electronic engi-neering from Khulna University of Engineer-ing & Technology (KUET), Bangladesh in 2009. In 2009, he joined in the department of electrical & electronic engineering of Interna-tional Business Administration and Informa-tion System University (IBAIS University), Dhaka, Bangladesh as a lecturer. His re-search interests include electromagnetic

bandgap structures, microstrip patch antennas and also microwave engineering fields. He is an associate member of the Institution of Engineers Bangladesh.

Mohammad Nurunnabi Mollah was born in Jhenidah, Bangladesh, in 1964. He received the B.Sc. degree in electrical and electronic engineering from the Rajshahi University of Engineering & Technology (RUET) in 1986, the M.Sc. degree in electrical and electronic engineering from the Bangladesh University of Engineering and Technology (BUET) in 1997 and the Ph.D. degree from Nanayang Technological University (NTU), Singapore in 2005. In 1990, he joined the Department of

Electrical and Electronic Engineering, Khulna University of Engineer-ing & Technology (KUET), Khulna, as a Lecturer and became a Pro-fessor in 2005. He is currently working as a Dean in the Faculty of Engineering and Technology of Eastern University, Dhaka, Bangla-desh. He has authored or coauthored over 45 referred journal and conference papers and one book chapter. His research interests include microstrip patch antennas and arrays, microwave passive devices and electromagnetic bandgap structures. Dr. Mollah is a Member of IEEE, USA and Fellow of the Institution of Engineers Bangladesh (IEB).


Analysis of Odd Order Distortion in Mach-Zehnder Modulator for CATV System

M. Shahidul Islam, M. S. Islam, Mohammad Shorif Uddin

Abstract— For good performance, external modulator like Mach-Zehnder (MZ) modulator is used in CATV system, but it

produces some nonlinear distortion such as intermodulation distortion that limits the optical transmission performance

significantly. Using dual parallel Mach-Zehnder modulator (DPMZM) at bias condition, all even order distortions are suppressed

but odd order distortions still remain. In this paper an analytical model of DPMZM is proposed to ensure third and fifth order

products minimization. We have determined the optimal input optical power splitting ratio and electrode length ratio for a

DPMZM. It is found that the effect of CTB is in the allowable range if the input power splitting ratio and electrode length ratio of

the primary and secondary MZ modulators are 0.76 and 1.5 respectively.

Keywords— Composite second order, composite triple order, odd order distortion, CATV, intermodulation distortion and dual

parallel Mach-Zehnder modulator.

1 INTRODUCTION

ATV system can be based on either direct laser modulation or an external modulator like MZ modulator for transmission of analog RF signals

over the optical channel. Due to varied disadvantages of direct laser modulator, external modulator is used at laser output. The transfer function of MZ modulator is a sine wave function of the input voltage. For this reason, signal distortion is always found in a MZ modulator output. Difference intermodulation distortion terms such as even order and odd order are generated by MZ modulator which severely limits the performance of the analog AM optical transmission system [1]. Many research works have been carried out to analyze and suppress the effects of even and odd order distortion for analog optical transmission system [2-3]. In [4], he has shown that if the optical power and electrode are kept certain values then third order distortion becomes minimum. A solution to the three sections serially cascaded MZ device which is used to eliminate both third and fifth order distortion [5]. A novel wavelength insensitive RF dc biasing technique is reported which significantly reduces the CSO [6]. Differ-ent methods for linearization of the MZM transfer charac-teristic have been developed. Jackson et. al. has improved the dynamic range of the input RF signals and kept the carrier to intermodulation distortion within the required limits. Simple models of a two stage modulator are pro-posed for increased linearity [7]. The splitting ratios of input optical power and the input RF power values are

obtained by using trail and error method and it analyzes the IMD performance maximum up to sixteen channels [8].

In this paper, we have analyzed the DPMZ modulator and found out the input optical power splitting ratio with given electrode length ratio and optical modulation index to solve odd order distortion

2 THEORETICAL ANALYSIS

2.1 Dual Parallel Mach-Zehnder Modulator

Two separate MZ modulators are used to producs DPMZ modulator. The basic configuration of optical DPMZ modulator is shown below;

Figure 1: Dual parallel Mach-Zehnder modulator

The DPMZ shown in Figure 1 consists of a primary and

secondary modulator where those are connected in paral-

lel focusing optically and electrically. The optical input

C

————————————————

M. Shahidul Islam is with the department of Computer Science and Engineering of The Millennium University, Momenbagh, Dhaka-1217, Phone: +8801714494333, Email: [email protected]

M. S. Islam is with the IICT of BUET, Dhaka-1000, Bangladesh, Email: [email protected]

M. Shorif Uddin is with the department of CSE of Jahangirnagar University, Savar, Dhaka-1342, Email: [email protected]

Manuscript received on May 4, 2010 and accepted for publication on Sep-tember 19, 2010.

© 2010 ULAB JSE


power splits between primary and secondary modulator

at a ratio of )1( . The aim is to keep the value of the

optical power splitting ratio γ in a specific range where

the optical power loss will be minimum. For accomplish-

ing this task, we’ve to make secondary modulator elec-

trode, α times bigger than the primary modulator elec-

trode. According to these phenomena, the transfer func-

tion [9] of the DPMZ can be written like the following

)V

Vcos()1()

V

Vcos(1

2

II ssi

out

(1)

where, sV is the modulating RF signal voltage, V is the

voltage required to change the output light intensity from

its maximum values to its minimum values, outI is the

output light intensity and iI is the input light intensity,

is a static phase shift of the two arms of the modulator,

γ is the input optical power splitting ratio and α is the

electrode length ratio of primary and secondary modula-

tor.

Assuming the modulating signal sV is a sinusoidal vol-

tage with angular frequency i and amplitude A, we can

write

tsinAVN

1iis

(2)

where, N is the total number of channel. Putting the value of

equation (2) into equation (1) we find:

)))tsin(V

A)(cos(1(

)))tsin(V

Acos(1

2

II

N

1ii

N

1ii

iout (3)

sin).tsinV

Asin(cos).tsin

V

Acos()1(

)sin).tsinV

Asin(cos).tsin

V

Acos(1

2

II

N

1ii

N

1ii

N

1ii

N

1ii

iout

(4)

The expression can be simplified by assuming the mod-

ulation index (m) per channel small and by making the

approximations

V

Vm . Using Bessel expression

)1i2sin()x(J2)sin.xsin(

1i1i2 (5)

1ii20 i2cos)x(J2)x(J)sin.xcos( (6)

Where )x(J 1i2 is the ordinary Bessel function of the

first kind and of order (2i-1)

)))tsin()m(J((sin2

)))tcos()m(J((2)m(Jcos1(

)1(

)))tsin()m(J((sin2

)))tcos()m(J((2)m(Jcos1(

2

II

N

1ii

N

1i

N

1ii

N

1i

N0

N

1ii

N

1i

N

1ii

N

1i

N0

iout

i

i

i

i

i

i

i

i

i

onlyinteger even , i

onlyinteger odd (7)

Using equation (7), it is easy to show that the amplitude

of the fundamental output carrier with frequency i

, N,....,2,1i i.e.;

sin)m(J)m(J)1()m(J)m(JI

IC 1N

011N

o1

i

fund

(8)

The amplitude of an output second order component

with 1ji , and remaining indices become zero.

i.e.;

cos)m(J)m(J)1()m(J)m(JI

ICSO 2N

02

12N

o2

1

i

nd2

(9)

When modulator is operated at bias point condition the

even order term is suppressed [6]. So it is enough to con-

sider odd order distortion. The amplitude of an output

third orders component with 1kji , and

remaining indices become zero. i.e.;


ICTB 3N

03

13N

o3

1

i

rd3

(10)

Once the third order distortions are reduced [4], the fifth order distortion becomes dominant. Therefore, it is im-portant to include fifth order distortion analysis here. The amplitude of an output fifth order component is


ICIR 5N

05

15N

o5

1

i

th55

(11)

On the basis of the relations obtained for the fundamental output signal and power of the CTB products, C/CTB ratio can be obtained as:

ctb

2

3N0

31

3N0

31

1N01

1N01 N

)m(J)m(J)1()m(J)m(J

)m(J)m(J)1()m(J)m(J

CTB

C

(12)

The power ratio of carrier to fifth order distortion is:

12

N

)m(J)m(J)1()m(J)m(J

)m(J)m(J)1()m(J)m(J

CIR

C 42

5N0

51

5N0

51

1N01

1N01

5

(13)

For calculating odd order distortion let, CTB=0 and it has

found the following relation between and is:

M. SHAHIDUL ISLAM ET AL.: ANALYSIS OF ODD ORDER DISTORTION IN MACH-ZEHNDER MODULATOR 13

3N0

31

3N0

31

3N0

31

)m(J)m(J)m(J)m(J

)m(J)m(J

(14)

3 RESULTS AND DISCUSSION

Expression of equations (8)-(14) can be used to generate a data base for intermodulation performance of a DPMZ modulator. The variation limits of the modulation index must be determined. It is well known that the increasing m improves the CNR, yet it does increase impairment caused by IMD too. Hence optimum operating values of m is a balance between noise and distortion. With CATV system range the modulation index is 0.03 to 0.06 for ad-missible minimum value of the CNR and C/CTB parame-ters. In Figure 2, the optical power splitting ratio γ is the func-tion of the modulation index m for three values of α. For fixed value of α, parameter γ is slightly changing with in admissible limits on m (0.03 to 0.06) given in Table.1.

Figure 2: Optical power splitting ratio (γ) vs. modulation index (m) under electrode length ratio (α)

TABLE.1: THE SPLITTING RATIO VALUES VERSUS ELECTRODE

LENGTH RATIO

α γ

1.5 2.0 2.5

γ max 0.77 0.88 0.93

γ min 0.76 0.87 0.92

The following sets of parameters are selected for reducing odd order distortion in term of IMD performance to meet C/distortion at -60dB [4], which has shown in table 2.

TABLE 2: SET OF PARAMETER TO REDUCE CTB PERFORMANCE

Case No α γ OMI

I 1.5 0.76 1%-5.6%

II 2.0 0.88 1%-4.5%

III 2.5 0.93 1%-4.4%

(a)

(b) Figure 3: Case studies of DPMZM (a) OMI vs. C/CTB (b) OMI vs C/CTB & fifth order distortion

For obtaining good performance of odd order distortion, these cases are analyzed. Figure 3a and 3b show the dis-tortion curve of CTB versus OMI without and with fifth order distortion respectively. As seen from Figure 3, the third and fifth order distortions have similar severe dis-tortion as OMI increases. From Figure 3b, it is shown that if fifth order distortion is added with third order distor-tion then OMI is decreased. But both third and fifth order are minimized using DPMZ modulator when optical in-put power splitting ratio and electrode length ratio are 0.76 and 1.5 respectively.

4 CONCLUSION

In this paper, fifth order distortion analysis of an external modulator using dual parallel Mach-Zehnder modulator has been presented. The investigations have shown that the even order distortion products cancellation occurs in the DPMZ modulator, if both modulators work in qua-rdrature point. In this paper, if only third order distortion


is considered for a system, more OMI is found (OMI= 5.6%), but if fifth order distortion is added with third or-der distortion, OMI is decreased (OMI= 4.5%). So, the odd order distortions such that third and fifth order distortion are minimized using DPMZ modulator when the optical power splitting ratio and electrode length ratio are 0.76 and 1.5 respectively.

REFERENCES

[1] F. Ramos and J. Marti, “Compensation for fiber-induced composite second-order distortion in exter-nally modulated lightwave AM-SCM systems using optical-phase conjugation”, Journal of Lightwave Tech-nology, vol. 18 (8), pp. 1387-1391, 1998.

[2] X. J. Meng,, A. Yacoubian and J. H. Bechtel, “Electro-optical pre-distortion technique for linearization of mach-Zehnder Modulators”, Electronics Letters, vol. 37, no. 25, pp. 1545-1547, 2001.

[3] H. V. Pham, H. Murata and Y. Okamura, “Electro-optic modulators with controlled frequency res-ponses by using non-periodically polarization-reversed structure”, Advances in Opto-Electronics, vol. 1, article ID 948294, 2008.

[4] M. Shahidul Islam, “Analysis and suppression of in-termodulation distortion effects in Mach-Zehnder Modulator for analog optical transmission systems”, M.Sc. Engineering Thesis, Institute of Information and Communication Technology, BUET, Dhaka, 2010.

[5] K. B. William, “Linearized optical modulator with fifth order correction”, Journal of Lightwave Technology, vol. 13, no. 8, pp. 1724-1727, 1995.

[6] S. Dubovitsky, H. Steier, S. Yegnanarayanan and B. Jalali, “Analysis and Improvement of Mach–Zehnder Modulator Linearity Performance for Chirped and Tunable Optical Carriers’, Journal of Lightwave Tech-nology, vol. 20 (5), pp. 886-891, 2002.

[7] M. K. Jackson, V. M. Smith, W. J. Hallam, and J. C. Maycock “Optically linearized modulators: chirp control for low-distortion analog transmission”, Jour-nal of Lightwave Technology, vol. 15, no. 8, pp. 1538-1545, 1997.

[8] T. Wang, Q. Chang and Y. Su, “Generation of linea-rized optical single sideband signal for broadband radio over fiber systems”, Chinese Optics Letters, vol. 7, no. 4, pp. 339-343, 2009.

[9] J. Brooks, G. Maurer and R. Becker, “Implementation and evaluation of dual parallel linearization systems for AM-SCM video transmission“, Journal of Lightwave Technology, vol. 11, no. 1, 1993.

M. Shahidul Islam received the B.Sc. degree in Information and Communication Engineering from University of Rajshahi in 2007 and M. Sc. (Engg.) degree in ICT from Institute of Information and Communication Technology (IICT), Bangladesh University of Engineering and Technology (BUET) in 2010. Now he is pursuing his Ph.D. at the De-partment of Applied Physics, Electronics and

Communication Engineering, University of Dhaka. He has been

working as a Lecturer of Computer Science and Engineering in the Millennium University, Dhaka since April, 2009. His research field includes Fiber Nonlinearity, SCM-WDM, Optical Communication, Wireless Communication, etc. He is author or coauthor of 5 national and international journal and conference papers. He is a member (member no.: 80336949) of International Association of Computer Science and Information Technology (IACSIT), Singapore and asso-ciate member (AM-05390) of Bangladesh Computer Society.

M. S. Islam obtained Ph.D. from Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh in 2008, M. Sc. in Computer Science and Engineering from Shanghai University, China in 1997 and B.Sc. in Electrical and Electronic Engineering from BUET in 1989. He has published many re-search papers in national and international

journals and conferences. Currently, He is working as an Associate Professor in the Institute of Information and Communication Tech-nology (IICT) of BUET. His research interests include DWDM trans-mission system, dispersion, nonlinearity and wireless communica-tion.

Mohammad Shorif Uddin received PhD

in Information Science from Kyoto Institute of Technology, Japan, Master of Education in Technology Education from Shiga University, Japan and Bachelor of Science in Electrical and Electronic Engineering from Bangladesh University of Engineerong and Technology

(BUET). He joined in the Department of Computer Science and En-gineering, Jahangirnagar University, Dhaka in 1992 and currently he is a Professor of this department. He started his teaching career in 1991 as a Lecturer of the Department of Electrical and Electronic Engineering, Chittagong University of Engineering and Technology, (CUET). He did postdoctoral researches at Bioinformatics Institute, A-STAR, Singapore, Toyota Technological Institute, Japan and Kyo-to Institute of Technology, Japan. His research is motivated by appli-cations in the fields of computer vision, pattern recognition, blind navigation, bioimaging, medical diagnosis and disaster prevention. He has published a remarkable number of papers in peer-reviewed international journals and conference proceedings including well-reputed IEEE Transactions on ITS, British IOP Journal, Japanese IEICE Transactions, Optics Express and Applied Optics (Optical society of America), Elsevier Science Journal. He holds two patents for his scientific inventions. He received the best presenter award in the International Conference on Computer Vision and Graphics (ICCVG 2004), Warsaw, Poland. He is the author of two books. He is a member of IEEE, SPIE, and IEB.


Wideband Compact Double Inverted-F Antenna for WLAN/WiMAX/RFID Applications Debabrata Kumar Karmokar, Khaled Mahbub Morshed, Md. Selim Hossain, Md. Aminur Rahman,

Md. Nurunnabi Mollah

Abstract—This paper presents a wideband compact double Inverted-F antenna (DIFA) for WLAN/WiMAX/RFID applications by

means of numerical simulation. The antenna has compact size of 9×18 mm2 and provides a wide bandwidth of 2.5 GHz

(5000MHz~7500MHz) which cover the 5.2 GHz WLAN, 5.5 GHz WiMAX and 5.8 GHz WLAN/RFID application bands. Moreover

it has very high peak gain of 7.14, 7.11 and 6.50 dBi with less than 0.5, 0.7 and 0.6 dBi gain variation within the 10 dB return

loss bandwidth at 5.2, 5.5 and 5.8 GHz band respectively. Also the VSWR of DIFA varies from 1.09877 to 1.61467 within the

antenna bandwidth.

Keywords— Inverted-F antenna (IFA), Double IFA (DIFA), Radio frequency identification (RFID), Worldwide interoperability for

microwave access (WiMAX), Wireless local area networks (WLAN).

1 INTRODUCTION

ODERN wireless communication systems are ris-ing rapidly and the function of these devices is in-creasing as well as the size decreasing. The size of

the antenna often has a great influence on the whole size of wireless systems so for meet up the demand of multi-function small wireless devices, the antenna has to be compact, light and easy to be embedded with the system. Antenna designer’s encountered difficulty in designing antennas that could maintain high performance; even the antenna size is smaller. In order to satisfy these demands, IFA has been widely used in mobile devices due to its low profile, ease of fabrication and superior electrical perfor-mance. At present the demand of WLANs are increasing numerously worldwide, because they provide high speed connectivity and easy access to networks without wiring. Also in recent times the applications of WiMAX, which can provide a long operating range with a high data rate for mobile broadband wireless access, faultless internet access for wireless users becomes more popular [1-4]. On the other hand the RFID system has recently using effi-ciently for tracking and identifying objects in the various supply chains from security and control point of view [6-7]. The fast growing WLAN protocals operating bands are IEEE 802.11 b/a/g at 2.4 GHz (frequency ranges 2400–2484 MHz), 5.2 GHz (frequency ranges 5150–5350 MHz) and 5.8 GHz (frequency ranges 5725–5825 MHz).

The operating bands of WiMAX are 2.5 (frequency ranges 2500 –2690), 3.5 (frequency ranges 3400–3600) and 5-GHz (frequency ranges 5250–5850 MHz) bands [1–5]. The fre-quency band used for the RFID system is 125 kHz; 13.56, 869 and 914 MHz; 2.45 and 5.8 GHz band [6-7]. There is a trend all over the world for the advance of compact, low-profile, multi-function antenna with the ability to support various commercial protocols [8]. For this reason compact antenna with suitable gain, low gain variation and satis-factory bandwidth for WLAN/WiMAX/RFID applica-tions are extremely enviable.

A novel composite monopole antenna for 2.4/5.2/5.8 GHz WLAN and 2.5/3.5/5 GHz WiMAX operation in a laptop computer [1], a CPW-fed triangle-shaped mono-pole antenna for 2.4/5 GHz WLAN and 3.4 GHz WiMAX applications [2], a capacitively fed hybrid monopole/slot chip antenna for 2.5/3.5/5.5 GHz WiMAX operation in the mobile phone [3], a printed antenna with a quasi-self-complementary structure for 5.2/5.8 GHz WLAN opera-tion [4], a novel dual-broadband T-shaped monopole an-tenna with dual shorted L-shaped strip-sleeves for 2.4/5.8 GHz WLAN operation [5], a simple coplanar waveguide (CPW)-fed patch antenna and a novel CPW-fed F-shaped planar monopole antenna obtained by embedding folded slots in a rectangular patch on a single-layer substrate for 5.8 GHz RFID application [6–7], a compact monopole an-tenna for dual industrial, scientific and medical (ISM) band (2.4 and 5.8 GHz) operation [8], a novel wideband metal-plate antenna suitable for application as an internal laptop antenna for 2.4/5.2/5.8 GHz WLAN or 2.83–5.85 GHz WMAN operation [9], a printed antenna which is working in 2.4 GHz bluetooth, 3.5 and 5.8 GHz WiMAX, 2.4–2.5 and 5.0–5.8 GHz Wi-Fi, 2.4–2.84 GHz, 5.15–5.35 and 5.72–5.83 GHz WLAN operation [10], a broadband low-profile printed T-shaped monopole antenna for 5 GHz WLAN application [11] and a compact PIFA for

M

© 2010 ULAB JSE

————————————————

D. K. Karmokar, K. M. Morshed and Md. S. Hossain are with the Faculty of Electrical & Electronic Engineering, Khulna University of Engineering & Technology (KUET), Khulna-9203, Bangladesh. E-mail: [email protected].

Md. A.Rahman is with the Department of Electrical & Electronic Engi-neering, IBAIS University, Dhaka, Bangladesh.

M. N. Mollah is with the Department of Engineering & Technology, East-ern University, Dhaka, Bangladesh



Bluetooth, satellite-digital multimedia broadcasting (S-DMB), wireless broadband (WiBro), WiMAX and WLAN applications [12] have been proposed. To provide the in-creasing demand and cover up the widespread applica-tions of WLAN, WiMAX or RFID an antenna with com-pact size, wider bandwidth, high gain and less gain varia-tion within the antenna bandwidth is desired. To meet up most of mentioned requirements, IFA is one of the good candidates within the micro-strip printed antennas be-cause of its compact size and good input impedance than other printed antennas.

2 ANTENNA DESIGN

In designing the compact wideband antenna for WLAN, WiMAX and RFID operation, we examine the possibility of increasing antenna bandwidth with simplifying its structure. Using method of moments (MoM’s) in Numeri-cal Electromagnetic Code (NEC) [13], we conducted pa-rameter studies to ascertain the effect of different loading on the antenna performance to find out the optimal de-sign. In our analysis we assume the copper conductor and the antenna was intended to be matched to 50 Ω system impedance.

For the analysis of the accuracy optimum segmenta-tion of each geometrical parameter are used in NEC. Fig-ure 1 represents the basic geometry of the IFA. Here one leg of IFA directly connected to the feeding and another leg spaced s from the ground plane. For the simulation we consider printed circuit board (PCB) with permittivity of εr = 2.2 and substrate thickness of 1.58 mm.

The antenna is assumed to feed by 50 Ω coaxial con-

nector, with its central conductor connected to the feeding point and its outer conductor connected to the ground plane just across the feeding point. In the analysis the

(a)

(b)

(c)

Figure 1: Structure of Inverted-F Antenna (IFA) (a) 3-D front, (b) 3-D top and (c) 2-D view.

(c)

Figure 2: Structure of Double Inverted-F Antenna (DIFA) (a) 3-D front, (b) 3-D top and (c) 2-D view.

(a)

(b)

Feed

w

l t

h h1

s

Feed

w

l t

h h1

h1

s

d


dimensions of the ground plane considered as 60 × 60 mm2. Figure 2 represents the modified IFA where load equal to the IFA is applied to the horizontal strip by shorting the end terminals is titled as double IFA (DIFA).

For IFA of Figure 1, the resonant frequency related to w given as [14]

(1) Where c is the speed of light. The effective length of

the current is l+t+h1+w. Under this case the resonant con-dition can be expressed as

(2)

The other resonant frequency that is a part of linear combination with the case 0<w< (1+t) and is expressed as

(3) The resonant frequency (fr) is a linear combination of

resonant frequency associated with the limiting case. For the antenna geometry of Figure 1, fr can be written from equation (1) and (2) as [15]

f r=r. f 1 +(1-r )f 2 (4) Where r=w/(l+t). With the help of resonant frequency

theory of IFA and impedance matching concept, we con-sider the dimension of the IFA as l=14 mm, t=6 mm, h1=4 mm, h=4 mm, s=0 mm, w=3 mm. Figure 3 (a) and (b) shows the effects of l and s on the antenna performance. From the simulated results, antenna has desired bandwidth at l=13 mm and s=1 mm. When l=14 or 15 mm, the values of return loss much better than l=13 mm but at that condi-tion antenna does not cover the whole 5 GHz operating band (frequency ranges 5150 – 5850 MHz) because our aim to design an antenna for 5 GHz operation so that it can cover the whole operating band. A higher value of l shifts the antenna resonance to the higher frequencies. When s=0 mm the value of return loss stay above the 10 dB level throughout the 5 GHz band and when s=2 mm the antenna has very poor S11 characteristics. Figure 4 (a) and (b) shows the effects of t and w on the antenna per-formance. From the simulation, the optimum dimensions of IFA are l=13 mm, t=5 mm, h=4 mm, h1=3 mm, w=4 mm and s=1 mm.

4 5 6 7 8-25

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-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

l=11 mm

l=12 mm

l=13 mm

l=14 mm

l=15 mm

(a)

4 5 6 7 8-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

s=0 mm

s=1 mm

s=2 mm

(b)

Figure 3: Effects of (a) length l and (b) spacing s on the return loss as a function of frequency on the antenna structure of Figure 1.

4 5 6 7 8-25

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-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

t=4 mm

t=5 mm

t=6 mm

t=7 mm

(a)

4 5 6 7 8-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

w=2 mm

w=3 mm

w=4 mm

(b)

Figure 4: Effects of (a) tap distance t and (b) width w on the return loss of the antenna of Figure 1 as a function of frequency.

)(4 11

htl

cf

4

01

whtl

)(4 12

whtl

cf


When load is applied to the horizontal strip of IFA then the modified structure is shown in Figure 2 which titled as double IFA (DIFA). In this double IFA the struc-ture of load is the same as source IFA. But the change made in separation d for the better performance. Figure 5 presents the characteristics of S11 as a function of fre-quency with different spacing s and separation d. From the obtained data, antenna provides better performance when d is set to 2 mm and s is to 1 mm. Variation of l and its effects on S11 for DIFA is shown in Figure 6. It is clear from the characteristics of S11, when l=12 mm the antenna provide good characteristics than l=13 mm but the band-width does not cover the whole 5 GHz band. For different values of t and w for the antenna of Figure 2, S11 are shown in Figure 7 (a) and (b) respectively. From the ob-served data proposed antenna cover the 5 GHz band, when t=5 mm and w=4 mm. When strip width is at w=3 mm, then the nature of S11 for the variation of l and t are

shown in Figure 8 (a) and (b). Moreover, at w=2 mm the characteristics of S11 are shown in Figure 9 (a) and (b) with the change in l and t. From Figure 8 and 9, when l=14 mm the DIFA has much better return loss characteris-tics than l=13or 15 mm. Also, the antenna has good S11 characteristics at l=15 mm when w=2 mm with respect to

l=13or 14 mm. But the problem is that, when w=2 or 3 mm, DIFA does not cover the whole 5 GHz band and reso-nance shifted to the frequency greater than 6 GHz.

Under these values of w (=2, 3 mm) with different val-ues of t, antenna resonance shifts are not desired for the mentioned application. From Figure 5 to 9, in overall analysis, DIFA fully cover the 5 GHz WLAN operating band, when l=13 mm and w=4 mm. The optimized dimen-sions of the proposed DIFA are listed in Table 1.

4 5 6 7 8-60

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0

S1

1 (

dB

)

Frequency (GHz)

d=0 mm

d=2 mm

d=4 mm

(a)

4 5 6 7 8-60

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0

S1

1 (

dB

)

Frequency (GHz)

s=0 mm

s=1 mm

s=2 mm

(b)

Figure 5: Return loss as a function of frequency with the different (a) separation d and (b) spacing s of the antenna of Figure 2.

4 5 6 7 8-60

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0

S1

1 (

dB

)

Frequency (GHz)

t=4 mm

t=5 mm

t=6 mm

t=7 mm

(a)

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0

S1

1 (

dB

)

Frequency (GHz)

l=11 mm

l=12 mm

l=13 mm

l=14 mm

l=15 mm

Figure 6: Effects of length l on the S11 as a function of frequency while t, h, h1 and w remains unchanged of the antenna of Figure 2.

TABLE 1 OPTIMIZED DIMENSIONS OF THE PROPOSED ANTENNA

Antenna Name

Antenna Parameters

Value (mm)

Dimension (mm2)

DIFA

l 13

9×18

t 5 h 4

h1 3 d 2

w 4 s 1


3 NUMERICAL SIMULATION RESULTS

The proposed antenna is constructed and numerically analyzed using MoM’s. The numerical results of the an-tenna are shown below. The proposed antenna have the return loss appreciable than the commonly required 10 dB level. If we apply a suitable structured load equal to the IFA on the horizontal branch of IFA and shorted the ends of the both IFA as shown in Figure 2, the impedance bandwidth improves extensively. The numerical simula-tion analysis of the proposed DIFA to realize the opera-tion for WLAN/WiMAX/RFID is presented below.

Figure 10 (a) shows the voltage standing wave ratio (VSWR) variation and Figure 10 (b) shows the return loss variation of DIFA with frequency. The DIFA provides a large impedance bandwidth of 2500 MHz (5000–7500 MHz) which fully covers the 5.2, 5.5 and 5.8 GHz bands and the peak value of return loss is -50.51082 dB. The value of VSWR of DIFA varies from 1.09877 to 1.61467 within the 5 GHz operating band that indicates the varia-tion of VSWR is very low and it is near to 1 as shown in Figure 10 (a).

4 5 6 7 8-60

-50

-40

-30

-20

-10

0S

11 (

dB

)

Frequency (GHz)

w=2 mm

w=3 mm

w=4 mm

(b)

Figure 7: Return loss as a function of (a) tap distance t and (b) width w for the antenna of Figure 2.

4 5 6 7 8-30

-25

-20

-15

-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

l=11 mm

l=12 mm

l=13 mm

l=14 mm

l=15 mm

(a)

4 5 6 7 8-30

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-10

-5

0

S1

1 (

dB

)

Frequency (GHz)

t=3 mm

t=4 mm

t=5 mm

t=6 mm

t=7 mm

(b)


4 5 6 7 8-50

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-10

0

S1

1 (

dB

)

Frequency (GHz)

l=11 mm

l=12 mm

l=13 mm

l=14 mm

l=15 mm

(a)

4 5 6 7 8-40

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-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

t=4 mm

t=5 mm

t=6 mm

t=7 mm

(b)



Figure 11 (a) shows the gain variation of DIFA. The peak

gains of DIFA is 7.14, 7.11 and 6.50 dBi with less than 0.5, 0.7 and 0.6 dBi gain variation within the 10 dB return loss band-width at 5.2, 5.5 and 5.8 GHz band respectively, which indi-cates that the antenna has stable gain within the operating bandwidth which is desired for the wireless applications. Fig-ure 11 (b) represents the antenna input impedance variation and Figure 12 represents the antenna phase shift causes due the impedance mismatch as a function of frequency. From the obtained results, the input impedance of DIFA is near about 50 Ω which is desired for the impedance matching with the feeding system. Also, from the simulation study, within the return loss bandwidth, DIFA has phase shift closer to 00 all over the antenna bandwidth except at the start of 5.2 GHz band, where phase shift closer to 300. A comparison between the reference antennas and proposed DIFA in gain, band-width and size are listed in Table 2. In overall considerations, DIFA is much better than all other antennas. Figure 13 to 15 shows the normalized radiation patterns of DIFA at 5.2, 5.5 and 5.8 GHz bands respectively. The antenna’s normalized total radiation in H and E-plane is almost omnidirectional which is desired for the WLAN/WiMAX/RFID applications. For the better analysis of the antenna, for three resonant fre-

quencies antenna’s normalized radiation patterns are shown as: total gain in H-plane, total gain in E-plane, horizontal gain in E-plane and vertical gain in H-plane.

4 5 6 7 8

0

2

4

6

8

An

ten

na G

ain

(d

Bi)

Frequency (GHz)

(a)

4 5 6 7 80

20

40

60

80

100

Inp

ut

imp

ed

an

ce (

Oh

m)

Frequency (GHz)

(b)

Figure 11: (a) Total gain and (b) Impedance variation of DIFA with frequency.

4 5 6 7 8-90

-60

-30

0

30

60

90

Ph

ase

(d

eg

ree)

Frequency (GHz)

Figure 12: Phase variation of DIFA with frequency.

4 5 6 7 80

1

2

3

4

5

6

7

8V

SW

R

Frequency (GHz)

(a)

4 5 6 7 8-60

-50

-40

-30

-20

-10

0

S1

1 (

dB

)

Frequency (GHz)

(b)

Figure 10: (a) VSWR and (b) Return loss variation of DIFA with frequency.


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150180

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270

300

330

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(a) (b)

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0

0

30

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180

210

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330

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0

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030

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330

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(c) (d)


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330

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0

030

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150180

210

240

270

300

330

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0

(a) (b)

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0

0

30

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120

150

180

210

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330

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TABLE 2 GAIN, BANDWIDTH AND SIZE COMPARISON BETWEEN THE PROPOSED AND REFERENCE ANTENNAS

Antenna Peak Gain (dBi) Bandwidth

at 5 GHz

Band

Dimension

(mm2) 5.2 GHz

WLAN

5.5 GHz

WiMAX

5.8 GHz

WLAN/RFI

D

DIFA (Proposed) 7.14 7.11 6.50 2.5 GHz 9×18

Composite monopole antenna [1] 4.6 ~ 5.3 841 MHz 8×19.5

CPW-fed triangle-shaped monopole antenna [2] 3.59 - 3.05 3.1 GHz 25×34

Capacitively fed hybrid monopole/slot chip an-

tenna [3]

2.7-3.8 945 MHz 5.2×16

Printed antenna with a quasi-self-complementary

structure [4]

3.3-4.0 - 3.2 ~ 3.8 1.462 GHz 6×21

T-shaped monopole antenna with dual Shorted

L-shaped strip-sleeves [5]

- 1.0 554 MHz 40×68

Simple coplanar waveguide (CPW)-fed patch

antenna [6]

- - 2.9 ~ 4.7 490 MHz 15×10

Coplanar waveguide (CPW)-fed F-shaped planar

monopole antenna [7]

- - 3.4 ~ 4.3 640 MHz 16.8×13

Compact monopole antenna [8] - - 2.105 330 MHz 4×30

Metal-plate antenna [9] 4.6 ~ 5.2 3.9 GHz 8.5×36

Printed antenna [10] 1.6 & 3.05

(H & E

Plane)

3.07 & 4.67

(H & E

Plane)

1.49 & 3.21

(H & E

Plane)

850 MHz 7.6×20

Low-profile printed T-shaped monopole antenna

[11]

3.5 - 3.5 1.155 GHz 3×11

Compact PIFA [12] 4.95 at 6.3 GHz 2.53 GHz 8.2×24.3


4 CONCLUSION

An optimized wideband double IFA for WLAN/WiMAX/RFID applications is proposed using numerical simulations. Effects of antenna geometry pa-rameters are also presented here. The proposed antenna occupies a small area of 9×18 mm2 with bandwidths of 2.5 GHz (5000MHz~7500MHz). Moreover the gain of the antenna is incredibly high and the gain variation of the antenna within the return loss bandwidth are very low at the required band means the antenna provides stable gain for the desired applications. From the analysis on the an-tenna’s gain, radiation pattern, return loss and input im-pedance is suitable for the specified applications then the antennas proposed earlier. Due to the compactness of the antenna, it is promising to be embedded within the dif-ferent portable devices employing WLAN/WiMAX/RFID applications.

REFERENCES

[1] K. -L. Wong and L. -C. Chou, “Internal Composite Monopole Antenna for WLAN/WiMAX Operation in A Laptop Computer,” Microwave and Optical Technology Letters, Vol. 48, No. 5, pp. 868-871, 2006.

[2] Y. Song, Y. -C. Jiao, G. Zhao and F. -S. Zhang, “Multiband CPW-Fed Triangle-Shaped Monopole Antenna for Wireless Applications,” Progress in Electromagnetics Research, PIER 70, pp. 329–336, 2007.

[3] P. -Y. Lai and K. -L. Wong, “Capacitively Fed Hybrid Monopole/Slot Chip Antenna for 2.5/3.5/5.5 GHz WiMAX Operation in the Mobile Phone,” Microwave and Optical Technology Letters, Vol. 50, No. 10, pp. 2689-2694, 2008.

[4] K. -L. Wong, T. -Y. Wu, S. -W. Su and J. -W. Lai, “Broadband Printed Quasi-Self-Complementary Antenna for 5.2/5.8 GHz WLAN Opera-tion,” Microwave and Optical Technology Letters, Vol. 39, No. 6, pp. 495-496, 2003.

[5] J. -W. Wu, Y. -D. Wang, H. -M. Hsiao and J. -H. Lu “T-Shaped Mono-pole Antenna with Shorted L-Shaped Strip-Sleeves for WLAN 2.4/5.8-

GHz Operation,” Microwave and Optical Technology Letters, Vol. 46, No. 1, pp. 65-69, 2005.

[6] W. -C. Liu, “A Coplanar Waveguide-Fed Folded-Slot Monopole An-tenna for 5.8 GHz Radio Frequency Identification Application,” Micro-wave and Optical Technology Letters, Vol. 49, No. 1, pp. 71-74, 2007.

[7] W. -C. Liu and C. -M. Wu, “CPW-Fed Shorted F-Shaped Monopole Antenna for 5.8-GHz RFID Application,” Microwave and Optical Tech-nology Letters, Vol. 48, No. 3, pp.573-575, 2006.

[8] J. Jung, H. Lee and Y. Lim, “Compact Monopole Antenna for Dual ISM-

Bands (2.4 and 5.8 GHz) Operation,” Microwave and Optical Technology

Letters, Vol. 51, No. 9, pp. 2227-2229, 2009. [9] K. L. Wong and L. C. Chou, “Internal wideband metal-plate

monopole antenna for laptop application,” Microwave and Optical Technology Letters, Vol. 46, No. 4, pp. 384–387, 2005.

[10] S. -Y. Sun, S. -Y. Huang and J. -S. Sun, “A Printed Multiband Antenna for Cellphone Applications,” Microwave and Optical Technology Letters, Vol. 51, No. 3, pp. 742-744, 2009.

[11] S. -W. Su, K. -L. Wong and H. -T. Chen, “Broadband Low-Profile Printed T-Shaped Monopole Antenna for 5-GHz WLAN Operation,” Microwave and Optical Technology Letters, Vol. 42, No. 3, pp. 243-245, 2004.

[12] Y. -S. Shin and S. -O. Park “A novel compact PIFA for Wireless Communication applications,” IEEE Region 10 Conference 2007, pp. 1-3, 2007. [13] G. J. Burke, and A. J. Poggio, “Numerical Electromagnetic Code-2,” Ver. 5.7.5, Arie Voors, 1981.

[14] M. –C. T. Huynh, “A Numerical and Experimental Investigation of Planar Inverted-F Antennas for Wireless Communication Applica-tions,” M.Sc. Thesis, Virginia Polytechnic Institute and State University, October 2000.

[15] K. Hirisawa and M. Haneishi, “Analysis, Design, and Measurement of small and Low-Profile Antennas,” Artech House, Boston, 1992.

Debabrata Kumar Karmokar was born in Satkhira, Bangladesh. He received the B. Sc. in electrical & electronic engineering (EEE) from Khulna University of Engineering & Technology (KUET), Khulna-9203, Bangla-desh, in 2007. He is currently working as a Lecturer in the same department of this uni-versity. He has authored or coauthored over 10 referred journal and conference papers. His main interests include analysis and de-sign of microstrip antennas, antennas for

biomedical and RFID applications, antenna miniaturization, high gain microstrip antennas for satellite communications, power system, nano-particles and nano medicine. Mr. Karmokar is a member of Consultancy Research and Testing Services (CRTS), Dept. of EEE, KUET and a Member of Institute of Engineers Bangladesh (IEB).

Khaled Mahbub Morshed received Bache-lor of Science in electronics & communica-tion engineering (ECE) with honors from Khulna University of Engineering & Technol-ogy, Khulna – 9203, Bangladesh, in 2007. He is currently working as a Lecturer in the same department of this university. He au-thored and co-authored more than 18 publi-cations in refereed journals and conference proceedings in national and international level. His current research interests include

analysis and design of microstrip/patch antennas, antennas for bio-medical and RFID applications, antenna miniaturization, high gain microstrip antennas for satellite communications, eletromagnetics. Mr. Morshed is a Member of Institute of Engineers Bangladesh (IEB), Life Member of Bangladesh Electronic Society (BES).

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Md. Selim Hossain was born in Kushtia, Bangladesh. He received the Bachelor of Science in electrical and electronic engineer-ing (EEE) from Khulna University of Engineer-ing & Technology (KUET), Khulna-9203, Bangladesh, in 2008. He completed the SPACE (Saga University Programs for Academic Exchange) program from Saga University, Japan in 2007. He is currently working as a Lecturer in the same department of EEE, KUET. His research interests include

analysis and design of Microstrip filter for microwave communication, measurement system, microstrip antennas, antennas for biomedical and RFID applications, antenna miniaturization. Mr. Hossain is a member of Consultancy Research and Testing Services (CRTS), KUET and an Assiociate Member of Institute of Engineers Bangla-desh (IEB).

Muhammad Aminur Rahman obtained his B.Sc. degree in electrical & electronic engi-neering from Khulna University of Engineer-ing & Technology (KUET), Bangladesh in 2009. In 2009, he joined in the department of electrical & electronic engineering of Interna-tional Business Administration and Informa-tion System University (IBAIS University), Dhaka, Bangladesh as a lecturer. His re-search interests include electromagnetic

bandgap structures, microstrip patch antennas and also microwave engineering fields. He is an associate member of the Institution of Engineers Bangladesh.

Mohammad Nurunnabi Mollah was born in Jhenidah, Bangladesh, in 1964. He received the B.Sc. degree in electrical and electronic engineering from the Rajshahi University of Engineering & Technology (RUET) in 1986, the M.Sc. degree in electrical and electronic engineering from the Bangladesh University of Engineering and Technology (BUET) in 1997 and the Ph.D. degree from Nanayang Technological University (NTU), Singapore in 2005. In 1990, he joined the Department of

Electrical and Electronic Engineering, Khulna University of Engineer-ing & Technology (KUET), Khulna, as a Lecturer and became a Pro-fessor in 2005. He is currently working as a Dean in the Faculty of Engineering and Technology of Eastern University, Dhaka, Bangla-desh. He has authored or coauthored over 45 referred journal and conference papers and one book chapter. His research interests include microstrip patch antennas and arrays, microwave passive devices and electromagnetic bandgap structures. Dr. Mollah is a Member of IEEE, USA and Fellow of the Institution of Engineers Bangladesh (IEB).


A Simple Approach to Recognize a Person Using Hand Geometry

R. H. M. Alaol Kabir, Md. Atikur Rahman, Mohammad Ahsanul haque, Mohammad Osiur Rahman,

M. H. M. Imrul Kabir

Abstract— A new method is presented for person verification based on inner joining lines of fingers of right hand. This paper

attempts to improve the performance of hand geometry based verification system by reducing the amount of features and

integrating new features. It also decreases computational time by introducing a moderated edge detection method based on

high pass filter. The image acquisition of this system is different than other hand geometry based biometric systems. The

system requires only the upper portion of a palm image instead of image of full palm. Hence it reduces the database size. The

proposed system is suitable for capturing images by a digital camera or a normal scanner. The best performance of the proposed system will be found by Euclidean distance metric. The method has been tested on a medium size dataset of

100 images with promising results of 0.02% false rejection rate (FRR), 0.02% false acceptance rate (FAR) and 99.98% total

success rate.

Keywords— Hand geometry, verification, authentication, recognition, FAR, FRR, GAR, TSR.

1 INTRODUCTION

UTOMATIC human identification has become an

important issue for today’s information and net-

work based society. The techniques for automatically

identifying an individual based on his physical or beha-

vioral characteristics are called biometrics. The personal

attributes used in a biometric identification system can be

physiological, such as facial features, fingerprints, iris,

retinal scans, hand, and hand geometry; or behavioral,

such as voice print, gait, signature, and keystroke style.

From anatomical point of view, human hand can be cha-

racterized by its length, width, thickness, geometrical

composition, shapes of the palm, and shape and geome-

try of the fingers. It is generally accepted that fingerprint,

retinal and iris patterns can uniquely define each member

of an extremely large population which makes them

suitable for large-scale recognition (establishing a sub-

ject’s identity). However, in many applications, because

of privacy or limited resources, we only need to au-

thenticate a person (confirm or deny the person’s

claimed identity). Moreover, suitability of a particular

biometric to a specific application depends upon several

factors [1]. In these situations, we can use different dis-

tinguishing features with less discriminating power such

as face, voice or hand shape. One distinct advantage the

hand modality offers is that its imaging conditions are

less complex, for example a relatively simple digital cam-

era or flatbed scanner would be sufficient. Consequently,

hand-based biometry is user-friendlier and it is less prone

to disturbances and more robust to environmental condi-

tions and to individual anomalies. Moreover, hand geo-

metry has long been used for biometric verification and

identification because of its acquisition convenience and

good verification and identification performance [2]-[4].

Hand geometry measurement is non-intrusive and the

verification involves a simple processing of the resulting

features [5]. Hand geometry based authentication is also

very effective for various other reasons. Almost all of the

working population have hands and exception processing

for people with disabilities could be easily engineered [6]

In contrast, face modality is known to be quite sensitive to

pose, facial accessories, expression, and lighting varia-

tions; iris or retina-based identification requires special

illumination and is much less friendly; fingerprint imag-

ing requires good frictional skin etc., and up to 4% of the

population may fail to get enrolled [7]. Therefore, authen-

tication based on hand shape can be an attractive alterna-

tive due to its unobtrusiveness, low-cost, easy interface,

and low data storage requirements. Some of the presently

deployed access control schemes based on hand geometry

range from passport control in airports to international

banks, from parents’ access to child daycare centers to

university student meal programs, from hospitals, pris-

ons, to nuclear power plants [8]. In fact, there exist a

number of patents on hand information-based personnel

identification, using either geometrical features or on

hand profile [8]. Sanchez-Reillo et al. [9] select 25 features,

such as finger widths at different latitudes, finger and

A

————————————————

R.H.M.A. Kabir is a Faculty of Computer Science & Engineering, DIU, Dhaka, Bangladesh. E-mail: [email protected].

M.A. Rahman is a Faculty of Computer Science & Engineering, IIUC, Chittagong, Bangladesh. E-mail: [email protected].

M.A. Haque is a Faculty of Computer & Communication Engineering, IIUC, Chittagong, Bangladesh. E-mail: [email protected].

M.O. Rahman is a Faculty of Computer Science & Engineering, CU, Chit-tagong, Bangladesh. E-mail: [email protected]

M.H.M.I. Kabir is a faculty of East West University, Dhaka, Bangladesh. E-mail: [email protected]

Manuscript received on 3 June 2010 and accepted for publication on 5 September 2010. © 2010 ULAB JSE


palm heights, finger deviations and the angles of the inter

finger valleys with the horizontal, and model them with

Gaussian mixtures. Jain et al. [10] have used a peg-based

imaging scheme and obtained 16 features, which include

length and width of the fingers, aspect ratio of the palm

to fingers, and thickness of the hand. Öden et al. [11], in

addition to geometric features such as finger widths at

various positions and palm size, have made use of finger

shapes. These shapes have been represented with fourth

degree implicit polynomials, and the resulting sixteen

features are compared with the Mahalanobis distance. A

recent work utilizes both hand geometry and palm print

information as in Kumar et al. [12], which use decision

level fusion. Alexandra L.N. Wong [13] use 16 features,

such as finger lengths, finger widths and fingertip re-

gions.

In this paper, we present a system where are two phases

one for enrollment and another for verification purpose.

Both phases have common phase consists of image acqui-

sition, preprocessing, feature extraction, template con-

struction, and creation of reference database. During the

enrolment phase three samples have been taken. After

feature extraction, calculated mean value and standard

deviation of individual feature will construct the template

of the person. The verification phase consists of image

acquisition, preprocessing, feature extraction, classifica-

tion and decision. During verification, this input data is

compared with the corresponding data. The reference

data is selected from the reference database when user

enters their personal identification number. In the pro-

posed system six coordinate values will be taken from

hand image. Using these six points 9 features will be ob-

tained. The features will be used to construct the template

data.

2 METHODOLOGY

When the input data is fed into the biometric system it may be unsuitable for feature extraction. This is due to the several noise elements which may creep into the data. After removing noise the resized image is used to extract and store features. The last module of the biometric sys-tem is matching.

2.1 Image Acquisition and Resizing

The images are captured using a flatbed scanner with 24 bit color and 200 dpi resolution. The input image is a co-lored image of the right palm (fingers are combined to-gether) without any deformity. The captured image, shown in Figure 1(a) is stored in tif format. In cases of standard deformity such as a missing finger the system expresses its inability to process the image. For resizing and cropping the captured image a photo editor is required such as Microsoft paint. The hand im-age will be converted to 25% of the original image. By cropping eliminate the unnecessary portion of the hand and stored in bmp file format as shown in Figure 1(b).

This image acquisition setup is simple and neither the employs require any special illumination nor uses any peg to cause any inconvenience to users. Only the users will be requested to place their hands on the surface of the scanner in such a manner that their fingers touch neighbor fingers. If the quality of the image is not satisfac-tory then the image is rejected. As a result, the database contains only good quality templates and the system ac-curacy improves.

(a) (b) (c)

(d) (e) (f) Figure 1: Process of features extraction (a) Original image, (b) Resized

image, (c) Filtered image using 5x5 high pass filter, (d) Monochromic im-

age, (e) Monochromic noise free image, (f) Extracted features.

2.2 Preprocessing

In this section, a moderated edge detection algorithm, based on high pass filer is applied to extract contour of hand. The first step of this edge detection algorithm is translating the hand image in such a way that all edges become black, shown in Figure 1(c). Then extract only edges by applying a threshold a value as shown in Figure 1(d). Noise exists between the fingers, the inside of the palm perimeter or in background. A convolution filter is applied which checks if a black pixel is surrounded on all sides by white pixels. If that is found will be considered as noise and is converted to a white pixel, shown in Fig-ure 1(e). The size of the convolution filter is variable. First the filter uses a 3*3 template, then a 5*5, after that a 7*7 and finally a 9*9. This progressively removes larger and larger noise elements from the image.

2.3 Feature extraction

Initially the coordinate values of the five points are de-tected from the acquired and preprocessed image. Four points of them are the topmost four points of four fingers. The first, second, third, and fourth points are the top points of the little, ring, middle and index finger respec-tively. These four points are named as A, B, C, and D re-

R.H.M.A. KABIR ET AL.: A SIMPLE APPROACH TO RECOGNIZE A PERSON USING HAND GEOMETRY 21

spectively. The last and fifth one is between middle and ring fingers named E. All of these five points are marked and shown in Figure 2.

Figure 2

Using these five points, features of hand geometry verifica-

tion are extracted. At first, possible distances are considered.

There are six possible distances are taken by using these five points. The distances are AB, BC, CD, AE, DE and AD.

2.4 Template Construction

Templates are only data representing key or distinctive features of a biometric and are not a complete image or record of the original biometric (such as a fingerprint, voice recording or digital image). In this work, the template will be generated from three snapshot of each person. At first, we calculate distances for individual snapshot. Four distance metrics [9] are used for verification. Two of them need only mean values another one needs both mean values and standard devia-tion and the rest one needs both mean values and va-riance of individual distances. Thus mean values, va-riance and standard deviations of individual distances are calculated. The mean values will be used to construct the template for each person. That means, Template F= (d1, d2,….……, di) Where di average value of individual distance i=1, 2, 3 number of features.

2.5 Matching

Matching is the process of calculating a similarity and dissimilarity between current feature representation of the biometrics data of a user and the respective reference data set. Snapshot of the hand are taken and the feature vector is computed. The given feature vector is then com-pared with the feature vector stored in the database asso-ciated with the claimed identity. Let

),.....,,( 21 dfffF represent the d-dimensional feature vector in the database associated with the claimed identi-ty and ),......,,( 21 dyyyY be the feature vector of the hand whose identity has to be verified. The size of the feature vector dimension is nine. The verification is posi-tive if the distance between F and Y is less than a thre-

shold value. Four distance metrics i) absolute, ii) weighted absolute, iii) Euclidean, and iv) weighted Eucli-dean corresponding to the following four equations were explored [10]:

i)

d

j

aii fy1

……………………(1)

ii) wa

d

j j

ii fy

1

………………….(2)

iii) e

d

j

ii fy 1

………………..(3)

iv)

we

d

j j

ii fy

1

2

2

……………..(4)

where σj2 is the feature variance of the jth feature and εa, εwa, εe, and εwe are threshold values for each respective distance metric.

3 EXPERIMENTAL RESULT

One of the tasks to be studied for the enrollment process is the number of feature vectors that form the user’s tem-plate. It is obvious that the bigger the number of samples used the better the calculated template will be created. The hand geometry authentication system was trained and tested using a database of 18 users. At least four im-ages of each user’s hand were captured over different sessions. Total 125 images were made available. Out of 125 images, only 100 were used for testing our hand geo-metry system. The remaining 25 images were discarded due to incorrect placement of the hand by the user. Thus, user adaptation of this biometric is necessary. Three im-ages of each user’s hand were randomly selected to com-pute the feature vector which is stored in the database along with the user’s name.

3.1 FAR-FRR Analysis

The performance of a biometric system is measured in certain standard terms. These are given below: False Acceptance Rate (FAR) is the ratio of the number of unauthorized (unregistered) users accepted by the biome-tric system to the total of identification attempts made.

Number of False Attempts

Number of Impostor accesses

(λ) = Security Level False Rejection Rate (FRR) is the ratio of the number of number of authorized users rejected by the biometric sys-tem to the total number of attempts made.

Number of False Rejects

Number of Client accesses

FAR (λ) =

FRR (λ) =


(λ) = Security Level

Figure 3 : FAR-FRR Rate

False acceptance poses much more serious problem than false rejection. It is therefore desired that the biometric system keep the FAR to the minimal possible limit. This can be achieved by setting a high threshold so that only very near matches are recognized and all else are rejected. The higher the security requirement from the system the higher the threshold required to maintain it.

Now FAR-FRR analysis is going to be conducted for each of the distances used in this study. For Absolute Distance Initially an arbitrary threshold, roughly at the center of the match-score spread was chosen. After testing with the images the arbitrary threshold proved to be fairly good. In 100 tests for false acceptance there are a total of 6 false acceptances, giving the threshold 17 an FAR of 0.06. Also in 100 tests for false rejections it is found to be 1 false re-jects giving the FRR a value of 0.01. During these tests the match-score for each false accep-tance has been noted. Also the match-score for each false rejection are noted The FAR-FRR curve is shown in Figure 4(a). The ERR obtained from this curve is 0.04. For Euclidean Distance For threshold value 8 FAR is 0.03 and FRR is 0.01. The FAR-FRR curve is shown in Figure 4(b). The ERR ob-tained from this curve is 0.02. For Weighted Absolute Distance For threshold value 12 FAR is 0.03 and FRR is 0.02. The FAR-FRR curve is shown in Figure 4(c). The ERR ob-tained from this curve is 0.03. For Weighted Euclidean Distance For threshold value 5 FAR is 0.02 and FRR is 0.02. The FAR-FRR curve is shown in Figure 4(d). The ERR ob-tained from this curve is 0.02.

(a)

(b)

(c)

(d)

Figure 4: FAR - FRR curve for (a) Absolute Distance, (b) Euclidean Distance, (c) Weighted Absolute Distance, and (d) Weighted Euclidean

Distance.


(a)

(b)

(c)

(d)

Figure 5: ROC curve for (a) Absolute Distance, (b) Euclidean Distance, (c) Weighted Absolute Distance, and (d) Weighted Euclidean Dis-

tance.

3.2 ROC Curve Analysis

The Receiver Operating Characteristic (ROC) is used instead of thresholds for this purpose. The ROC is a plot depicting the genuine acceptance rate along the Y-axis and the false acceptance rate along the X-axis. Time in some cases is of crucial importance in the performance of a biometric system. In a offline system it is not crucial but in the case of online systems it is of importance that the system works fast enough so as not to cause the user un-necessary annoyance. The ROC curve shown in Figure: 5 depict the perfor-mance of the system for the Absolute, Euclidean, Abso-lute, Weighted Euclidean distance. From the above curves we get best hit ratio against the false acceptance rate by Euclidean distance.

3.3 Comparison Analysis

To evaluate the system performance, three well-known measurements are used, such as False Rejection Rate (FRR), False Acceptance Rate (FAR) and Total Success Rate (TSR). The system performance could be significant-ly improved by having habituated users. A relative comparison is made based on the outcomes of Absolute, Euclidean, Weighted Absolute and Weighted Euclidean distance of proposed system and shown in Ta-ble1. In Table 2, a comparison is made among the results of the proposed method and the results of the existing methods.

TABLE I

COPMPARISON STUDY OF FOUR DISTANCE MATRICS

Feature Vector

Dimension

Name of the Distance

Metrics

Decision

Threshold FAR % FRR % TSR%[9]

6

Absolute 17 0.06 0.01 99.96

Euclidean 8 0.03 0.01 99.98

Weighted Absolute 12 0.03 0.02 99.97

Weighted Euclidean 5 0.02 0.02 99.98


TABLE II

COMPARISON AMONG PROPOSED METHOD AND EXISTING METHODS

Name of the Paper Techniques Applied

for Verification

Feature

Vector Di-

mension

Classification

Success Rate

(%)

Biometric Identification through Hand

Geometry Measurement [7]

Euclidian distance

Metric 15 86

Hand Reorganization using Implicit

Polynomial and Geometric Features [9] Geometry 16 89

Personal Verification using Palmprint

and Hand Geometry Biometric [10]

Normalized

Correlation 16 91.66

A prototype Hand Geometry Based

Verification System [8]

Absolute Distance

Metric 14 94.99

Peg-Free Hand Geometry Recognition

Using Hierarchical Geometry and Shape

Matching [11]

Gaussian Mixture

Models (GMMs) 16 96

A Simple and Effective Technique for

Human Verification with Hand

Geometry [13]

Distance

Based Nearest Neighbor

(DBNN)

15 99.11

Authentication of Individuals Using

Hand Geometry Biometrics: A Neural

Network Approach [12]

Multi layer perception

(MLP) 10 99.62

Personal Authentication Using Hand

Geometry [14] Absolute without mean 15 99.71

Proposed System Euclidean & Weighted Euc-

lidean distance Metrics 6 99.98

3.4 Computational Complexity Analysis

The first three steps of the proposed system can be per-

formed using only simple image processing tools such as

image resizing, filtering and point selection. The last step

can be done using only simple and tiny arithmetic. Both

are fully computationally non-intensive operations. The proposed system is examined on a heterogeneous dataset collected for real world experiment environment. It can be observed evidently that the performance of the proposed system is better than existing systems in broad perspectives.

4 CONCLUSION

This system is based on new features selection for hand geome-

try based personal verification systems. This systems is very

much user friendly and convenient to implement. The system is

peg free and images can be captured by a normal scanner. Or-

ganizer need not to manage a high image captured instrument or

pegged scanner so it can be implemented in where any time.

User can place his/her hand in any orientation less than 45 de-

gree along vertical axis. Generally a large number of feature

decrease the performance of computation here only one set of

feature vector (nine features) are used which improves the

computational efficiency. One special contribution of this sys-

tem is that it can detect actual valley points although there is a

small gap between tips of two fingers. This system runs on hand

with nailed finger accurately. The remarkable achievement ob-

tained from the proposed method is the result of verification,

which is best among the prevailing techniques of hand geome-

try based verification system. The system showed promising

results with accuracy around 99.98%. The FRR is found to be

close to 0.02 and the FAR to be around 0.02.

The proposed approach utilizes primarily the geometry of the

hand and work on colored images. If a grayscale image is uti-

lized for the system, then databases search will take a short time

and decreases computational time more. If the system works

properly when a user placed his/her hand in any angle, it will be

more users friendly. The use of neural network based classifier

trained on a larger database may result in further improvement

of the system accuracy.

REFERENCES

[1] A. Jain, L. Hong, S. Pankanti, and R. Bolle, “Online identity-

authentication system using finger-prints," Proceedings of IEEE,

vol. 85, pp. 1365-1388, September 1997.

[2] J. Ashbourn, “Biometrics: Advanced Identity Verification”,

Springer-Verlag, New York, 2000.

[3] R. Sanchez-Reillo, “Hand geometry pattern recognition

through Gaussian mixture modeling”, in 15th International

Conference on Pattern Recognition, vol.2, Sep, 2000. pp. 937-940.


[4] A.K. Jain and N. Duta, “Deformable matching of hand shapes

for verification”, IEEE International Conference on Image

Processing, Oct, 1999. Pp. 857-861.

[5] J. R. Young and H. W. Hammon, “Automatic Palmprint Ve-

ri_cation Study", Rome Air Devel- opment Center, RADC-TR-

81-161 Final Techni- cal Report, June1981.

[6] R. Zunkel, “Hand Geometry Based Authentication" in “Biome-

trics: Personal Identification in Networked Society", A. Jain, R.

Bolle, and S. Pankanti (Eds.), Kluwer Academic Publishers,

1998.

[7] A. K. Jain, A. Ross, and S. Prabhakar, Feb. 2004, “An introduc-

tion to biometric recognition,” IEEE Trans. Circuits Syst. Video

Technol., vol. 14, no. 1, pp. 4–20.

[8] R. L. Zunkel, 1999, “Hand geometry based verification,” in

Biometrics, A. Jain, R. Bolle, and S. Pankanti, Eds. Norwell,

MA: Kluwer, pp. 87–101.

[9] R. Sanchez-Reillo, C. Sanchez-Avila, and A. Gonzalez-Marcos,

Oct. 2000, “Biometric identification through hand geometry

measurements,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 22,

no. 10, pp. 1168–1171.

[10] A. K. Jain, A. Ross, and S. Pankanti, Mar. 1999, “A prototype

hand geometry based verification system,” Proc. 2nd Int. Conf.

Audio- and Video-Based Biometric Person Authentication, pp. 166–

171.

[11] C. Öden, A. Erçil, and B. Büke, 2003, “Combining implicit po-

lynomials and geometric features for hand recognition,” Pat-

tern Recognit. Lett., vol. 24, pp. 2145–2152.

[12] Y. A. Kumar, D. C.M.Wong, H. C. Shen, and A. K. Jain, Jun. 9–

11, 2003, “Personal verification using palmprint and hand

geometry biometric,” Proc. 4th Int. Conf. Audio Video-Based

Biometric Person Authentication, Guildford, U.K., pp. 668–678.

[13] Alexandra L.N. Wong and Pengcheng Shi “Peg-Free Hand

Geometry Recognition Using Hierarchical Geometry and

Shape Matching”, Department of Electronic and Electrical En-

gineering, Hong Kong University of Science and Technology.

[14] Ying-Han Pang, Andrew, David and Hiew Fu San, February 2-6,

2003, “Palmprint Verification with Moments”, Journal of WSCG,

vol.12, no.1-3, ISSN 1213-6972, 2004.

R.H.M. Alaol Kabir received BSc degree in Com-puter Science and Engineering from University of Chittagong, Bangladesh, in 2008, MS degree in Information Technology from University of Dhaka, Bangladesh, in 2010. He is a Lecturer of Darul Ihsan University, Dhaka, Bangladesh. His re-search interest includes Biometrics, Image Processing, Biomedical Engineering, and Wireless

Communication Networks.

Md. Atikur Rahman received BSc degree in Computer Science and Engineering from Universi-ty of Chittagong, Bangladesh, in 2008. He is a Lecturer of International Islamic University Chitta-gong, Bangladesh. His research interest includes Biometrics, Image Processing, Biomedical Engi-neering, and Microprocessor Architechture.

Mohammad Ahsanul Haque received BSc de-gree in Computer Science and Engineering from University of Chittagong, Bangladesh, in 2008. Currently, he is pursuing his MS degree in Com-puter and Information Technology in the University of Ulsan, South Korea. He is a Lecturer of Interna-tional Islamic University Chittagong, Bangladesh. His research interest includes Biometrics, Image Processing, Embedded Ubiquitus Computing System Design, Multimedia Processing, and Mul-ticore System Design.

Mohammad Osiur Rahman received B.Sc. Engg. degree in Computer Science and Engi-neering from Shahjalal University of Science & Technology, Bangladesh in1997, and M.Sc. Engg. degree in Information & Communication Technology from Bangladesh University of En-gineering Technology in 2005. Currently he is pursuing his PhD in the department of Electrical , Electronic and Systems Engineering, Universi-ty Kebangsaan Malaysia, Malaysia. He is an Assistant Professor in the CSE department of the University of Chittagong, Bangladesh. His research interest includes Biometrics, Image

Processing, DNA Computing, and Pattern Recognition.

M.H.M. Imrul Kabir received BSc degree in Applied Statistics from University of Dhaka, Bangladesh, in 2008, MS degree in Applied Statistics from University of Dhaka, 2010. His research interest includes Statistical Machine Translation, Biometrics,and Image Processing,.


Human Emotion Recognition Using PCA, ICA and NMF

Paresh Chandra Barman, Chandra Shekhar Dhir, Soo-Young Lee

Abstract—Recognizing human facial expression and emotion by computer is an interesting and challenging problem. In this

paper, Principal component analysis (PCA), independent component analysis (ICA) and Non-negative Matrix Factorization

(NMF) are exploited for feature extraction of face images. The features are low-dimensional representation of the original

multivariate high dimensional data with minimal loss in data representation [1]. In addition, the features are also required to give

good class discrimination for recognition experiments. Feature selection based on information gain criterion has been studied

for finding efficient features to improve the classification performance of face recognition tasks [2]. This work presents a detailed

study on the application of information gain for efficient feature selection and is compared with Fisher criterion. Individual,

emotion recognition experiments using face images of Korean nationals are performed to compare the two feature selection

criteria (Information gain and Fisher criterion). The face images of Korean nationals are obtained from the Postech Faces ’01

(PF01) database [3].

Keywords—Human emotion recognition, NMF, PCA, ICA.

1 INTRODUCTION

UMAN-computer intelligent interaction (HCII) is an emerging field of science aimed at providing natu-ral ways for humans to use computers as aids. It is

argued that for the computer to be able to interact with humans, it needs to have the communication skills of humans. One of these skills is the ability to understand the emotional state of the person. The most expressive way humans display emotions is through facial expres-sions. In recent years there has been a growing interest in improving all aspects of the interaction between humans and computers. Faces are much more than keys to indi-vidual identity. Human beings possess and express emo-tions in day to day interactions with others. The problem of handling facial images for recognition is also due to the large pixel size and demands on computa-tional resources. Therefore, several researchers have ex-ploited linear low-dimensional representation of images using orthogonal basis by Principal component analysis (PCA) and independent features using Independent com-ponent analysis (ICA). ICA is a multivariate approach of data representation with statistically independent fea-tures [5]. It has also found wide applications in the field on blind source separation. In [15] Cauchy Naive Bayes Classifier has been used for emotion recognition. Face recognition using eigenfaces was one of the prelimi-nary works in the field of face recognition using low di-mensional features [6]. While ICA and NMF give more local representation of data, PCA features are global. Al-

though, feature extraction methods helps in low-dimensional representation of multivariate data by using unsupervised methods, all the feature may not be impor-tant for classification. Hence, the features extracted give a good data representation and the next task is to select proper features for good classification performance. Va-riance of features and Fisher criterion (between class va-riance over within class variance) has been widely used for selection of features for classification [7]. Variance of feature gives an estimate of the power of the features that can be considered important. Recently, feature selection criterion based on information gain to face images is stu-died for efficient feature selection and improving classifi-cation performance [2]. A comparative study on the performances of the features will be done on feature selection criterion based on in-formation gain to facial images is studied for efficient feature extraction and improving classification perfor-mance. Information gain criterion is extensively studied in the field of text categorization [8]. The motivation to apply information gain was to maximize the information between the class and the given features. Since, the ICA features are independent we can get a score value for each feature based on information gain and a proper number of features can be selected. However, in case of PCA and NMF features which are dependent this crite-rion in its crude form cannot be applied. The information gain criterion presented in the paper does not consider the dependency among features which may be present in case of PCA and NMF features. In section II, feature extraction using PCA, ICA and NMF are discussed. Section III concentrates on feature selection using Fisher criterion and proposed information gain for application to face recognition. Experimental setup is pre-sented in section IV followed by results in section V. Sec-

H

————————————————

Paresh Chandra Barman is with the Department of Information and Com-munication Engineering, Kushtia, Bangladesh. E-mail: [email protected].

Chandra Shekhar is with the Department of Bio and Brain Engineering, KAIST, Republic of Korea.

Soo-Young Lee is with the Department of Electrical Engineerig, KAIST, Republic of Korea.


© 2010 ULAB JSE

PARESH C. BARMAN ET AL.: HUMAN EMOTION RECOGNITION USING PCA, ICA AND NMF 27

tion V1 discusses the experimental results followed by conclusions. A brief overview on the two dataset used is given below:

In this paper we utilize the publicly available Postech Faces ’01 (PF01) *3+ face database. PF01 has 56 males’ fac-es with 4 emotions of each, and the resolution is 150150. The four different emotion categories are: Smile, Surprised, Sad and Closed eyes as shown in figure1. There are 168 training samples per class, 56 test samples per class. We used 4 fold cross-validations for recognition process.

Figure 1: Example of 4 facial emotion expressions.

2 FEATURE EXTRACTION METHODS

Classification of emotion images with high resolution is a difficult problem and is computationally demanding if no pre-processing is done on the raw images. In an at-tempt to reduce the computational burden several effi-cient feature extraction methods have been studied. PCA is a well known method in image processing and has been widely used to extract meaningful features. Working on same philosophy, ICA and NMF are also used for representing low dimension feature space.

2.1 Principal Component Analysis (PCA)

PCA tries to obtain a representation of the inputs based on uncorrelated variables. The eigenfaces, E, are the or-thogonal axis or the uncorrelated basis for representation of face data. Let XPxN be the data matrix consisting on im-age data (each column consists of pixels of one image). Here P is the number of pixels and N is the number of images. Using singular value decomposition, the data can be represented as:

R

r

T

rrr

T veEDVX1

(1)

where D is a diagonal matrix with elements λr, and V is a orthonormal matrix with elements vijNxR. Hence, we can choose the number of basis (eigenfaces) depending on the square of the value of λr, which is the same as the ei-genvalues of covariance matrix of X. Thus, the dimension of the images is reduced from P pixels to R coefficients (P << R) with minimal loss in data representation.

2.2 Independent Component Analysis (ICA)

ICA is an unsupervised learning algorithm that tries to remove higher order dependencies among the basis of natural scenes [6]. The observed image is assumed to be a linear combination of basis images scaled by independent coefficients. The task is to find basis, A= [a1 a2 …aP], such that the coefficients, UPxN are independent of each other and X ≈ AU, where M is the number of basis and N is the number of images. This is also referred as factorial code representation [1]. Considering the high dimensionality of X it is often bene-ficial to represent the data by the coefficients pertaining to the important principal components. PCA is performed on the data and the dimension is reduced to R×N. The input to the ICA network is the low-dimensional repre-sentation of X which comprises of R eigenfaces. Let the low-dimensional representation of X be XPCA. ICA is performed using FASTICA algorithm to find the inde-pendent features. FASTICA uses the criterion of maximi-zation of negentropy and provides fast convergence [11, 12]. Since, ICA features extracted using informax learning algorithm is reported to be similar to the performance using FastICA the informax learning algorithm is not considered in the simulations [13]. 2.3 Nonnegative Matrix Factorization (NMF)

Given a non-negative data matrix Xnm is factorized into a non-negative basis factors, Wnr, and a coefficient factor Hrm, such that: X ≈ WH or

a ajiaijij HWWHX )(

(2)

where r is chosen as )/( mnnmr . To obtain the factors W and H we used the well known multiplicative update rule of [4].

3 FEATURE SELECTION METHODS

The basis of orthogonal decomposition of data matrix using PCA is arranged in the order of the descending magnitude of eigenvalues. Fisher criterion and Informa-tion Gain is used to select good basis from already ex-tracted basis mentioned in section 2 for classification per-formance.

3.1 Class Discrimination using Fisher Criterion

Class With results from nearest mean classifier (NMC), efficient feature selection or reducing the number of basis based on variation ratio (Fisher criterion score). The class discriminability ratio is given as [1]

j i

jij

j

j

xx

xx

r2

2

(3)


where, xj are the features, jx is the mean of feature cor-responding to class j, and x is the mean of the feature. The bases are rearranged in the descending order based on the value of r for each feature. 3.2 Class Discrimination using Information Gain

Feature selection for proper classification can also be done using information gain criterion. Information gain is defined as [2]

xp

jxpjxpjp

xpjp

xjpxjpI

j

j

2

2

log

,log,

(4)

where p(j,x) is the joint distribution of the class j and fea-ture x. p(x) is the probability distribution of the feature and p(j) is the probability distribution of the class. The features rearranged based on the value of I and the per-formance of feature selection using information gain is compared with fisher criterion.

4 EXPERIMENTAL SETUP

Experiments are performed on PF01 (Postech Faces) as described in section 1. In this recognition experiment, the features obtained from the training data set will be uti-lized to recognize the test image labeled according to the emotions. The expressions images of 56 male individuals are used for the emotion recognition problems. Each cross validation training data set consists of 168 images consist-ing of 42 images per emotion. The cross validation test data set consists of 56 images with 16 images per emotion. The following classifier has been used to empirically find the classification performance.

4.1 Nearest Mean Classifier (NMC)

Four distances metric: L1-metric, L2-metric, cosine dis-tance and Mahanalobis distance are used to test the per-formance of nearest neighbor classifier.

L2-metric is the Euclidean distance between the two vectors a and b and is given as:

k

i

ii babaL1

2

2 , .

Cosine distance (CD) is the similarity measure between

the two vectors and is given as ba

babaCD

,,

4.2 Support Vector Machines

Classification analysis with Support Vector Machine (SVM) will also be performed with inputs having fixed number of basis. SVM light is used in our experimental

study [14]. The inputs to the SVM are features extracted using PCA and ICA. Linear, polynomial and Gaussian kernels are used for the SVM classifier. For the linearly separable case, SVM provides the optimal hyper-plane that separates the training patterns. The optimal hyper-plane maximizes the sum of the distances to the closest positive and negative training patterns. This sum is called margin. For the non-linearly separable case, the training patterns are mapped onto a high-dimensional space using a kernel function. In this space the decision boundary is expected to be linear. The most commonly used kernel functions are polynomials, Radial basis function (RBF) and sigmoid functions.

5 EXPERIMENTAL RESULTS

Figures and For all tables the following notations are applicable: M- Maximum recognition performance is ob-tained using M features, where the features are arranged in the descending order of fisher score (FS (f1) > FS(f2) >…> FS(fM). (N, L)- Maximum recognition performance is obtained using N number of bins and L number of fea-tures. Features are arranged in descending order of mu-tual information with respect to class, i.e., MI(f1,C)> MI(f2,C)>……> MI(fL,C). For example, Table 1 represents recognition performance for the PCA extracted features. Let us consider 20 is the predefined PCA dimension, it means we extracted 20 PCA feature vectors then out of these 20 feature vectors using Fisher Score or Mutual In-formation score we used M selected features. In case of the element (3, 3) of


A

B

C

A

B

C


Figure 2: Comparison among feature selection methods (Mutual Information and Fisher Criteria) with NMC (Nearest mean classifier) and Cosine (cosine similarity measure) classifier for case: A. Fea-tures extracted by PCA, B. Features extracted by ICA Arch-I, C. Features extracted by ICA Arch-II, and D. Features extracted by NMF

table 1, 83.93 (14) means: M = 14 features with top values of fisher score gives recognition performance of 83.93% for training set1. We get recognition performance of 87.5% with L = 14 features (features are the ones with maximum mutual information value) and N = 24 bins are used to estimate the probability distribution function (pdf) of the PCA extracted features. Similar explanation is also appli-cable for other cases.

From the tables it has been observed that in maximum cases the feature selection by mutual information is better than Fisher criteria. The two criterions are different, hence, they need not be compared, and however, the im-portant factor is the decay in the values of the two scores. Figure 2 shows the emotion recognition performance for four different approaches (PCA, ICA-I, ICA-II and NMF) of dimension reduction or feature extraction methods. Two different feature selection criteria (Mutual Informa-tion (MI) and Fisher Selection criteria (FS)) and two dif-ferent classifiers (NMC and cosine similarity) have been used for each feature extraction process. The X-axis of figure indicates the number of input features to the clas-sifier, which are selected by MI or FS followed by one of the feature extracted methods, and the Y-axis represents the recognition rate. Figure 1.A. is the combination of PCA+(MI or FS)+(NMC or Cosine), 1.B. is the combination of ICA Arch-I+(MI or FS)+(NMC or Cosine), 1.C. is the combination of ICA Arch-II+(MI or FS)+(NMC or Cosine), and 1.D. is the combination of NMF+(MI or FS)+(NMC or Cosine).

Figure 3 represents the emotion recognition perfor-mance between feature selection methods of MI and FS for both classifiers. 2.A. PCA+(MI-FS)+ (NMC or Cosine), 2.B. ICA Arch-I+ (MI-FS) +( NMC or Cosine), 2.C. ICA Arch-II +(MI-FS)+(NMC or Cosine) and 2.D. NMF+ (MI-FS) + (NMC or Cosine).

Figure 3: Improvement of performance by Mutual information over Fisher criterion feature selection method with NMC (Nearest mean classifier) and Cosine (cosine similarity measure) classifier for case: A. Features extracted by PCA, B. Features extracted by ICA Arch-I, C. Features extracted by ICA Arch-II, and D. Features extracted by NMF

6 CONCLUSIONS AND FUTURE WORKS

Feature extraction algorithms like PCA, ICA, and NMF are evaluated in case of emotion. Feature selection based on Fisher criterion and information gain was applied to find efficient features from given basis. Information Gain criterion shows improved performance with ICA, NMF and PCA feature when applied to Nearest Mean Classifier with Euclidean and cosine distance measure. Cosine dis-tance measure performs better with PCA features in con-trast to the better performance of Euclidean distance measure when applied to ICA features. When SVM is used as classifier, slight improvement is seen when fea-tures are selected based on information gain compared to the feature selection method based on fisher score.

Architecture 1 for image representation of ICA will be implemented and compared with the architecture 2 as proposed in [1]. Architecture 1 finds statistically indepen-dent basis images, in comparison to architecture 2 which finds factorial code representation consisted of indepen-dent coefficients.

ACKNOWLEDGMENT

This research was supported as the Brain Neuroinformat-ic Research Program by Korean Ministry of Commerce, Industry, and Energy.

REFERENCES

[1] W M. S. Bartlett, J. R Movellan, and T. J. Sejnowski, “Face rec-ognition by independent component analysis”, IEEE Transac-tions on Neural Networks, 13(6) pp. 1450-64, 2002.

[2] C. S. Dhir, N. Iqbal, and S.-Y. Lee, “Efficient feature selection based on information gain criterion for face recognition”, Ac-cepted for publication in the proceedings of IEEE Int. conf. on In-formation Acquisition 2007.

[3] IMDB, Intelligent Multimedia Laboratory, “Asian face image database PF01”, Technical report POSTECH, Korea, 2001. (http://nova.postech.ac.kr/)

D

D D

http://nova.postech.ac.kr/


[4] D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization”, Advances in Neural Information Processing, vol. 13, MIT Press, 2001.

[5] A. Hyvarinen, J. Karhunen, and E. Oja, “Independent Compo-nent Analysis”, John Wiley & sons, Inc., 2001,

[6] M. A. Turk and A.P Pentland. “Eigenfaces for Recognition”, Cognitive Neuroscience, 3(1):71–86, 1991.

[7] P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman, “Eigen-faces vs. Fisherfaces: Recognition using class specific linear pro-jection”, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 19, No. 7, pp. 711-720, July 1997.

[8] G. Wang, F. H. Lochovsky, and Q. yang, “Feature selection with conditional mutual information MaxMin in text categoriza-tion”, Proc. Int. conf. on information and knowledge management, pp. 342-349, 2004.

[9] http://cvc.yale.edu/projects/yalefaces/yalefaces.html [10] A. S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, “From

Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose”, IEEE Trans. Pattern analysis and Machine Intelligence, vol. 23, no. 6, pp. 643-660, 2001.

[11] A. Hyvärinen, “Fast and Robust Fixed-Point Algorithms for Independent Component Analysis,” IEEE Transactions on Neural Networks, 10 (3): pp. 626-634, 1999.

[12] http://www.cis.hut.fi/projects/ica/fastica/ [13] B. A Draper et al., “Recognizing faces using PCA and ICA,”

Computer Vision and Academic understanding, vol. 91, pp. 115 – 137, 2003.

[14] http://svmlight.joachims.org/ [15] Nicu Sebe, Michael S. Lew, Ira Cohen, Ashutosh Garg, Thomas

S. Huang, “Emotion Recognition Using a Cauchy Naive Bayes Classifier”, 16th International Conference on Pattern Recognition (ICPR'02), vol. 1, pp. 100, 2002.

Paresh Chandra Barman has completed his M.Sc. degree from the University of Rajshahi-Bangladesh in 1995 and Ph.D. degree from KAIST, Republic of Korea in 2008. He is working as an Associate Professor and Chair of the the

department of Information and Communication Engineering, Islamic University, Kushtia, Bangladesh.

Chandra Shekhar Dhir has completed his M.Sc. degree from KAIST, Republic of Korea in 2006 and currently he is pursuing his Ph.D.degree in the same university.

Soo-Young Lee is working as a Professor in KAIST, Republic of Korea.

http://cvc.yale.edu/projects/yalefaces/yalefaces.html

http://www.cis.hut.fi/projects/ica/fastica/

http://svmlight.joachims.org/

ULAB JOURNAL OF SCIENCE AND ENGINEERING VOL. 1, NO. 1, NOVEMBER 2010 (ISSN: 2079-4398 32

Design and Simulation of Duobinary Encoder Circuit for Communication System

R. R. Mahmud, M. A. G. Khan, S. M. A. Razzak

Abstract—This paper presents microcontroller based schematic circuit design with simulation results of a duobinary encoder

(duobinary code from binary bit) for data communication system. Binary code has two levels of bit sequence that are 1 and 0.

On the other side, duobinary (DB) is a three-level code that is 1, 0 and -1 level. Microcontroller based duobinary encoder can

encode the binary signal to duobinary signal by simple circuit operation. The three bits comparison part of the encoding tech-

nique can be done by microcontroller portion very easily. Using duobinary transmission instead of binary transmission, it can

improve the system performance and bandwidth efficiency of output signal.

Keywords— Duobinary Encoder, Duobinary Decoder, Microcontroller, Two Input Inverting Adder.

1 INTRODUCTION

N efficient use of channel bandwidth is achieved through duobinary coding scheme. A binary data stream can be encoded into a duobinary signal

(three level data (1, 0, -1)) simply by adding the binary data stream with its one bit delayed stream or by precod-ing technique. Duobinary transmission was first invented in 1960 but applied on 1990 in the fiber optic communica-tion [5]. The advantages of duobinary transmission over binary transmission are: (a) it has a narrower bandwidth than binary format; (b) it has a greater spectral band-width; (c) It suffers less than Stimulated Brillouin Scatter-ing (SBS); (d) Easy to implement and (e) the average power level of duobinary signal is less than the average power level of binary signal. Our topic is different from the other researchers who have done their research on the same area. To show in difference between our findings and others, we would like to explain their researches. One of the researchers Jiang who have shown that the com-plexity setup to the transmitter portion can be reduced by using a single-arm Mach-Zender modulator (MZM) for bandwidth 10 GB/s and for 252 km of uncompensated standard single mode fiber (SSMF) [6]. A 3 dB bandwidth of Bessel Low Pass Filter could be used to generate elec-trical duobinary signals for 40 GB/s duobinary system which was designed by A. Rahman et al [9]. In 2008, Y. C. Lu et al demonstrated that 100% driving voltage did not need for optimal duobinary system [4]. All the mentioned papers explained about the performance of duobinary transmission, the bandwidth of low pass filters and mod-

ulation technique of communication system. But so far as we know that there is no paper explains about this duo-binary encoder technique with detail circuit design and simulation results. So our paper is unique that is micro-controller based schematic circuit design and simulation of a complete duobinary encoder (duobinary code from binary bit) for data communication system. One example of duobinary encoder and decoder bit sequence from bi-nary is given below in Figure 1.

Figure 1: Example of a duobinary encoder and decoder bit sequence

from binary bit stream.

2 DUOBINARY ENCODER

The duobinary encoding technique is a part of trans-

mitter portion. First binary bit is generated. Then it is

encoded to duobinary bit sequence which is given be-

low in Figure 2.

A

————————————————

Russel Reza Mahmud is with the Electrical and Electronic Engineering Department, Ahsanullah University of Science and Technology (AUST), Rajshahi Campus, Talaimary, Rajshahi-6204, Bangladesh.

E-mail: r.r.mahmud @gmail.com. Dr. Muhammad Abdul Goffar Khan is with the Department of Electrical

and Electronic Engineering, Rajshahi University of Engineering and Tech-

nology (RUET), Bangladesh. E-mail: qmagk @ yahoo.com Dr. S. M. Abdur Razzak is with the Department of Electrical and Electron-

ic Engineering, RUET, Bangladesh. E-mail: razzak91@ yahoo.com

Manuscript received on 31 July 2010 and accepted for publication on 30 September 2010.

© 2010 ULAB JSE

mailto:[email protected]


R. R. MAHMUD ET AL. : DESIGN AND SIMULATION OF DUOBINARY ENCODER 33

2.1 BLOCK DIAGRAM OF A DUOBINARY ENCODER

The duobinary encoding technique is a part of transmitter portion. First binary bit is generated. Then it is encoded to duobinary bit sequence which is given below in Figure 2.

Figure 2: Block diagram of conversion technique from binary to duo-

binary code and total communication system (encoder and decoder).

2.2 ALGORITHM OF DUOBINARY ENCODER

The conversion technique from binary to duobinary bit stream follows some rules called algorithm which is given below. Step 1: It contains three level means 1, 0, -1. Step 2: Duobinary code depends on comparison of every 3 bit numbers for each and every position. Step 3: If the neighbor 2 bits among 3 bits are same then it

tends to change the state. If it is not same then it holds the level means 0 level.

Step 4: Initially the level starts from -1. Step 5: If the signal is on state 1 and getting signal of state rise then it will be on state 1 level because 1 is the highest level in positive side. Step6: Similarly, if the signal is on state -1 and getting signal of state fall then it will be on state -1 level because -1 is the lowest level in negative side.

2.3 DESCRIPTION OF DUOBINARY ENCODER

Pseudo Random Bit Sequence (PRBS) is a binary bit gene-rator that generates binary data of two levels (1 and 0). The data will be random and the time delay of the bit gap is fixed for an interval. The PRBS is inverted by applying NOT logic gate. The precoding output has two levels of bit sequence that is 1 and 0 which can be achieved by ap-plying an exclusive-or (XOR) gate. Among the two inputs of the XOR gate, one is the output of NOT gate and another is the previous bit of exclusive-or gate. So 1 bit delay can be done by using a single D flip-flop. From the truth table 1, it is observed that state changing is followed from the second bit to the third bit of the precoded bit showing by arrow. When 1 comes after 0 and among 3 bits two 1’s or two 0’s are neighbor then it will be state rise. But when 0 comes after 1 and among 3 bits two 1’s or

0’s are neighbor then it will be state fall. Besides these for 101 and 010, it will be state hold because among 3 bits two 1’s or 0’s are not neighbor. When state rise and state fall are not active then it will be state hold means 0 level. From the table Karnaugh map can be obtained by the case of sum of product (SOP).

TABLE 1 TRUTH TABLE OF THE COMPARISON OF DUOBINARY CODING

STATE WITH EVERY THREE BITS

Figure 3: Karnaugh map and logical equation for (a)state rise and (b)state fall of duobinary encoding technique.

3 MICROCONTROLLER BASED DUOBINARY

ENCODER CIRCUIT

Microcontroller is a programmable device which contains a microprocessor, random access memory (RAM), read only memory (ROM), registers etc as same as single chip computer. As microcontroller is a low cost programmable device, it is used in the automatic control application. For example robot, microwave oven, digital watch, mobile phone, electronic display and some conditions where log-ical circuit operation is difficult. Algorithm of the assem-bly language program for microcontroller of duobinary encoder is given below. Atmega32 type microcontroller is used in simulation circuit.


3.1 ALGORITHM AND FLOW CHART OF THE ASSEMBLY LANGUAGE PROGRAM Step 1: Initialize the segment arrangement. Step 2: Initially output port will be -5 volt. Step 3: Take previous state data from output port for determine state condition. Step 4: Take next state data from input port. Step 5: Compare the input port data with previous state for step up, step down and step hold. Step 6: Give the output data to the output port. Step 7: Loop Step 8: End

For converting from precode to duobinary encode a micro

controller atmega32 is used. Two input ports (P, Q) and

two output ports (X, Y) are need for this program. Let

PPIA and PPIB are the output ports represent X and Y.

On the other side PPIC and PPID are the input ports

represent P and Q in the program. The truth table of the

program that follows the rule to convert precode to duo-

binary code is given in the table 2. Initially the output

port should be started from -1 level means state fall

representing PPIA=0 and PPIB=1. For PPIA =0/1 and PPIB

= 0/1 represent 0 level means state hold and PPIA=1 and

PPIB=0 represent 1 level means state rise. After initializa-

tion the encoded bit from -1 level, the program will take

the previous output bits from PPIA to the base register

lower side BL and PPIB to the base register upper side

BH. Then compare PPIA with PPIB by subtracting. If

PPIA is less than PPIB then it means the code is on -1 lev-

el and it goes to the L1 level of the program. If PPIA is

greater than PPIB then it means the code is on 1 level and

it goes to the L4 level of the program and for PPIA is

equal to PPIB, the program goes to the level L7.

TABLE 2

TRUTH TABLE OF MICROCONTROLLER INPUT AND OUTPUT

STATE CONDITION OF ASSEMBLY LANGUAGE PROGRAM FOR

DUOBINARY ENCODING TECHNIQUE

After that take the input codes PPIC to the data register lower side DL and PPID to the data register upper side DH respectively and then making comparison AL=DL-

DH. If PPIC is less than PPID then the output port will tend to fall the state. If PPIC is equal to PPID give the re-sult will tend to hold 0 level. If PPIC is greater than PPID the output port will tend to rise level according. If the previous bit PPIA is equal to PPIB then the state is on 0 level and it will change its level according to the input bits of PPIC and PPID. If the port value PPIC is equal to PPID then the output port PPIA will be 1/0 and PPIB will be 1/0 means state hold. If the previous bit PPIA is great-er than PPIB then the state is on 1 level and it will change its level according to the input bits of PPIC and PPID. If PPIC is greater than PPID then the coding bit will be on 1 level. If the PPIC is less than PPID value then it will be 0 level. If the port value PPIC is equal to PPID then the output port PPIA will be 1/0 and PPIB will be 1/0 means state hold. If the previous bit PPIA is less than PPIB then the state is on -1 level and it will change its level accord-ing to the input bits of PPIC and PPID. If PPIC is greater than PPID then the coding bit will be on 0 level. If the PPIC is less than PPID value then it will be the level -1. If the port value PPIC is equal to PPID then the output port PPIA will be 1/0 and PPIB will be 1/0 means state hold. In this way the program compares 3 bits numbers each and every time and gives the output result until the interrupt code is active. After this programming three types of output bits to the output ports PPIA = X and PPIB = Y can be obtained.

TABLE 3

THREE CASES OR LEVELS OF DUOBINARY ENCODER From the above table 3 these outputs of PPIA and PPIB have the values of positive and zero level logic voltage. But we need negative level logic means -1 level but there is no logic gate which will give -1 logic output. So we have to apply these programming outputs to the circuits called inverting amplifier and two inputs inverting adder circuit which is given below and finally 1level, 0 level and -1level logic voltage of duobinary coding can be obtained from the output of two inputs inverting adder circuit which is given below in the Table 4.

TABLE 4

TRUTH TABLE THAT FOLLOWS THE DUOBINARY THREE (1, 0,-1) LEVEL OF THE TWO INPUT INVERTING ADDER

Footnote) col

R. R. MAHMUD ET AL. : DESIGN AND SIMULATION OF DUOBINARY ENCODER 35

Figure 5: Schematic diagram of a clock pulse generator circuit (asta-ble multivibrator)

From Figure 5 the duty cycle of the clock pulse can be

changed by varying R and C. The frequency of the pulse

is (1)

Figure 4: Flow chart of assembly language program

CRRf

BA )(695.0

1


Figure 6: Schematic full circuit diagram of duobinary encoding sys-tem from binary

4 WAVE SHAPES AND RESULTS

Figure 7 is the simulation result by Protious 7.6 simula-

tion software. The yellow shape of duobinary encoder

represents X, blue shapes represents Y and red shape

represents duobinary code in Figure 6 which is the exam-

ple of Figure 1.

Figure 7: Simulation result of duobinary encoder

5 CONCLUSION

The design circuit for duobinary encoder can be imple-

mented any required place in communication system as

duobinary has greater advantages than binary format.

Our microcontroller based duobinary encoder generates

low average power and that is why it can travel long dis-

tance in communication system. The circuit generates

duobinary data at Mbps speed. For using microcontroller,

the circuit becomes simple for the three bits comparison

portion and additional clock pulse is not need to the

above circuit. Our circuit gives hundred percent accurate

results which are given in Figure 7 with respect to the

time interval and bit sequence.

REFERENCES

[1] J. Builting, “Introduction to Duobinary Encoding and Decod-

ing,” Elektor Electronics, pp. 50-52, January 1990.

[2] P. Bravetti, L. Moller et al, “Impact of Response Flatness on

Duobinary Transmission Performance: An Optimized Trans-

mitter with Improved Sensitivity,” IEEE Photon. Technol. Lett.,

vol. 16, no. 9, pp. 2159-2161, Sep. 2004.

[3] X. Gu, S.J. Dodds et al, “Duobinary Technique for Dispersion

Reduction in High Capacity Optical Systems Modelling, Expe-

riment and Field Trial,” IEEE Proc. Optoelectron, vol. 143, no. 4,

August 1996.

[4] L. A. Jiang, “Propagation Properties of Duobinary Transmission

in Optical Fibers,” MSC thesis submitted to Massachusetts In-

stitute of Technology, May 1998.

[5] W. Kaiser, T. Wuth et al, “A Simple System Upgrade from Bi-

nary to Duobinary,” National Fiber optic Engineers conference, pp.

1043-1050, 2001.

[6] H. Kim, and C. X. Yu, “Optical Duobinary Transmission System

Featuring Improved Receiver Sensitivity and Reduced Optical

Bandwidth,” IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1205-

1207, August, 2002.

[7] R. Miller, “A Bessel Filter Crossover, And Its Relation to Other

Types,” The 105 Convention of the Audio Engineering Society, San

Francisco, CA, September 26-29, 1998.

[8] A. Rahman, M. Broman et al, “Optimum Low Pass Filter

Bandwidth For Generating Duobinary Signal For 40 Gb/S Sys-

tems,” Thin Film Technology Corp.1980 Commerce drive, North

Mankato, MN, 56003, USA.

[9] C. Xie et al, “Improvement of Optical NRZ and RZ Duobinary

Transmission Systems with Narrow Bandwidth Optical Fil-

ters,” IEEE Photon. Technol. Lett., vol. 16, no. 9, pp. 2162-2164,

Sep. 2004.

[10] R. R. Mahmud, M. A. G. Khan and S. M. A. Razzak, “Design of

a Duobinary Encoder and Decoder Circuits for Communication

Systems,” Accepted in International Conference on Electrical and

Computer engineering (ICECE 2010), Dhaka, Bangladesh.

Russel Reza Mahmud was born in Rajshahi, Bangladesh in 1983. He received B.Sc. engineer-ing degree in EEE from Islamic University of Technology (IUT), Dhaka, Bangladesh, in 2003 and M.Sc. Engineering degree in EEE from Raj-shahi University of Engineering and Technology (RUET), Bangladesh in 2010. Currently he is a

lecturer in EEE Department, Ahsanullah University of Science and Technology (AUST), Bangladesh.

Muhammad Abdul Goffar Khan is currently Professor and Head, Department of Electrical and Electronic Engineering, Rajshahi University of Engineering and Technology (RUET), Bangla-desh.

S. M. Abdur Razzak was born in Natore, Bangla-desh in 1974. He received B.Sc. engineering de-gree from Rajshahi University of Engineering and Technology (RUET), Bangladesh, in 1998, M.Eng.degree in EEE from the University of the Ryukus, Okinawa, Japan in 2007 and PhD in elec-tronics and information engineering from the same

University in 2010. Currently he is an assistant professor of EEE department of Rajshahi University of Engineering and Technology (RUET), Bangladesh.


Development of a Knowledge-Based Diagnosis and Management System for

Diabetes Mellitus through Web

Mohammad Shorif Uddin and Morium Akter

Abstract—Diabetes mellitus is a common metabolic disorder that is characterized by hyperglycemia, due to absolute or relative

deficiency of insulin, is increasing worldwide. It is a medical condition resulting in an excessive amount of sugar (glucose) in the

blood and is associated with a range of severe complications including renal and cardiovascular diseases and blindness.

Preventive care helps in controlling the severity of this disease. However, preventive measures require the correct educational

awareness and routine health check. Medical doctors help in effective diagnosis as well as treatment of diabetes but it obviously

associated with high costs. With this view, the purpose of the present research is to develop a low- cost automated knowledge-

based system that helps in self diagnosis and management of this chronic disease. The system is implemented through a web-

based technique, which is workable both in offline and online with a convenient interface. It works in analyzing the patient data

to make decisions regarding diagnosis, prevention, and treatment of patients. To confirm the effectiveness of the system we

have experimented with 100 data taking doctors prescriptions as ground truth. Among these 89 cases give correct responses.

Keywords—Diabetes mellitus, insulin deficiency, insulin resistance disease diagnosis, health care management, knowledge-based system.

1 INTRODUCTION

N the year 2000, a study [1] among 191 World Health Organization (WHO) member states confirms that 2.8% people for all age groups had diabetes, and this is ex-

pected to be 4.4% by the year 2030. This implies that the total number of people with diabetes is projected to rise from 171 million in 2000 to 366 million in 2030.

In Bangladesh, diabetes is reaching epidemic propor-

tions; in some sectors of our society more than 10% of people have diabetes [2]. The most important demo-graphic [3] change to diabetes prevalence across the world appears to be the increase in the proportion of people>65 years of age. Diabetes causes [4] severe life threatening complications, such as hypoglycemic coma, blurred vision, loss of memory, severe impairment of ren-al function, insulin allergy, acute neuropathy, etc. All of these complications contribute to the excess morbidity and mortality in individuals with diabetes. Each year, 3.2 million deaths worldwide are attributable to diabetes-related causes.

Hypertension is very common in diabetes affecting 20 to 60% of patients depending on obesity, ethnicity and age [5]. The prevalence of hypertension in Bangladesh among diabetic population is 1.5 to 3 times higher than

that of nondiabetic age-matched groups. It is estimated that 30 to 75% of diabetic complication can be attributed to hypertension [4]. Among patients with type-II diabetes [6], [7] the mortality of cardiovascular disease is about 70 to 80%, with around 15% of patients dying from stroke. Coronary heart disease among diabetic population is 2 to 6 times higher than that of the nondiabetic population and there is a loss of pre-menopausal protection among diabetic women. Hypertension is also a major risk factor for cardiovascular disease and microvascular complica-tions such as retinopathy and nephropathy. In type-I di-abetes, hypertension often results of underlying nephro-pathy. Proper treatment of hypertension can reduce the complications of diabetes.

Diabetes management requires dietary control togeth-

er with insulin administration. Medical doctors help in effective diagnosis as well as treatment of diabetes. However, it obviously associates with high costs. Despite remarkable medical advances, patient self-management remains the cornerstone of diabetic treatment. Know-ledge-based intelligent system tool has been proven effec-tive in solving many real-world problems requiring ex-pert skills. Hence, to reduce the cost and to improve the early detection as well as self-awareness of diabetes melli-tus, automated knowledge-based system might be a promising solution.

But at present in our country, there is no such system

by the government or by the private hospitals or NGOs for the management of diabetes themselves. The only one way is the doctor. For these reasons, we have developed

I

————————————————

Mohammad Shorif Uddin is with Dept. of Computer Science and Engi-neering, Jahangirnagar University, Savar, Dhaka, Bangladesh. E-mail: [email protected]).

Morium Akter is with Dept. of Computer Science and Engineering, Uni-versity of Development Alternative, Dhanmondi, Dhaka, Bangladesh. E-mail: [email protected]).

Manuscript received on 31 July 2010 and accepted for publication on 4 Septem-ber 2010. © 2010 ULAB JSE



a low cost automated knowledge-based system for the diagnosis and management of diabetes.

Knowledge-based system for diagnosis can be used in variety of domains: plant disease diagnosis, crop man-agement problem diagnosis, credit evaluation and autho-rization, financial evaluation, identification of software and hardware problems and integrated circuit failures etc. [8]-[10]. Recently, expert systems have been devel-oped in laboratory stage for diabetes awareness and man-agement, insulin administration [11]-[15]. Compared to these systems, our approach is more simple and pragmat-ic. The ultimate goal of this research is to develop a knowledge-based system incorporating the skills of med-ical doctors for diabetes diagnosis as well as manage-ment. Previously, we have developed a prolog-based di-abetes management system [16]. In the present research we implemented the system using a web-based tech-nique.

The paper is organized as follows. In section 2 the

medical knowledge about diabetes is described briefly, section 3 describes diagnosis process, section 4 describes method of treatment of diabetes, section 5 presents archi-tecture and implementation of the system as well as some experimental results, and finally section 6 draws the con-clusions and future works.

2 MEDICAL KNOWLEDGE OF DIABETES

Diabetes mellitus is a common metabolic disorder that is characterized by hyperglycemia, due to absolute or relative deficiency of insulin. It is a medical condition resulting in an excessive amount of sugar (glucose) in the blood. This is caused by a deficiency of insulin, which is a hormone secreted by the pancreas. Insulin allows glucose to go from the blood into the cells of the body for use. The clinical signs seen in diabetes are largely related to the elevated concentrations of blood and urine glucose and the inability of the body to use glucose as an energy source due to the deficiency of insulin [2]-[4].

Diabetes is classified as follows [2], [4].

Type-I (Insulin-Dependent Diabetes Mellitus-IDDM) diabetes tends to occur in the young, al-though it can occur at any age, and usually in people who are lean. It is caused by autoimmune destruction of the beta-cells in the pancreas, re-sulting in no insulin production. Patient with type-I diabetes are dependent on insulin to sur-vive, so they are called insulin dependent di-abetes mellitus(IDDM).

Type-II (Non-Insulin-Dependent Diabetes Melli-tus-NIDDM) diabetes mellitus occurs more often in older people who are obese and had sedentary lifestyles. In many cases symptoms is lower and the disease may remain undiagnosed for many

years. It is associated with both impairment of insulin secretion and resistance to insulin action (insulin resistance). Type-II diabetes is often as-sociated with a strong genetic predisposition. Once diagnosed, an improvement may result from weight reduction, dietary modification and increased exercise. Oral hypoglycemic agents and in advanced cases insulin may required.

Gestational diabetes mellitus (GDM) is a glucose

intolerance of any severity detected in a pregnant woman who was not known to have these ab-normalities prior to conception .A significant por-tion of this type of diabetes become normal after delivery. Once the GDM woman becomes nor-mal, she has increased risk of developing GDM in subsequent pregnancies. She have also an in-crease risk of becoming a diabetic in later life.

3 DIAGNOSIS

Diagnosis [13], [14] is a process by which a doctor searches for the cause (disease) that best explains the symptoms of a patient. Our knowledge-based system is mainly used for performing diagnosis based on patient data. Patient data can be demographic or clinical. Demo-graphic data relates the information such as patient’s age, sex, location, income, etc. Clinical data is divided into physical signs and laboratory results. Physical signs are those detected by a physical examination of patient, like BMI (body-mass index), pulse rate and blood pressure. Laboratory results are those detected via laboratory tests, like blood test, urine test, etc. The diagnosis system is based on the following patient data [12].

a. Uurine test for glucose and ketones. b. Measure random or fasting blood glucose:

Fasting plasma glucose >= 7.0 mmol/l Random plasma glucose >= 11.0 mmol/l.

c. Oral glucose tolerance test: Fasting plasma glucose 6.1-6.9 mmol/l Random plasma glucose 7.0-11.0 mmol/l.

4 Method of Treatment Diabetes mellitus is manageable through proper diag-

nosis and preventive measure. Diet can play a role in the treatment of Diabetes.

Diet alone— 50% can be controlled ade-quately.

Diet + oral hypoglycemic agent— 20-30% can be controlled.

Diet and insulin— 30% can be controlled.

5 ARCHITECTURES AND IMPLEMENTATION OF THE

SYSTEM

We have realized our system using a web-based tech-nique. The architecture of this technique consists of sys-

UDDIN AND AKTER: DEVELOPMENT OF A KNOWLEDGE-BASED DIAGNOSIS AND MANAGEMENT 39

tem admin, patient computer, web server, diabetes data-base, database server, php processor and php rules. We have implemented the system using php and mysql. The architecture of the knowledge-based system implement-ing through a web-based technique is shown in Fig. 1 as below. In this system there are two phases. One is diagnosis and another is database. In the diagnosis phase, patient input

the data and then shows the result of diagnosis and man-agement of diabetes. Figs. 3 and 4 present a sample input and output pattern obtained by our system. In the data-base phase the user have login window with user name and password, then shows the recorded data of the pa-tient. The login window is shown in Fig. 5 and patient records are shown Fig. 6.

Fig. 1 Architecture of the system through web-based technique.

Fig.2 Starting window for diabetes management system.

Fig. 3 Input data for the management of diabetes.

Fig. 4 Output for the inputs shown in Fig. 3.

Fig. 5 Login window of the database.

www

Web

server

Database

server

Diabetes

database

Php pro-

cessor

Php rules

Patient

computer

System Admin


Fig. 6 Patient records.

We have implemented our system through web-based technique which is workable both in offline and online mode and it has more convenient interface. At present our system works on 30 rules. We have tested this system with 100 data taking doctors prescriptions as ground truth. There are 89 correct outputs of system. So these real life experimentations confirmed the effectiveness of the proposed system. The system can be used in both home and hospital environments in online as well as offline modes.

6 CONCLUSIONS AND FUTURE WORKS

A knowledge-based system for diagnosis and manage-ment of diabetes has been introduced in this research. Its objective is to provide a cost effective treatment and man-agement system for the diabetes patients. We have im-plemented our system through a web-based technique, which is workable both in offline and online mode and it has more convenient interface. We have tested our system with 100 data taking doctors prescriptions as ground truth. The test result gives 11% error. There are some limitations in the developed knowledge-based system. For example, the number of rules are not sufficient for a general robust knowledge-based system. Moreover, wide real-life experimentations are not per-formed yet. There are ample scopes for improvement of our developed expert system on the basis of patient’s feedbacks. Our future goal is to overcome the above limi-tations to make a pragmatic one. We hope that our system will be an effective tool for millions of peoples with better diagnosis and management of diabetes.

REFERENCES

[1] S. Wild, G. Roglic, A. Green et al., “Global prevalence of di-

abetes - estimates for the year 2000 and projections for 2030”,

Diabetes Care, vol. 27, pp. 1047-1053, (2004).

[2] Diabetic Association of Bangladesh, “Diabetes Mellitus”, 2005,

(ISBN: 984-32-2552-X).

[3] Sarah Wild, Gojka Roglic, Anders Green, Richard Sicree, Hilary

King, “Global Prevalence of Diabetes-Estimates for the year

2000 and projections for 2030”, DIABETES CARE, Vol. 27,

Number 5, May 2004, pp-1047-1053.

[4] Hajera Mahtab, Zafar A Latif, Md. Faruque Pathan, “Diabetes

Mellitus - A Handbook For Proffessionals”, BIRDEM, 3rd Ed.,

2004, (ISBN: 984-31-0100-6).

[5] Square Pharmaceuticals Ltd., Bangladesh vol. 3, no. 1, January-

March 2005, “Inside Bangladesh”, available online at

http://www.squarepharma.com.bd/DiabetesNewsletter/3.1_Jan

uaryMarch_2005.pdf (accessed on January 22, 2008).

[6] Giuseppe Derosa, Sibill Salvadeo, Arrigo F. G. Cicero, “Rec-

ommendations for the Treatment of Hypertension in patients

with DM: Critical Evaluation Based on Clinical Trials”, availa-

ble online at http://www.bentham.org/ccp/samples/ccp1-

1/Derosa.pdf (accessed on February 15, 2008).

[7] P. Swaby, E. Wilson, S. Swaby, R. Sue-Ho, R. Pierre, “Chronic

diseases management in the Jamaican setting: Hope worldwide

Jamaica’s experience”, available online at

http://www.pngimr.org.pg/Chronic%20diseases%20-%20Sep-

Dec%202001.pdf (accessed on January 20, 2008).

[8] Jie Yang, Chenzhou Ye, Xiaoli Zhang, “An expert system for

fault diagnosis”, Robotics, vol.19, pp-669-674, (2001).

[9] Karthik Balakrishnan and Vasant Honavar, “Intelligent diagno-

sis systems”, available online at

http://www.cs.iastate.edu/~honavar/aigroup.html (accessed on

December 10, 2008).

[10] Costas Papaloukas, I. Dimiritrios, Aristidis Likas, S. Christos

Stroumbis, Lampros K. Michalis, “Use of novel rule-based ex-

pert system in the detection of changes in the ST segment and

the T wave in long duration ECGs, J. Electrocardiology, vol. 35,

no.1, (2002).

[11] V. Ambrosiadou and A. Boulton, “A knowledge-based system

for education on management of diabetes”, Proc. IMACS World

Congress on Scientific Computation, 1988, pp. 186-189.

[12] Rudi Rudi, and Branko G. Celler, “Design and Implementation

of Expert-Telemedicine ystem for Diabetes Management at

Home”, Intl. Conf. on Biomedical and Pharmaceutical Engineering,

2006 (ICBPE 2006), pp.595-599.

[13] Kyung-Soon Park, Nam-Jin Kim, Ju-Hyun Hong, Mi-Sook Park,

Eun-Jong Cha, Tae-soo Lee, “PDA based Point-of-care Personal

Diabetes Management System”, Proceedings of the 2005 IEEE En-

gineering in Medicine and Biology 27th Annual Conference Shang-

hai, China, September 1-4, 2005, pp3749-3752.

[14] V. Ambrosiadou, Diabetes, “An expert system for education in

diabetes management”, in Expert Systems Applications, Sigma

Press, UK, 1989, pp.227-238.

[15] G. Gogou, N. Maglaveras, V. Ambrosiadou, D. Goulis, C. Pap-

pas, “A neural network approach in diabetes management by

insulin administration”, J. Med. Syst. Vol. 25, no. 2, pp. 119-31,

2001, (ISSN: 0148-5598).

[16] Morium Akter, Mohammad Shorif Uddin, Aminul Haque , “A

Knowledge-Based System for Diagnosis and Management of

Diabetes Mellitus”, 13th International Conference on Biomedical

Engineering (ICBME 2008), Singapore, pp. 1000-1003.

UDDIN AND AKTER: DEVELOPMENT OF A KNOWLEDGE-BASED DIAGNOSIS AND MANAGEMENT 41

Mohammad Shorif Uddin received PhD in Information Science from Kyoto Institute of Technology, Japan, Master of Education in Technology Education from Shiga University, Japan and Bachelor of Science in Electrical and Electronic Engineering from Bangladesh University of Engineerong and Technology

(BUET). He joined in the Department of Computer Science and En-gineering, Jahangirnagar University, Dhaka in 1992 and currently he is a Professor of this department. He started his teaching career in 1991 as a Lecturer of the Department of Electrical and Electronic Engineering, Chittagong University of Engineering and Technology, (CUET). He did postdoctoral researches at Bioinformatics Institute, A-STAR, Singapore, Toyota Technological Institute, Japan and Kyo-to Institute of Technology, Japan. His research is motivated by appli-cations in the fields of computer vision, pattern recognition, blind navigation, bioimaging, medical diagnosis and disaster prevention. He has published a remarkable number of papers in peer-reviewed international journals and conference proceedings including well-reputed IEEE Transactions on ITS, British IOP Journal, Japanese IEICE Transactions, Optics Express and Applied Optics (Optical society of America), Elsevier Science Journal. He holds two patents for his scientific inventions. He received the best presenter award in the International Conference on Computer Vision and Graphics (ICCVG 2004), Warsaw, Poland. He is the author of two books. He is a member of IEEE, SPIE, and IEB.

Morium Akter was born in Gazipur, in Bangla-desh in 1981. She received her BSc and MS in Computer Science and Engineering from Jahan-girnagar University, Savar, Dhaka in 2005 and 2009, respectively. She has been working as a faculty in the University of Develpoment Alterna-tive (UODA) from January 2009 to till now. She has four publications in the peer-reviewed confe-

rences. Her research interests include Image Analysis and Soft-ware–Based Medical Diagnostic Systems.

ULAB JOURNAL OF SCIENCE AND ENGINEERING VOL. 1, NO.1, NOVEMBER 2010 (ISSN: 2079-4398) 54

©2010 ULAB JSE

A Finite Difference Method for One Dimensional Heat Equation

M. H. Kabir, A. Afroz, M. M. Hossain, M. O. Gani

Abstract—We consider one dimensional heat equation which is a Parabolic type of partial differential equations (PDE) as an initial boundary

value problem (IBVP). The derivation of heat equation is presented here. We also present the derivation of a numerical scheme named explicit centered difference scheme for the heat equation. We develop a computer program to implement the scheme for the heat equation and present the numerical solution of the heat equation. We compare the analytic solution and numerical solution by error estimation.

Keywords— Heat Equation, initial boundary value problem (IBVP), finite difference method, partial differential equations (PDE).

1 INTRODUCTION

HE simplest model of heat flow is based on three

principles: conservation of energy, Fouriers law of cooling

and a constitutive law. The heat equation is characterized

by the heat flow in terms of the measures of temperature. The

heat equation is a second order partial differential equation

that governs flow of heat within an object. We can see how the

temperature changes with the time along an object by

observing this equation. Let us note that the boundary value

problems for the PDE belong to a large class of great

importance problems in many scientific fields.

Since there are few papers devoted to the finite difference

method named crank-nicolson scheme in Malgorzalaic [1].

Sharanjeet [2] found a numerical solution of one dimensional

heat equation using cubic spline basis functions. In [2] one

dimensional heat equation is solved using Galerkin B-spline

finite element.

The aim of this article is to investigate an efficient finite

difference scheme for one dimensional heat equation as an

IBVP. In order to verify some qualitative behaviors of the

scheme for one dimensional heat equation, we would like to

make a comparative study between analytic solution and

numerical solution of the heat equation.

In this paper we present the derivation of the heat equation

based on Adam [9] and Raishinhania [5]. We study the analytic

solution of this equation as an IBVP (Initial Boundary Value

Problem) by the method of separation of variables from Gerald

[3] and Raishinghania [5] . The derivation of the explicit finite

difference scheme for heat equation as an IBVP is presented in

section 4 based on Gerald [3], Smith [4] and Burden & Fares [7].

We develop a computer programming code to perform some

numerical experiments and present relative error in section 5.

2 ONE DIMENSIONAL HEAT EQUATION

Here we present the derivation of the one dimensional heat

equation based on Adam[9] and Raishinghania[5].

We consider the flow of heat by conduction in a thin rod

made of a homogeneous material and perfectly insulated along

its length so that heat can only flow through its ends. Any

position along the rod is denoted by x , and the length of the

rod is denoted by L (in meters) so that Lx 0 .

a b

0 x xx L

Fig 2.1: A thin rod of length L meters

Therefore, the temperature, ),( txu of the rod at any point is a

function of position, x (in meters) and time t (in second).

Suppose that the rod is raised to an assigned temperature

distribution at time 0t and then heat is allowed to flow by

conduction. We wish to compute ),( txu at any point x and

T

————————————————

M H Kabir is with Department of Mathematics, Jahangirnagar University, Savar, Dhaka ( E-mail: [email protected]).

A Afroz is with International University of Business Agricultural and Technology (IUBAT), Dhaka (E-mail: [email protected].).

M M Hossain is with Department of Mathematics, Jahangirnagar University, Savar, Dhaka.

M O Gani is with Department of Mathematics, Jahangirnagar University, Savar, Dhaka (E-mail: [email protected]).

Manuscript received on 31 July 2010 and accepted for publication on 26 October 2010.

M H KABIR ET AL.: A FINITE DIFFERENCE METHOD FOR ONE DIMENSIONAL HEAT EQUATION 55

at any time, 0t . We should make the following

assumptions:

a) The rod is homogeneous, i. e. the mass of the rod per

unit volume is constant, (say)

b) The rod is insulated along its length.

c) The amount of heat crossing any section of the rod is

given by tx

uKS

Where, S = Area of cross section of the rod.

x

uTemperature gradient at the section, U

t Time of flow of heat

K Thermal conductivity of the material of the rod

Now, the quantity of heat flowing into the element through U

at ax in time t is given by

= tx

uKS

x

where the negative sign has been taken because heat flows in

the direction of decreasing temperature.

Again, the quantity of heat flowing through U at x=b in time

t

tx

uKS

xx

Therefore, the amount of heat U obtains at time t is given by

t

x

uKS

x

tx

uKS

xx

xxx x

u

x

utKS

------ (2.1)

We assume that the above heat raises the temperature of the

element by a small quantity u . Then the same quantity of

heat is given by

ucxS )( ------ (2.2)

where, c is the specific heat of the rod.

Since, the expressions (2.1) and (2.2) are equal, the we have

xxx x

u

x

utKS

ucxS )(

t

uc

x

txutxxuK xx

),(),(

------- (2.3)

As 0x and 0t , equation (2.3) reduces to

t

uc

x

uK

2

2

2

2

x

uk

t

u

---------(2.4)

where, c

Kk

is called the thermal diffusivity of the

material of the rod. This equation is more popularly written

with subscript notation as

xxt kuu (2.5)

We have now derived heat equation, also known as the

diffusion equation.

3 ANALYTIC SOLUTION OF THE HEAT EQUATION

In this section we present the analytic solution of the heat

equation follows from Gerald [3], Smith [4] and Adam [9].

To find the analytic solution of the one dimensional heat

equation we have to make it as an initial boundary problem

(IBVP) by setting some initial conditions and boundary

conditions.

If we have a rod of length 5.1L meter and 02.0k .

Setting the initial temperature distribution xxu )0,( and

the boundary conditions defined with the condition that if one

end of the rod w submerged in a liquid that is a constant 00

and the other end in a liquid at0120 , then 0),0( tu and

120),5.1(),( tutLu for all 0t .

Finally, we arrive with the problem

0120),5.1(0),0(

5.100)0,(

0

5.10),(02.0),(

tfortuandtu

xforxu

tand

xfortxutxu xxt

------(3.1)

Since the heat equation is linear, so we can find a linear

combination of two solutions to equal another solution.

First of these solution is steady state solution )(xu s , such that

xTxL

TTxu L

s 80)( 0

0

The remaining part suvu where suuv .so it

satisfies IBV problem,

05.10,),(),( tandxfortxkvtxv xxt

Lxforxuxuxv s 0)()()0,( 0 -------(3.2)

0),1(0),0( tfortvtv


By using separation of variable we will find the solution of

v because separation of variables requires the problem

homogeneous .Therefore we want to find the product solutions

of the form )()(),( tTxXtxv .

By separation of variable we get two ODE’s for T and X. If we

plug )()( tTxXv in to the heat equation, we get

)()()()( tTxXKtTxX .

Dividing both sides by

)()( xXandtKT gives,)(

)(

)(

)(

xX

xX

tKT

tT

Let be a constant such that

)(

)(

tKT

tT and

)(

)(

xX

xX

Or, 0 KTT and 0 xX

Case I: If 0 , the differential equation is 0X and has

solution of general form, BAxxX )( with boundary

conditions BX )0(0 and BALLX )(0 .

Now we get , 0 BA , again we arrive at a zero solution.

Case II: If 2 then 02 xX ,

teX .

The general solution has the form tt eCeCtX 21)(

and the boundary conditions are 21)0(0 CCX

tt eCeCLX 21)(0 ------------(3.3)

12 CC

Therefore from (3.3) )(0 1

LL eeC

This implies that 01 C and 02 C which makes

0)( xX .

Case III: If 2 then 02 xX .

This has the general solution of the form

xBxAxX sincos)(

with the boundary conditions 0)0( X which means 0A

and 0)( LX becomes 0sin Lb .

Because 0A the cosine term disappears which means we

need to solve 0sin Lb .

Here, 0sin L , since Sinx is equal to zero for positive

integer values of , 0sin L

will only happen when nL .

This leads to 2

222

L

n .

Therefore,

L

xnbxX

sin)( .

Since we are looking for non-zero solutions we set 1b ,

2

22

L

nn

and

L

xnxX n

sin)( .

Here n is an eigen-value of the Sturn-Liouville problem and

)(xX n is an eigenfunction.

The complete solution to the Sturn-Liouville problem is the

group of eigenvalues and eigenfunctions for 1n to n .

For the solutions to the heat equation, we have the product

solution,

L

xnetxv L

Ktn

n

sin),(

22

which satisfies the boundary conditions.

Again any linear combination of two solutions is also a

solution. Therefore, we have

L

xnebtxv L

Ktn

n

n

sin),(

22

1

----(3.4)

which is also a solution to the heat equation. This solution

satisfies all the conditions except the initial conditions, so we

need to find the co-efficients nb that satisfy the initial

conditions. we use the initial condition to get

,

L

xnbxv

n

n

sin)0,(

1

For our problem, xn

Sinbxn

n5.1

801

This is known as the half range sine series expansion and nb

are calculated with

dxL

xnxv

Lb

L

n

sin)(

2

0

0

Expanding this gives


n

n

n

Sinnn

Cosnn

dxxn

Sinxb

)1(240

)0(5.1

)05.1(160

5.1)80(

5.1

25.1

0

nb n

n

240)1(

Plugging this function of into equation (3.4) gives a complete

solution to the IBVP (3.2)

xn

Sinen

txv tn

n

n

5.1

)1(240),(

2202.0

1

We conclude that the temperature in the rod is

),()(),( txvxutxu s

which gives

xn

Sinen

xtxu tn

n

n

5.1

)1(24080),(

2202.0

1

---------(3.5)

which is the analytic solution to the IBVP (3.1).

4 NUMERICAL SCHEME FOR HEAT EQUATION

As mentioned in section 2, the one dimensional heat equation

with initial and boundary equation gives an initial boundary

value problem (IBVP).

We investigate an efficient numerical scheme for the equation

(2.5), follows from Gerald [3], Smith [4] and Burden [7].

In order to determine the scheme, we have to discretize the

length and time. The discretization of t

u

is obtained by first

order forward difference in time and the discretization of 2

2

x

u

is obtained by central difference in length.

The possible finite difference approximations for t

u

and2

2

x

u

:

Forward difference in time:

From Taylor’s series we write

...,

!2

,,,

2

22

t

txuh

t

txuhtxuhtxu

ho

h

txuhtxu

t

txu

,,,

h

txuhtxu

t

txu ,,,

------(4.1)

Central difference in space:

)

,,(

,2

2

k

tkxutxu

x

txu

)2.4(),(),(2),(

),(),(),(),(

2

2

k

tkxutxutkxu

k

tkxutxutxutkxu

We assume the uniform grid spacing with step size h and k

for time and length respectively htt nn 1and

kxx ii 1 .

We also write n

iu for txu , in equation (4.1) and (4.2).

Now equation (2.5) takes the form

2

11

2

1

1 2

i

n

i

n

i

n

i

n

n

i

n

i

x

uuuk

t

uu

n

i

n

i

n

i

i

n

n

i

n

i uuux

tkuu 112

2

1

1 2

n

i

n

i

n

i

n

i uuuu 11

1 )21(

---(4.3)

where 2

2

1

i

n

x

tk

This is the explicit scheme for the equation (2.5).

Therefore, equation (4.3) leads the desired scheme for the heat

equation.

The stencil for the explicit scheme (4.3) is presented below


1n

iu

n

i

n

i

n

i uuu 11

Fig 4.1: Stencil of the explicit scheme.

4.1 STABILITY CONDITION

Recalling the explicit finite difference scheme (4.3) for one

dimension heat equation described the derivation in section 2

n

i

n

i

n

i

n

i uuuu 11

1 )21(

The equation implies that if ,2

1 the new solution is a

convex combination of the three previous solutions that is the

solution at new time-step )1( n at a spatial-node i, is an

average of the solutions at the previous time-step at the spatial-

nodes 1i , i and 1i .

Therefore the stability condition for the explicit scheme is

2

1:

2

x

tk

which can be verified in the computer programming code very

easily.

Finally, we have to choose t such that k

xt

2

2

1 , where

k is the thermal diffusivity of the material of the object (taken

here 22.0k ).

5 NUMERICAL EXPERIMENTS AND RESULTS

To estimate the relative error between analytic solutions (3.5)

stated in section 3 and numerical solution. We perform

numerical experiments in 022.0t with step size

15.0x and the thermal diffusivity of the material of rod is

k=0.36 which guarantees stability condition 2

11267.0 .

The relative error in estimated in L1 norm defined by

1

1

1:

e

nee

for all time where e is the exact solution

(3.5) and n is the numerical solution computed by the finite

difference scheme (4.3). Figure (5.1) represents the relative

error. Fig 5.2 we present the initial temperature distribution of

the rod.

Fig 5.1: Relative Error.

Fig 5.2: Initial Temperature distribution.

Fig 5.3 represents the temperature of initial position and after

10 minutes. We present the temperature profile for different

time in Fig 5.4.

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5x 10

-15

Time

Err

or

in L

1 n

orm

0 0.5 1 1.5 2 2.50

20

40

60

80

100

120

Length

Te

mp

era

ture

Initial Temperature of the rod


Fig 5.3: Initial temperature & temperature after 10 minutes.

Fig 5.4: Temperature profile.

6 CONCLUSIONS

We have presented the derivation of a one dimensional heat

equation and the analytic solution of heat equation as a BVP by

the method of separation of variables. The derivation of

explicit scheme for heat equation as an IBVP has been

described and the stability condition of this scheme has also

been presented. The relative error between the numerical

solution and the analytic solution of heat equation has been

computed using 1L norm and the relative error is quite

acceptable. We have presented temperature profiles for various

time steps verifies well known qualitative behaviors of the heat

equation.

REFERENCES

[1] A. Malgorzata, A. Jankowaski, Andrzej Marciniak, “An Interval finite

difference method for solving one dimensional heat equation”,

Institute of Applied Mechanics, Porzan University of Technology,

Poland 2006.

[2] Sharanjeet Dhawan and Sheo Kumar, “A Numerical solution one

dimensional heat equation using cubic B-spline basis functions”,

International Journal of Research and Reviews in Applied Science, vol. 1,

October, 2009.

[3] Gerald W. Recktenwald , “Finite Difference Approximations to the

Heat equation”, Portland State University, Portland, Oreon, 2004.

[4] G. D. Smith, “Numerical Solution of Partial Differential Equations”,

second edition, Calerdon Press. Oxford, 1979.

[5] M. D. Raishinghania, “Advanced Differential Equations”, S. Chand &

Company, New Delhi, 2000.

[6] J.L. Randall, “Numerical Methods for Conservation Laws”, second

Edition, Springer, Verlag, 1992.

[7] Richard L. Burden and J Douglas Faires, “Numerical Analysis”,

seventh edition, THOMSON, 2007.

[8] Gerald and Wheaty, “Applied Numerical Analysis”, Pearson

Education Ltd, 2002.

[9] Adam Abrahamsen and David Richards, “The One dimensional heat

equation”, 2002.

M H Kabir was born in Kishoregonj, Bangladesh in 1982. He received his B. Sc. (Hons) and MS in Mathematics from Jahangirnagar University, Savar, Dhaka in 2005 and 2006 respectively. Currently he is doing his M phil degree in the Department of Mathematics, Jahangirnagar University. He has been serving as a Lecturer in the Department of Mathematics, Jahangirnagar University from December, 2009 to till now. His research interests are Partial Differential Equations and Traffic Flow Simulation. He is a life member of Bangladesh Mathematical

Society.

A Afroz was born in Narshingdi, Bangladesh in 1985. She did her B. Sc. (Hons) and MS in Mathematics from Jahangirnagar University, Savar, Dhaka in 2005 and 2006 respectively. Currently she is doing her M phil degree in the Department of Mathematics, Jahangirnagar University. Her research interests are Partial Differential Equations and Ordinary Differential Equations.

0 0.5 1 1.5 2 2.50

20

40

60

80

100

120

Length [meter]

Te

mp

era

ture

[0c]

Temperature of the rod according to length

100 sec

200 sec

300 sec

400 sec

500 sec

600 sec

0 0.5 1 1.5 2 2.50

20

40

60

80

100

120

Length

Te

mp

era

ture

Initial Temperature of the rod

Initial

After 10 minues


M M Hossain was born in Magura, Bangladesh. He did his B. Sc. (Hons) and MSc in Mathematics from Dhaka University in 1970 and 1971 respectively. He started his teaching career as a Lecturer in the Department of Mathematics, Jahangirnagar University and currently he is an Associate professor of this department. His research interests include Partial Differential Equations and Algebra.

M O Gani was born in Laxmipur, Bangladesh in 1977. He received his M.Phil., MSc and B. Sc. (Hons) in Mathematics from Jahangirnagar University, Savar, Dhaka in 2010, 1999 and 1998, respectively. He joined in the Department of Mathematics, Jahangirnagar University in 2006 as a Lecturer and currently he is an Assistant Professor of this department. His research interests are Partial Differential Equations and Traffic Flow Simulation. He is a life member of Bangladesh Mathematical Society and BAAS.

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